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Search results for: periodic structures

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</div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: periodic structures</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4493</span> Kernel Parallelization Equation for Identifying Structures under Unknown and Periodic Loads</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Seyed%20Sadegh%20Naseralavi">Seyed Sadegh Naseralavi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a Kernel parallelization equation for damage identification in structures under unknown periodic excitations. Herein, the dynamic differential equation of the motion of structure is viewed as a mapping from displacements to external forces. Utilizing this viewpoint, a new method for damage detection in structures under periodic loads is presented. The developed method requires only two periods of load. The method detects the damages without finding the input loads. The method is based on the fact that structural displacements under free and forced vibrations are associated with two parallel subspaces in the displacement space. Considering the concept, kernel parallelization equation (KPE) is derived for damage detection under unknown periodic loads. The method is verified for a case study under periodic loads. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kernel" title="Kernel">Kernel</a>, <a href="https://publications.waset.org/abstracts/search?q=unknown%20periodic%20load" title=" unknown periodic load"> unknown periodic load</a>, <a href="https://publications.waset.org/abstracts/search?q=damage%20detection" title=" damage detection"> damage detection</a>, <a href="https://publications.waset.org/abstracts/search?q=Kernel%20parallelization%20equation" title=" Kernel parallelization equation "> Kernel parallelization equation </a> </p> <a href="https://publications.waset.org/abstracts/75655/kernel-parallelization-equation-for-identifying-structures-under-unknown-and-periodic-loads" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/75655.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">283</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4492</span> Theoretical Analysis of Mechanical Vibration for Offshore Platform Structures</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Saeed%20Asiri">Saeed Asiri</a>, <a href="https://publications.waset.org/abstracts/search?q=Yousuf%20Z.%20AL-Zahrani"> Yousuf Z. AL-Zahrani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A new class of support structures, called periodic structures, is introduced in this paper as a viable means for isolating the vibration transmitted from the sea waves to offshore platform structures through its legs. A passive approach to reduce transmitted vibration generated by waves is presented. The approach utilizes the property of periodic structural components that creates stop and pass bands. The stop band regions can be tailored to correspond to regions of the frequency spectra that contain harmonics of the wave frequency, attenuating the response in those regions. A periodic structural component is comprised of a repeating array of cells, which are themselves an assembly of elements. The elements may have differing material properties as well as geometric variations. For the purpose of this research, only geometric and material variations are considered and each cell is assumed to be identical. A periodic leg is designed in order to reduce transmitted vibration of sea waves. The effectiveness of the periodicity on the vibration levels of platform will be demonstrated theoretically. The theory governing the operation of this class of periodic structures is introduced using the transfer matrix method. The unique filtering characteristics of periodic structures are demonstrated as functions of their design parameters for structures with geometrical and material discontinuities; and determine the propagation factor by using the spectral finite element analysis and the effectiveness of design on the leg structure by changing the ratio of step length and area interface between the materials is demonstrated in order to find the propagation factor and frequency response. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=vibrations" title="vibrations">vibrations</a>, <a href="https://publications.waset.org/abstracts/search?q=periodic%20structures" title=" periodic structures"> periodic structures</a>, <a href="https://publications.waset.org/abstracts/search?q=offshore" title=" offshore"> offshore</a>, <a href="https://publications.waset.org/abstracts/search?q=platforms" title=" platforms"> platforms</a>, <a href="https://publications.waset.org/abstracts/search?q=transfer%20matrix%20method" title=" transfer matrix method"> transfer matrix method</a> </p> <a href="https://publications.waset.org/abstracts/11330/theoretical-analysis-of-mechanical-vibration-for-offshore-platform-structures" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/11330.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">289</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4491</span> The Structure of Invariant Manifolds after a Supercritical Hamiltonian Hopf Bifurcation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Matthaios%20Katsanikas">Matthaios Katsanikas</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We study the structure of the invariant manifolds of complex unstable periodic orbits of a family of periodic orbits, in a 3D autonomous Hamiltonian system of galactic type, after a transition of this family from stability to complex instability (Hamiltonian Hopf bifurcation). We consider the case of a supercritical Hamiltonian Hopf bifurcation. The invariant manifolds of complex unstable periodic orbits have two kinds of structures. The first kind is represented by a disk confined structure on the 4D space of section. The second kind is represented by a complicated central tube structure that is associated with an extended network of tube structures, strips and flat structures of sheet type on the 4D space of section. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamical%20systems" title="dynamical systems">dynamical systems</a>, <a href="https://publications.waset.org/abstracts/search?q=galactic%20dynamics" title=" galactic dynamics"> galactic dynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=chaos" title=" chaos"> chaos</a>, <a href="https://publications.waset.org/abstracts/search?q=phase%20space" title=" phase space"> phase space</a> </p> <a href="https://publications.waset.org/abstracts/125080/the-structure-of-invariant-manifolds-after-a-supercritical-hamiltonian-hopf-bifurcation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/125080.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">138</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4490</span> An Ancient Rule for Constructing Dodecagonal Quasi-Periodic Formations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rima%20A.%20Ajlouni">Rima A. Ajlouni</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The discovery of quasi-periodic structures in material science is revealing an exciting new class of symmetries, which has never been explored before. Due to their unique structural and visual properties, these symmetries are drawing interest from many scientific and design disciplines. Especially, in art and architecture, these symmetries can provide a rich source of geometry for exploring new patterns, forms, systems, and structures. However, the structural systems of these complicated symmetries are still posing a perplexing challenge. While much of their local order has been explored, the global governing system is still unresolved. Understanding their unique global long-range order is essential to their generation and application. The recent discovery of dodecagonal quasi-periodic patterns in historical Islamic architecture is generating a renewed interest into understanding the mathematical principles of traditional Islamic geometry. Astonishingly, many centuries before its description in the modern science, ancient artists, by using the most primitive tools (a compass and a straight edge), were able to construct patterns with quasi-periodic formations. These ancient patterns can be found all over the ancient Islamic world, many of which exhibit formations with 5, 8, 10 and 12 quasi-periodic symmetries. Based on the examination of these historical patterns and derived from the generating principles of Islamic geometry, a global multi-level structural model is presented that is able to describe the global long-range order of dodecagonal quasi-periodic formations in Islamic Architecture. Furthermore, this method is used to construct new quasi-periodic tiling systems as well as generating their deflation and inflation rules. This method can be used as a general guiding principle for constructing infinite patches of dodecagon-based quasi-periodic formations, without the need for local strategies (tiling, matching, grid, substitution, etc.) or complicated mathematics; providing an easy tool for scientists, mathematicians, teachers, designers and artists, to generate and study a wide range of dodecagonal quasi-periodic formations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dodecagonal" title="dodecagonal">dodecagonal</a>, <a href="https://publications.waset.org/abstracts/search?q=Islamic%20architecture" title=" Islamic architecture"> Islamic architecture</a>, <a href="https://publications.waset.org/abstracts/search?q=long-range%20order" title=" long-range order"> long-range order</a>, <a href="https://publications.waset.org/abstracts/search?q=quasi-periodi" title=" quasi-periodi"> quasi-periodi</a> </p> <a href="https://publications.waset.org/abstracts/35446/an-ancient-rule-for-constructing-dodecagonal-quasi-periodic-formations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35446.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">402</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4489</span> Micromechanics Modeling of 3D Network Smart Orthotropic Structures</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=E.%20M.%20Hassan">E. M. Hassan</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20L.%20Kalamkarov"> A. L. Kalamkarov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Two micromechanical models for 3D smart composite with embedded periodic or nearly periodic network of generally orthotropic reinforcements and actuators are developed and applied to cubic structures with unidirectional orientation of constituents. Analytical formulas for the effective piezothermoelastic coefficients are derived using the Asymptotic Homogenization Method (AHM). Finite Element Analysis (FEA) is subsequently developed and used to examine the aforementioned periodic 3D network reinforced smart structures. The deformation responses from the FE simulations are used to extract effective coefficients. The results from both techniques are compared. This work considers piezoelectric materials that respond linearly to changes in electric field, electric displacement, mechanical stress and strain and thermal effects. This combination of electric fields and thermo-mechanical response in smart composite structures is characterized by piezoelectric and thermal expansion coefficients. The problem is represented by unit-cell and the models are developed using the AHM and the FEA to determine the effective piezoelectric and thermal expansion coefficients. Each unit cell contains a number of orthotropic inclusions in the form of structural reinforcements and actuators. Using matrix representation of the coupled response of the unit cell, the effective piezoelectric and thermal expansion coefficients are calculated and compared with results of the asymptotic homogenization method. A very good agreement is shown between these two approaches. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20homogenization%20method" title="asymptotic homogenization method">asymptotic homogenization method</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element%20analysis" title=" finite element analysis"> finite element analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=effective%20piezothermoelastic%20coefficients" title=" effective piezothermoelastic coefficients"> effective piezothermoelastic coefficients</a>, <a href="https://publications.waset.org/abstracts/search?q=3D%20smart%20network%20composite%20structures" title=" 3D smart network composite structures"> 3D smart network composite structures</a> </p> <a href="https://publications.waset.org/abstracts/18190/micromechanics-modeling-of-3d-network-smart-orthotropic-structures" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/18190.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">400</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4488</span> Defuzzification of Periodic Membership Function on Circular Coordinates</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Takashi%20Mitsuishi">Takashi Mitsuishi</a>, <a href="https://publications.waset.org/abstracts/search?q=Koji%20Saigusa"> Koji Saigusa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents circular polar coordinates transformation of periodic fuzzy membership function. The purpose is identification of domain of periodic membership functions in consequent part of IF-THEN rules. The proposed methods are applied to the simple color construct system. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=periodic%20membership%20function" title="periodic membership function">periodic membership function</a>, <a href="https://publications.waset.org/abstracts/search?q=polar%20coordinates%20transformation" title=" polar coordinates transformation"> polar coordinates transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=defuzzification" title=" defuzzification"> defuzzification</a>, <a href="https://publications.waset.org/abstracts/search?q=circular%20coordinates" title=" circular coordinates"> circular coordinates</a> </p> <a href="https://publications.waset.org/abstracts/14722/defuzzification-of-periodic-membership-function-on-circular-coordinates" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/14722.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">309</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4487</span> Rogue Waves Arising on the Standing Periodic Wave in the High-Order Ablowitz-Ladik Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yanpei%20Zhen">Yanpei Zhen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The nonlinear Schrödinger (NLS) equation models wave dynamics in many physical problems related to fluids, plasmas, and optics. The standing periodic waves are known to be modulationally unstable, and rogue waves (localized perturbations in space and time) have been observed on their backgrounds in numerical experiments. The exact solutions for rogue waves arising on the periodic standing waves have been obtained analytically. It is natural to ask if the rogue waves persist on the standing periodic waves in the integrable discretizations of the integrable NLS equation. We study the standing periodic waves in the semidiscrete integrable system modeled by the high-order Ablowitz-Ladik (AL) equation. The standing periodic wave of the high-order AL equation is expressed by the Jacobi cnoidal elliptic function. The exact solutions are obtained by using the separation of variables and one-fold Darboux transformation. Since the cnoidal wave is modulationally unstable, the rogue waves are generated on the periodic background. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Darboux%20transformation" title="Darboux transformation">Darboux transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=periodic%20wave" title=" periodic wave"> periodic wave</a>, <a href="https://publications.waset.org/abstracts/search?q=Rogue%20wave" title=" Rogue wave"> Rogue wave</a>, <a href="https://publications.waset.org/abstracts/search?q=separating%20the%20variables" title=" separating the variables"> separating the variables</a> </p> <a href="https://publications.waset.org/abstracts/174512/rogue-waves-arising-on-the-standing-periodic-wave-in-the-high-order-ablowitz-ladik-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/174512.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">183</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4486</span> Hybrid Inventory Model Optimization under Uncertainties: A Case Study in a Manufacturing Plant</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=E.%20Benga">E. Benga</a>, <a href="https://publications.waset.org/abstracts/search?q=T.%20Tengen"> T. Tengen</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Alugongo"> A. Alugongo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Periodic and continuous inventory models are the two classical management tools used to handle inventories. These models have advantages and disadvantages. The implementation of both continuous (r,Q) inventory and periodic (R, S) inventory models in most manufacturing plants comes with higher cost. Such high inventory costs are due to the fact that most manufacturing plants are not flexible enough. Since demand and lead-time are two important variables of every inventory models, their effect on the flexibility of the manufacturing plant matter most. Unfortunately, these effects are not clearly understood by managers. The reason is that the decision parameters of the continuous (r, Q) inventory and periodic (R, S) inventory models are not designed to effectively deal with the issues of uncertainties such as poor manufacturing performances, delivery performance supplies performances. There is, therefore, a need to come up with a predictive and hybrid inventory model that can combine in some sense the feature of the aforementioned inventory models. A linear combination technique is used to hybridize both continuous (r, Q) inventory and periodic (R, S) inventory models. The behavior of such hybrid inventory model is described by a differential equation and then optimized. From the results obtained after simulation, the continuous (r, Q) inventory model is more effective than the periodic (R, S) inventory models in the short run, but this difference changes as time goes by. Because the hybrid inventory model is more cost effective than the continuous (r,Q) inventory and periodic (R, S) inventory models in long run, it should be implemented for strategic decisions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=periodic%20inventory" title="periodic inventory">periodic inventory</a>, <a href="https://publications.waset.org/abstracts/search?q=continuous%20inventory" title=" continuous inventory"> continuous inventory</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20inventory" title=" hybrid inventory"> hybrid inventory</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=manufacturing%20plant" title=" manufacturing plant"> manufacturing plant</a> </p> <a href="https://publications.waset.org/abstracts/64054/hybrid-inventory-model-optimization-under-uncertainties-a-case-study-in-a-manufacturing-plant" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/64054.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">382</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4485</span> Periodical System of Isotopes</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Andriy%20Magula">Andriy Magula</a> </p> <p class="card-text"><strong>Abstract:</strong></p> With the help of a special algorithm being the principle of multilevel periodicity, the periodic change of properties at the nuclear level of chemical elements was discovered and the variant for the periodic system of isotopes was presented. The periodic change in the properties of isotopes, as well as the vertical symmetry of subgroups, was checked for consistency in accordance with the following ten types of experimental data: mass ratio of fission fragments; quadrupole moment values; magnetic moment; lifetime of radioactive isotopes; neutron scattering; thermal neutron radiative capture cross-sections (n, γ); α-particle yield cross-sections (n, α); isotope abundance on Earth, in the Solar system and other stellar systems; features of ore formation and stellar evolution. For all ten cases, the correspondences for the proposed periodic structure of the nucleus were obtained. The system was formed in the usual 2D table, similar to the periodic system of elements, and the mass series of isotopes was divided into 8 periods and 4 types of ‘nuclear’ orbitals: sn, dn, pn, fn. The origin of ‘magic’ numbers as a set of filled charge shells of the nucleus was explained. Due to the isotope system, the periodic structure is shown at a new level of the universe, and the prospects of its practical use are opened up. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=periodic%20system" title="periodic system">periodic system</a>, <a href="https://publications.waset.org/abstracts/search?q=isotope" title=" isotope"> isotope</a>, <a href="https://publications.waset.org/abstracts/search?q=period" title=" period"> period</a>, <a href="https://publications.waset.org/abstracts/search?q=subgroup" title=" subgroup"> subgroup</a>, <a href="https://publications.waset.org/abstracts/search?q=%E2%80%9Cnuclear%E2%80%9D%20orbital" title=" “nuclear” orbital"> “nuclear” orbital</a>, <a href="https://publications.waset.org/abstracts/search?q=nuclear%20reaction" title=" nuclear reaction"> nuclear reaction</a> </p> <a href="https://publications.waset.org/abstracts/192564/periodical-system-of-isotopes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/192564.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">17</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4484</span> Effect of Geometric Imperfections on the Vibration Response of Hexagonal Lattices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=P.%20Caimmi">P. Caimmi</a>, <a href="https://publications.waset.org/abstracts/search?q=E.%20Bele"> E. Bele</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Abolfathi"> A. Abolfathi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Lattice materials are cellular structures composed of a periodic network of beams. They offer high weight-specific mechanical properties and lend themselves to numerous weight-sensitive applications. The periodic internal structure responds to external vibrations through characteristic frequency bandgaps, making these materials suitable for the reduction of noise and vibration. However, the deviation from architectural homogeneity, due to, e.g., manufacturing imperfections, has a strong influence on the mechanical properties and vibration response of these materials. In this work, we present results on the influence of geometric imperfections on the vibration response of hexagonal lattices. Three classes of geometrical variables are used: the characteristics of the architecture (relative density, ligament length/cell size ratio), imperfection type (degree of non-periodicity, cracks, hard inclusions) and defect morphology (size, distribution). Test specimens with controlled size and distribution of imperfections are manufactured through selective laser sintering. The Frequency Response Functions (FRFs) in the form of accelerance are measured, and the modal shapes are captured through a high-speed camera. The finite element method is used to provide insights on the extension of these results to semi-infinite lattices. An updating procedure is conducted to increase the reliability of numerical simulation results compared to experimental measurements. This is achieved by updating the boundary conditions and material stiffness. Variations in FRFs of periodic structures due to changes in the relative density of the constituent unit cell are analysed. The effects of geometric imperfections on the dynamic response of periodic structures are investigated. The findings can be used to open up the opportunity for tailoring these lattice materials to achieve optimal amplitude attenuations at specific frequency ranges. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=lattice%20architectures" title="lattice architectures">lattice architectures</a>, <a href="https://publications.waset.org/abstracts/search?q=geometric%20imperfections" title=" geometric imperfections"> geometric imperfections</a>, <a href="https://publications.waset.org/abstracts/search?q=vibration%20attenuation" title=" vibration attenuation"> vibration attenuation</a>, <a href="https://publications.waset.org/abstracts/search?q=experimental%20modal%20analysis" title=" experimental modal analysis"> experimental modal analysis</a> </p> <a href="https://publications.waset.org/abstracts/110711/effect-of-geometric-imperfections-on-the-vibration-response-of-hexagonal-lattices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/110711.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">122</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4483</span> Response Solutions of 2-Dimensional Elliptic Degenerate Quasi-Periodic Systems With Small Parameters</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Song%20Ni">Song Ni</a>, <a href="https://publications.waset.org/abstracts/search?q=Junxiang%20Xu"> Junxiang Xu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper concerns quasi-periodic perturbations with parameters of 2-dimensional degenerate systems. If the equilibrium point of the unperturbed system is elliptic-type degenerate. Assume that the perturbation is real analytic quasi-periodic with diophantine frequency. Without imposing any assumption on the perturbation, we can use a path of equilibrium points to tackle with the Melnikov non-resonance condition, then by the Leray-Schauder Continuation Theorem and the Kolmogorov-Arnold-Moser technique, it is proved that the equation has a small response solution for many sufficiently small parameters. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=quasi-periodic%20systems" title="quasi-periodic systems">quasi-periodic systems</a>, <a href="https://publications.waset.org/abstracts/search?q=KAM-iteration" title=" KAM-iteration"> KAM-iteration</a>, <a href="https://publications.waset.org/abstracts/search?q=degenerate%20equilibrium%20point" title=" degenerate equilibrium point"> degenerate equilibrium point</a>, <a href="https://publications.waset.org/abstracts/search?q=response%20solution" title=" response solution"> response solution</a> </p> <a href="https://publications.waset.org/abstracts/175183/response-solutions-of-2-dimensional-elliptic-degenerate-quasi-periodic-systems-with-small-parameters" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/175183.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">86</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4482</span> Existence of positive periodic solutions for certain delay differential equations </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Farid%20Nouioua">Farid Nouioua</a>, <a href="https://publications.waset.org/abstracts/search?q=Abdelouaheb%20Ardjouni"> Abdelouaheb Ardjouni</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=delay%20differential%20equations" title="delay differential equations">delay differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=positive%20periodic%20solutions" title=" positive periodic solutions"> positive periodic solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20equations" title=" integral equations"> integral equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Krasnoselskii%20fixed%20point%20theorem" title=" Krasnoselskii fixed point theorem"> Krasnoselskii fixed point theorem</a> </p> <a href="https://publications.waset.org/abstracts/40904/existence-of-positive-periodic-solutions-for-certain-delay-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/40904.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">438</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4481</span> On Periodic Integer-Valued Moving Average Models</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Aries%20Nawel">Aries Nawel</a>, <a href="https://publications.waset.org/abstracts/search?q=Bentarzi%20Mohamed"> Bentarzi Mohamed</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with the study of some probabilistic and statistical properties of a Periodic Integer-Valued Moving Average Model (PINMA_{S}(q)). The closed forms of the mean, the second moment and the periodic autocovariance function are obtained. Furthermore, the time reversibility of the model is discussed in details. Moreover, the estimation of the underlying parameters are obtained by the Yule-Walker method, the Conditional Least Square method (CLS) and the Weighted Conditional Least Square method (WCLS). A simulation study is carried out to evaluate the performance of the estimation method. Moreover, an application on real data set is provided. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=periodic%20integer-valued%20moving%20average" title="periodic integer-valued moving average">periodic integer-valued moving average</a>, <a href="https://publications.waset.org/abstracts/search?q=periodically%20correlated%20process" title=" periodically correlated process"> periodically correlated process</a>, <a href="https://publications.waset.org/abstracts/search?q=time%20reversibility" title=" time reversibility"> time reversibility</a>, <a href="https://publications.waset.org/abstracts/search?q=count%20data" title=" count data"> count data</a> </p> <a href="https://publications.waset.org/abstracts/132956/on-periodic-integer-valued-moving-average-models" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/132956.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">202</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4480</span> Defect Modes in Multilayered Piezoelectric Structures</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=D.%20G.%20Piliposyan">D. G. Piliposyan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Propagation of electro-elastic waves in a piezoelectric waveguide with finite stacks and a defect layer is studied using a modified transfer matrix method. The dispersion equation for a periodic structure consisting of unit cells made up from two piezoelectric materials with metallized interfaces is obtained. An analytical expression, for the transmission coefficient for a waveguide with finite stacks and a defect layer, that is found can be used to accurately detect and control the position of the passband within a stopband. The result can be instrumental in constructing a tunable waveguide made of layers of different or identical piezoelectric crystals and separated by metallized interfaces. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=piezoelectric%20layered%20structure" title="piezoelectric layered structure">piezoelectric layered structure</a>, <a href="https://publications.waset.org/abstracts/search?q=periodic%20phononic%20crystal" title=" periodic phononic crystal"> periodic phononic crystal</a>, <a href="https://publications.waset.org/abstracts/search?q=bandgap" title=" bandgap"> bandgap</a>, <a href="https://publications.waset.org/abstracts/search?q=bloch%20waves" title=" bloch waves"> bloch waves</a> </p> <a href="https://publications.waset.org/abstracts/55400/defect-modes-in-multilayered-piezoelectric-structures" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/55400.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">224</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4479</span> Structural Identification for Layered Composite Structures through a Wave and Finite Element Methodology</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rilwan%20Kayode%20Apalowo">Rilwan Kayode Apalowo</a>, <a href="https://publications.waset.org/abstracts/search?q=Dimitrios%20Chronopoulos"> Dimitrios Chronopoulos</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An approach for identifying the geometric and material characteristics of layered composite structures through an inverse wave and finite element methodology is proposed. These characteristics are obtained through multi-frequency single shot measurements. However, it is established that the frequency regime of the measurements does not matter, meaning that both ultrasonic and structural dynamics frequency spectra can be employed. Taking advantage of a full FE (finite elements) description of the periodic composite, the scheme is able to account for arbitrarily complex structures. In order to demonstrate the robustness of the presented scheme, it is applied to a sandwich composite panel and results are compared with that of experimental characterization techniques. Excellent agreement is obtained with the experimental measurements. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=structural%20identification" title="structural identification">structural identification</a>, <a href="https://publications.waset.org/abstracts/search?q=non-destructive%20evaluation" title=" non-destructive evaluation"> non-destructive evaluation</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20elements" title=" finite elements"> finite elements</a>, <a href="https://publications.waset.org/abstracts/search?q=wave%20propagation" title=" wave propagation"> wave propagation</a>, <a href="https://publications.waset.org/abstracts/search?q=layered%20structures" title=" layered structures"> layered structures</a>, <a href="https://publications.waset.org/abstracts/search?q=ultrasound" title=" ultrasound"> ultrasound</a> </p> <a href="https://publications.waset.org/abstracts/109615/structural-identification-for-layered-composite-structures-through-a-wave-and-finite-element-methodology" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/109615.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">143</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4478</span> Stabilization of Displaced Periodic Orbit Using Feedback Linearization Control Scheme</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Arun%20Kumar%20Yadav">Arun Kumar Yadav</a>, <a href="https://publications.waset.org/abstracts/search?q=Badam%20Singh%20Kushvah"> Badam Singh Kushvah</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present work, we investigated displaced periodic orbits in the linear order in the circular restricted three-body Sun-Jupiter system, where the third mass-less body utilizes solar electric sail. The electric solar sail is a new space propulsion concept which uses the solar wind momentum for producing thrust, and it is somewhat like to the more well-known solar radiation pressure sail which is often called simply the solar sail. Moreover, we implement the feedback linearization control scheme to perform the stabilization and trajectory tracking for the nonlinear system. Further, we derived periodic orbits analytically in linear order by introducing a first order approximation. These approximate analytic solutions are utilized in a numerical search to determine displaced periodic orbit in the full nonlinear model. We found the displaced periodic orbit for the defined non-linear model and stabilized the model. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=solar%20electric%20sail" title="solar electric sail">solar electric sail</a>, <a href="https://publications.waset.org/abstracts/search?q=circular%20restricted%20three-body%20problem%20%28CRTBP%29" title=" circular restricted three-body problem (CRTBP)"> circular restricted three-body problem (CRTBP)</a>, <a href="https://publications.waset.org/abstracts/search?q=displaced%20orbit" title=" displaced orbit"> displaced orbit</a>, <a href="https://publications.waset.org/abstracts/search?q=feedback%20linearization%20control" title=" feedback linearization control"> feedback linearization control</a> </p> <a href="https://publications.waset.org/abstracts/83358/stabilization-of-displaced-periodic-orbit-using-feedback-linearization-control-scheme" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/83358.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">189</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4477</span> A Modified Periodic 2D Cellular Re-Entrant Honeycomb Model to Enhance the Auxetic Elastic Properties</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sohaib%20Z.%20Khan">Sohaib Z. Khan</a>, <a href="https://publications.waset.org/abstracts/search?q=Farrukh%20Mustahsan"> Farrukh Mustahsan</a>, <a href="https://publications.waset.org/abstracts/search?q=Essam%20R.%20I.%20Mahmoud"> Essam R. I. Mahmoud</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20H.%20Masood"> S. H. Masood</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Materials or structures that contract laterally on the application of a compressive load and vice versa are said to be Auxetic materials which exhibit Negative Poisson’s Ratio (NPR). Numerous auxetic structures are proposed in the literature. One of the most studied periodic auxetic structure is the re-entrant honeycomb model. In this paper, a modified re-entrant model is proposed to enhance the auxetic behavior. The paper aimed to investigate the elastic behaviour of the proposed model to improve Young’s modulus and NPR by evaluating the analytical model. Finite Element Analysis (FEA) is also conducted to support the analytical results. A significant increment in Young’s modulus and NPR can be achieved in one of the two orthogonal directions of the loading at the cost of compromising these values in other direction. The proposed modification resulted in lower relative densities when compared to the existing re-entrant honeycomb structure. A trade-off in the elastic properties in one direction at low relative density makes the proposed model suitable for uni-direction applications where higher stiffness and NPR is required, and strength to weight ratio is important. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=2D%20model" title="2D model">2D model</a>, <a href="https://publications.waset.org/abstracts/search?q=auxetic%20materials" title=" auxetic materials"> auxetic materials</a>, <a href="https://publications.waset.org/abstracts/search?q=re-entrant%20honeycomb" title=" re-entrant honeycomb"> re-entrant honeycomb</a>, <a href="https://publications.waset.org/abstracts/search?q=negative%20Poisson%27s%20ratio" title=" negative Poisson&#039;s ratio"> negative Poisson&#039;s ratio</a> </p> <a href="https://publications.waset.org/abstracts/110382/a-modified-periodic-2d-cellular-re-entrant-honeycomb-model-to-enhance-the-auxetic-elastic-properties" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/110382.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">138</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4476</span> Shear Elastic Waves in Disordered Anisotropic Multi-Layered Periodic Structure</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=K.%20B.%20Ghazaryan">K. B. Ghazaryan</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20A.%20Ghazaryan"> R. A. Ghazaryan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Based on the constitutive model and anti-plane equations of anisotropic elastic body of monoclinic symmetry we consider the problem of shear wave propagation in multi-layered disordered composite structure with point defect. Using transfer matrix method the analytic expression is obtained providing solutions of shear Floquet wave propagation in periodic disordered anisotropic structure. The usefulness of the obtained analytical expression was discussed also in reflection and refraction problems from multi-layered reflector as well as in vibration problem of multi-layered waveguides. Numerical results are presented highlighting the effects arising in disordered periodic structure due to defects of multi-layered structure. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=shear%20elastic%20waves" title="shear elastic waves">shear elastic waves</a>, <a href="https://publications.waset.org/abstracts/search?q=monoclinic%20anisotropic%20media" title=" monoclinic anisotropic media"> monoclinic anisotropic media</a>, <a href="https://publications.waset.org/abstracts/search?q=periodic%20structure" title=" periodic structure"> periodic structure</a>, <a href="https://publications.waset.org/abstracts/search?q=disordered%20multilayer%20laminae" title=" disordered multilayer laminae"> disordered multilayer laminae</a>, <a href="https://publications.waset.org/abstracts/search?q=multi-layered%20waveguide" title=" multi-layered waveguide"> multi-layered waveguide</a> </p> <a href="https://publications.waset.org/abstracts/48365/shear-elastic-waves-in-disordered-anisotropic-multi-layered-periodic-structure" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48365.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">408</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4475</span> Acoustic Radiation from an Infinite Cylindrical Shell with Periodic Lengthwise Ribs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yunzhe%20Tong">Yunzhe Tong</a>, <a href="https://publications.waset.org/abstracts/search?q=Jun%20Fan"> Jun Fan</a>, <a href="https://publications.waset.org/abstracts/search?q=Bin%20Wang"> Bin Wang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The vibroacoustic behavior of an immersed infinite cylindrical shell with periodic lengthwise ribs has been studied in this paper. The motions of the shell are described by the Donnell equations. Each lengthwise rib is modeled as an elastic beam. The motions of the bulkheads are decomposed into the longitudinal motions and flexural motions. The analytical expressions of the shell motions can be obtained through circumferential mode expansion, Fourier Transform and periodic boundary condition in the circumferential direction. Furthermore, the far-field radiated pressure has been obtained using the stationary phase. The analysis of wavenumber domain shows that periodic lengthwise stiffeners in the circumferential direction can produce flexural Bloch waves. The dominant feature in far-field pressure amplitude is the resonance of the supersonic components of the flexural Bloch waves in the circumferential direction. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=flexural%20Bloch%20wave" title="flexural Bloch wave">flexural Bloch wave</a>, <a href="https://publications.waset.org/abstracts/search?q=stiffened%20shell" title=" stiffened shell"> stiffened shell</a>, <a href="https://publications.waset.org/abstracts/search?q=vibroacoustics" title=" vibroacoustics"> vibroacoustics</a>, <a href="https://publications.waset.org/abstracts/search?q=wavenumber%20analysis" title=" wavenumber analysis"> wavenumber analysis</a> </p> <a href="https://publications.waset.org/abstracts/90699/acoustic-radiation-from-an-infinite-cylindrical-shell-with-periodic-lengthwise-ribs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/90699.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">209</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4474</span> Retrofitting of Historical Structures in Van City</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Eylem%20G%C3%BCzel">Eylem Güzel</a>, <a href="https://publications.waset.org/abstracts/search?q=Mustafa%20G%C3%BClen"> Mustafa Gülen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Historical structures are the most important symbols of a country that link the past with the future. In order to transfer them in their present conditions to the next generations, maintaining these historical structures are one of our main tasks. Seismic performance of historical structures damaged by the earthquake effects can be enhanced by repair and retrofitting applications. However, repair and retrofitting applications of historical structures are more complicated compared with the traditional structures. For this reason, they need much more attention in repair and retrofitting applications to preserve the spirit of historical structures. In this study, the present condition of selected historical structures built up in Van city that has a very rich historical heritage is given and the necessity of repair and retrofitting applications of historical structures are debated in detail. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=historical%20structures" title="historical structures">historical structures</a>, <a href="https://publications.waset.org/abstracts/search?q=repair" title=" repair"> repair</a>, <a href="https://publications.waset.org/abstracts/search?q=retrofitting" title=" retrofitting"> retrofitting</a>, <a href="https://publications.waset.org/abstracts/search?q=Van%20city" title=" Van city"> Van city</a> </p> <a href="https://publications.waset.org/abstracts/43496/retrofitting-of-historical-structures-in-van-city" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/43496.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">355</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4473</span> Homogenization of a Non-Linear Problem with a Thermal Barrier</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hassan%20Samadi">Hassan Samadi</a>, <a href="https://publications.waset.org/abstracts/search?q=Mustapha%20El%20Jarroudi"> Mustapha El Jarroudi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we consider the homogenization of a non-linear problem in periodic medium with two periodic connected media exchanging a heat flux throughout their common interface. The interfacial exchange coefficient λ is assumed to tend to zero or to infinity following a rate λ=λ(ε) when the size ε of the basic cell tends to zero. Three homogenized problems are determined according to some critical value depending of λ and ε. Our method is based on Γ-Convergence techniques. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=variational%20methods" title="variational methods">variational methods</a>, <a href="https://publications.waset.org/abstracts/search?q=epiconvergence" title=" epiconvergence"> epiconvergence</a>, <a href="https://publications.waset.org/abstracts/search?q=homogenization" title=" homogenization"> homogenization</a>, <a href="https://publications.waset.org/abstracts/search?q=convergence%20technique" title=" convergence technique"> convergence technique</a> </p> <a href="https://publications.waset.org/abstracts/29054/homogenization-of-a-non-linear-problem-with-a-thermal-barrier" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/29054.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">525</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4472</span> Developing Performance Model for Road Side Elements Receiving Periodic Maintenance</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ayman%20M.%20Othman">Ayman M. Othman</a>, <a href="https://publications.waset.org/abstracts/search?q=Hassan%20Y.%20Ahmed"> Hassan Y. Ahmed</a>, <a href="https://publications.waset.org/abstracts/search?q=Tallat%20A.%20Ali"> Tallat A. Ali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Inadequate maintenance programs and funds allocated for highway networks in the developed countries have led to fast deterioration of road side elements. Therefore, this research focuses on developing a performance model for road side elements periodic maintenance activities. Road side elements that receive periodic maintenance include; earthen shoulder, road signs and traffic markings. Using the level of service concept, the developed model can determine the optimal periodic maintenance intervals for those elements based on a selected level of service suitable with the available periodic maintenance budget. Data related to time periods for progressive deterioration stages for the chosen elements were collected. Ten maintenance experts in Aswan, Sohag and Assiut cities were interviewed for that purpose. Time in months related to 10%, 25%, 40%, 50%, 75%, 90% and 100% deterioration of each road side element was estimated based on the experts opinion. Least square regression analysis has shown that a power function represents the best fit for earthen shoulders edge drop-off and damage of road signs with time. It was also evident that, the progressive dirtiness of road signs could be represented by a quadratic function an a linear function could represent the paint degradation nature of both traffic markings and road signs. Actual measurements of earthen shoulder edge drop-off agree considerably with the developed model. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=deterioration" title="deterioration">deterioration</a>, <a href="https://publications.waset.org/abstracts/search?q=level%20of%20service" title=" level of service"> level of service</a>, <a href="https://publications.waset.org/abstracts/search?q=periodic%20maintenance" title=" periodic maintenance"> periodic maintenance</a>, <a href="https://publications.waset.org/abstracts/search?q=performance%20model" title=" performance model"> performance model</a>, <a href="https://publications.waset.org/abstracts/search?q=road%20side%20element" title=" road side element"> road side element</a> </p> <a href="https://publications.waset.org/abstracts/22603/developing-performance-model-for-road-side-elements-receiving-periodic-maintenance" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/22603.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">572</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4471</span> Fabrication of Periodic Graphene-Like Structure of Zinc Oxide Piezoelectric Device</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zi-Gui%20Huang">Zi-Gui Huang</a>, <a href="https://publications.waset.org/abstracts/search?q=Shen-Hsien%20Hu"> Shen-Hsien Hu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study proposes a fabrication of phononic-crystal acoustic wave device. A graphene-like atomic structure was adopted as the main research subject, and a graphene-like structure was designed using piezoelectric material zinc oxide and its periodic boundary conditions were defined using the finite element method. The effects of a hexagonal honeycomb structure were investigated regarding the band gap phenomenon. The use of micro-electromechanical systems process technology to make the film etched micron graphics, designed to produce four kinds of different piezoelectric structure (plat, periodic, single defect and double defects). Frequency response signals and phase change were also measured in this paper. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=MEMS" title="MEMS">MEMS</a>, <a href="https://publications.waset.org/abstracts/search?q=phononic%20crystal" title=" phononic crystal"> phononic crystal</a>, <a href="https://publications.waset.org/abstracts/search?q=piezoelectric%20material" title=" piezoelectric material"> piezoelectric material</a>, <a href="https://publications.waset.org/abstracts/search?q=Zinc%20oxide" title=" Zinc oxide"> Zinc oxide</a> </p> <a href="https://publications.waset.org/abstracts/26268/fabrication-of-periodic-graphene-like-structure-of-zinc-oxide-piezoelectric-device" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/26268.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">538</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4470</span> Effects of Continuous and Periodic Aerobic Exercises on C Reactive Protein in Overweight Women</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Maesoomeh%20Khorshidi%20Mehr">Maesoomeh Khorshidi Mehr</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Sajadian"> Mohammad Sajadian</a>, <a href="https://publications.waset.org/abstracts/search?q=Shadi%20Alipour"> Shadi Alipour</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The purpose of the present study was to compare the effects of eight weeks of continuous and periodic aerobic exercises on serum levels of CRP in overweight woman. 36 woman aged between 20 and 35 years from the city of Ahwaz were randomly selected as the sample of the study. This sample was further divided into three groups (n= 12) of continuous aerobic exercise, periodic aerobic exercise, and control. Subjects of the groups of continuous and periodic aerobic exercise participated in 8 weeks of specialized exercises while the control group subjects did not take part in any regular physical activity program. Blood samples were collected from subjects in 24 hours prior to and 48 hours past to the intervention period. Afterwards, the serum level of CRP was measured for each blood sample. Results showed that BMI and serum level of CRP both significantly reduced as a result of aerobic exercises. However, no statistically significant difference was recorded between the extent of effects of the former and latter aerobic exercise types. Eight weeks of aerobic exercise will probably result in reduced inflammation and cardiovascular diseases risk in overweight women. The reason for lack of difference between effects of continuous and periodic aerobic exercise may lie in the similarity of average intensity and length of physical administered activities. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=heart%20diseases" title="heart diseases">heart diseases</a>, <a href="https://publications.waset.org/abstracts/search?q=aerobic%20exercise" title=" aerobic exercise"> aerobic exercise</a>, <a href="https://publications.waset.org/abstracts/search?q=inflammation" title=" inflammation"> inflammation</a>, <a href="https://publications.waset.org/abstracts/search?q=CRP" title=" CRP"> CRP</a>, <a href="https://publications.waset.org/abstracts/search?q=overweight" title=" overweight"> overweight</a> </p> <a href="https://publications.waset.org/abstracts/81738/effects-of-continuous-and-periodic-aerobic-exercises-on-c-reactive-protein-in-overweight-women" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/81738.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">201</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4469</span> Motion of an Infinitesimal Particle in Binary Stellar Systems: Kepler-34, Kepler-35, Kepler-16, Kepler-413</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rajib%20Mia">Rajib Mia</a>, <a href="https://publications.waset.org/abstracts/search?q=Badam%20Singh%20Kushvah"> Badam Singh Kushvah</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The present research was motivated by the recent discovery of the binary star systems. In this paper, we use the restricted three-body problem in the binary stellar systems, considering photogravitational effects of both the stars. The aim of this study is to investigate the motion of the infinitesimal mass in the vicinity of the Lagrangian points. The stability and periodic orbits of collinear points and the stability and trajectories of the triangular points are studied in stellar binary systems Kepler-34, Kepler-35, Kepler-413 and Kepler-16 systems. A detailed comparison is made among periodic orbits and trajectories. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=exoplanetary%20systems" title="exoplanetary systems">exoplanetary systems</a>, <a href="https://publications.waset.org/abstracts/search?q=lagrangian%20points" title=" lagrangian points"> lagrangian points</a>, <a href="https://publications.waset.org/abstracts/search?q=periodic%20orbit" title=" periodic orbit"> periodic orbit</a>, <a href="https://publications.waset.org/abstracts/search?q=restricted%20three%20body%20problem" title=" restricted three body problem"> restricted three body problem</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a> </p> <a href="https://publications.waset.org/abstracts/28253/motion-of-an-infinitesimal-particle-in-binary-stellar-systems-kepler-34-kepler-35-kepler-16-kepler-413" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/28253.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">434</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4468</span> Sustainable Design in the Use of Deployable Structures</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Umweni%20Osahon%20Joshua">Umweni Osahon Joshua</a>, <a href="https://publications.waset.org/abstracts/search?q=Anton%20Ianakiev"> Anton Ianakiev</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Deployable structures have been used in various scenarios from moving roofs in stadia, space antennae or booms. There has been a lot of literature relating deployable structures but with main focus on space applications. The complexities in the design of deployable structures may be the reason only few have been constructed for earth based solutions. This paper intends to explore the possibilities of integrating sustainable design concepts in deployable structures. Key aspects of sustainable design of structures as applicable to deployable structures have not been explored. Sustainable design of structures have mainly been concerned with static structures in the built environment. However, very little literature, concepts or framework has been drafted as it relates to deployable structures or their integration to static structures as a model for sustainable design. This article seeks to address this flaw in sustainable design for structural engineering and to provide a framework for designing structures in a sustainable manner. This framework will apply to deployable structures for earth-based environments as a form of disaster relief measures and also as part of static structures in the built environment. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=deployable%20structures" title="deployable structures">deployable structures</a>, <a href="https://publications.waset.org/abstracts/search?q=sustainable%20design" title=" sustainable design"> sustainable design</a>, <a href="https://publications.waset.org/abstracts/search?q=framework" title=" framework"> framework</a>, <a href="https://publications.waset.org/abstracts/search?q=earth-based%20environments" title=" earth-based environments "> earth-based environments </a> </p> <a href="https://publications.waset.org/abstracts/15693/sustainable-design-in-the-use-of-deployable-structures" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15693.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">541</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4467</span> On the Effects of the Frequency and Amplitude of Sinusoidal External Cross-Flow Excitation Forces on the Vortex-Induced-Vibrations of an Oscillating Cylinder</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abouzar%20Kaboudian">Abouzar Kaboudian</a>, <a href="https://publications.waset.org/abstracts/search?q=Ravi%20Chaithanya%20Mysa"> Ravi Chaithanya Mysa</a>, <a href="https://publications.waset.org/abstracts/search?q=Boo%20Cheong%20Khoo"> Boo Cheong Khoo</a>, <a href="https://publications.waset.org/abstracts/search?q=Rajeev%20Kumar%20Jaiman"> Rajeev Kumar Jaiman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Vortex induced vibrations can significantly affect the effectiveness of structures in aerospace as well as offshore marine industries. The oscillatory nature of the forces resulting from the vortex shedding around bluff bodies can result in undesirable effects such as increased loading, stresses, deflections, vibrations and noise in the structures, and also reduced fatigue life of the structures. To date, most studies concentrate on either the free oscillations or the prescribed motion of the bluff bodies. However, the structures in operation are usually subject to the external oscillatory forces (e.g. due to the platform motions in offshore industries). Periodic forces can be considered as a combinations of sinusoids. In this work, we present the effects of sinusoidal external cross-flow forces on the vortex-induced vibrations of an oscillating cylinder. The effects of the amplitude, as well as the frequency of these sinusoidal external force on the fluid-forces on the oscillating cylinder are carefully studied and presented. Moreover, we present the transition of the response to be dominated by the vortex-induced-vibrations to the range where it is mostly dictated by the external oscillatory forces. Furthermore, we will discuss how the external forces can affect the flow structures around a cylinder. All results are compared against free oscillations of the cylinder. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=circular%20cylinder" title="circular cylinder">circular cylinder</a>, <a href="https://publications.waset.org/abstracts/search?q=external%20force" title=" external force"> external force</a>, <a href="https://publications.waset.org/abstracts/search?q=vortex-shedding" title=" vortex-shedding"> vortex-shedding</a>, <a href="https://publications.waset.org/abstracts/search?q=VIV" title=" VIV"> VIV</a> </p> <a href="https://publications.waset.org/abstracts/25480/on-the-effects-of-the-frequency-and-amplitude-of-sinusoidal-external-cross-flow-excitation-forces-on-the-vortex-induced-vibrations-of-an-oscillating-cylinder" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/25480.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">369</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4466</span> Onion Storage and the Roof Influence in the Tropics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=O.%20B.%20Imoukhuede">O. B. Imoukhuede</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20O.%20Ale"> M. O. Ale </a> </p> <p class="card-text"><strong>Abstract:</strong></p> The periodic scarcity of onion requires an urgent solution in Nigerian agro- economy. The high percentage of onion losses incurred after the harvesting period is due to non-availability of appropriate facility for its storage. Therefore, some storage structures were constructed with different roofing materials. The response of the materials to the weather parameters like temperature and relative humidity were evaluated to know their effects on the performance of the storage structures. The temperature and relative humidity were taken three times daily alongside with the weight of the onion in each of the structures; the losses as indicated by loss indices like shrinkage, rottenness, sprouting, and colour were identified and percentage loss per week determined. The highest mean percentage loss (22%) was observed in the structure with iron roofing materials while structure with thatched materials had the lowest (9.4%); The highest temperature was observed in the structure with Asbestos roofing materials and no significant difference in the temperature value in the structure with thatched and Iron materials; highest relatively humidity was found in Asbestos roofing material while the lowest in the structure with iron matetrials. It was conclusively found that the storage structure with thatched roof had the best performance in terms of losses. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nigeria" title="Nigeria">Nigeria</a>, <a href="https://publications.waset.org/abstracts/search?q=onion" title=" onion"> onion</a>, <a href="https://publications.waset.org/abstracts/search?q=storage%20structures" title=" storage structures"> storage structures</a>, <a href="https://publications.waset.org/abstracts/search?q=weather%20parameters" title=" weather parameters"> weather parameters</a>, <a href="https://publications.waset.org/abstracts/search?q=roof%20materials" title=" roof materials"> roof materials</a>, <a href="https://publications.waset.org/abstracts/search?q=losses" title=" losses"> losses</a> </p> <a href="https://publications.waset.org/abstracts/20721/onion-storage-and-the-roof-influence-in-the-tropics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20721.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">558</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4465</span> A Review on Enhancing Heat Transfer Processes by Open-Cell Metal Foams and Industrial Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20Cheragh%20Dar">S. Cheragh Dar</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Saljooghi"> M. Saljooghi</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Babrgir"> A. Babrgir</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the last couple of decades researchers' attitudes were focused on developing and enhancing heat transfer processes by using new components or cellular solids that divide into stochastic structures and periodic structures. Open-cell metal foams are part of stochastic structures families that they can be considered as an avant-garde technology and they have unique properties, this porous media can have tremendous achievements in thermal processes. This paper argues and surveys postulating possible in industrial thermal issues which include: compact electronic cooling, heat exchanger, aerospace, fines, turbo machinery, automobiles, crygen tanks, biomechanics, high temperature filters and etc. Recently, by surveying exponential rate of publications in thermal open-cell metal foams, all can be demonstrated in a holistic view which can lead researchers to a new level of understanding in different industrial thermal sections. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=heat%20transfer" title="heat transfer">heat transfer</a>, <a href="https://publications.waset.org/abstracts/search?q=industrial%20thermal" title=" industrial thermal"> industrial thermal</a>, <a href="https://publications.waset.org/abstracts/search?q=cellular%20solids" title=" cellular solids"> cellular solids</a>, <a href="https://publications.waset.org/abstracts/search?q=open%20cell%20metal%20foam" title=" open cell metal foam"> open cell metal foam</a> </p> <a href="https://publications.waset.org/abstracts/63781/a-review-on-enhancing-heat-transfer-processes-by-open-cell-metal-foams-and-industrial-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/63781.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">292</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4464</span> Effects of Roof Materials on Onion Storage</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Imoukhuede%20Oladunni%20Bimpe">Imoukhuede Oladunni Bimpe</a>, <a href="https://publications.waset.org/abstracts/search?q=Ale%20Monday%20Olatunbosun"> Ale Monday Olatunbosun</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Periodic scarcity of onion requires urgent solution in Nigerian agro-economy. The high percentage of onion losses incurred after harvesting period is due to non-availability of appropriate facility for its storage. Therefore, some storage structures were constructed with different roofing materials. The response of the materials to the weather parameters like temperature and relative humidity were evaluated to know their effects on the performance of the storage structures. The temperature and relative humidity were taken three times daily alongside with the weight of the onion in each of the structures; the losses as indicated by loss indices like shrinkage, rottenness, sprouting and colour were identified and percentage loss per week determined. The highest mean percentage loss (22%) was observed in the structure with iron roofing materials while structure with thatched materials had the lowest (9.4%); The highest temperature was observed in the structure with Asbestos roofing materials and no significant difference in the temperature value in the structure with thatched and Iron materials; highest relatively humidity was found in Asbestos roofing material while the lowest in the structure with Iron materials. It was conclusively found that the storage structure with thatched roof had the best performance in terms of losses. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=onion" title="onion">onion</a>, <a href="https://publications.waset.org/abstracts/search?q=storage%20structures" title=" storage structures"> storage structures</a>, <a href="https://publications.waset.org/abstracts/search?q=weather%20parameters" title=" weather parameters"> weather parameters</a>, <a href="https://publications.waset.org/abstracts/search?q=roof%20materials" title=" roof materials"> roof materials</a>, <a href="https://publications.waset.org/abstracts/search?q=losses" title=" losses"> losses</a> </p> <a href="https://publications.waset.org/abstracts/23280/effects-of-roof-materials-on-onion-storage" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/23280.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">612</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=periodic%20structures&amp;page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=periodic%20structures&amp;page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=periodic%20structures&amp;page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=periodic%20structures&amp;page=5">5</a></li> <li class="page-item"><a class="page-link" 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