Steel and Composite Structures

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Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories

  • Attia, Amina (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Bedia, E.A. Adda (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • Received : 2014.03.23
  • Accepted : 2014.05.06
  • Published : 2015.01.25
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Abstract

In this paper, various four variable refined plate theories are presented to analyze vibration of temperature-dependent functionally graded (FG) plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations for the present model is reduced, significantly facilitating engineering analysis. These theories account for parabolic, sinusoidal, hyperbolic, and exponential distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Uniform, linear, nonlinear and sinusoidal thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from Hamilton's principle. Analytical solutions for the free vibration analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent and temperature-independent FG plates and validated with known results in the literature. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature fields on the vibration characteristics. It can be concluded that the present theories are not only accurate but also simple in predicting the free vibration responses of temperature-dependent FG plates.

Keywords

References

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  99. Vibration and instability of nanocomposite pipes conveying fluid mixed by nanoparticles resting on viscoelastic foundation vol.21, pp.5, 2018, https://doi.org/10.12989/cac.2018.21.5.569
  100. Mathematical modeling of smart nanoparticles-reinforced concrete foundations: Vibration analysis vol.27, pp.4, 2015, https://doi.org/10.12989/scs.2018.27.4.465
  101. Nonlocal free vibration analysis of a doubly curved piezoelectric nano shell vol.27, pp.4, 2018, https://doi.org/10.12989/scs.2018.27.4.479
  102. Three dimensional finite elements modeling of FGM plate bending using UMAT vol.66, pp.4, 2018, https://doi.org/10.12989/sem.2018.66.4.487
  103. A novel four-unknown quasi-3D shear deformation theory for functionally graded plates vol.27, pp.5, 2015, https://doi.org/10.12989/scs.2018.27.5.599
  104. A new quasi-3D higher shear deformation theory for vibration of functionally graded carbon nanotube-reinforced composite beams resting on elastic foundation vol.66, pp.6, 2018, https://doi.org/10.12989/sem.2018.66.6.771
  105. Dynamic stability of nanocomposite Mindlin pipes conveying pulsating fluid flow subjected to magnetic field vol.67, pp.1, 2015, https://doi.org/10.12989/sem.2018.67.1.021
  106. Technical and economical assessment of applying silica nanoparticles for construction of concrete structures vol.22, pp.1, 2018, https://doi.org/10.12989/cac.2018.22.1.117
  107. Size-dependent free vibration and dynamic analyses of a sandwich microbeam based on higher-order sinusoidal shear deformation theory and strain gradient theory vol.22, pp.1, 2015, https://doi.org/10.12989/sss.2018.22.1.027
  108. Eigenfrequencies of advanced composite plates using an efficient hybrid quasi-3D shear deformation theory vol.22, pp.1, 2018, https://doi.org/10.12989/sss.2018.22.1.121
  109. Forced vibration response in nanocomposite cylindrical shells - Based on strain gradient beam theory vol.28, pp.3, 2015, https://doi.org/10.12989/scs.2018.28.3.381
  110. Single variable shear deformation model for bending analysis of thick beams vol.67, pp.3, 2015, https://doi.org/10.12989/sem.2018.67.3.291
  111. Numerical study for vibration response of concrete beams reinforced by nanoparticles vol.67, pp.3, 2018, https://doi.org/10.12989/sem.2018.67.3.311
  112. A new plate model for vibration response of advanced composite plates in thermal environment vol.67, pp.4, 2015, https://doi.org/10.12989/sem.2018.67.4.369
  113. Effect of homogenization models on stress analysis of functionally graded plates vol.67, pp.5, 2018, https://doi.org/10.12989/sem.2018.67.5.527
  114. Seismic analysis of AL2O3 nanoparticles-reinforced concrete plates based on sinusoidal shear deformation theory vol.15, pp.3, 2015, https://doi.org/10.12989/eas.2018.15.3.285
  115. A novel quasi-3D hyperbolic shear deformation theory for vibration analysis of simply supported functionally graded plates vol.22, pp.3, 2015, https://doi.org/10.12989/sss.2018.22.3.303
  116. Dynamic buckling of smart sandwich beam subjected to electric field based on hyperbolic piezoelasticity theory vol.22, pp.3, 2015, https://doi.org/10.12989/sss.2018.22.3.327
  117. Dynamic analysis of immersion concrete pipes in water subjected to earthquake load using mathematical methods vol.15, pp.4, 2015, https://doi.org/10.12989/eas.2018.15.4.361
  118. Analysis of wave propagation and free vibration of functionally graded porous material beam with a novel four variable refined theory vol.15, pp.4, 2018, https://doi.org/10.12989/eas.2018.15.4.369
  119. An analytical solution for free vibration of functionally graded beam using a simple first-order shear deformation theory vol.27, pp.4, 2015, https://doi.org/10.12989/was.2018.27.4.247
  120. A refined quasi-3D hybrid-type higher order shear deformation theory for bending and Free vibration analysis of advanced composites beams vol.27, pp.4, 2015, https://doi.org/10.12989/was.2018.27.4.269
  121. Size-dependent forced vibration response of embedded micro cylindrical shells reinforced with agglomerated CNTs using strain gradient theory vol.22, pp.5, 2015, https://doi.org/10.12989/sss.2018.22.5.527
  122. Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation vol.27, pp.5, 2018, https://doi.org/10.12989/was.2018.27.5.311
  123. A layerwise theory for buckling analysis of truncated conical shells reinforced by CNTs and carbon fibers integrated with piezoelectric layers in hygrothermal environment vol.6, pp.4, 2018, https://doi.org/10.12989/anr.2018.6.4.299
  124. Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory vol.28, pp.1, 2015, https://doi.org/10.12989/was.2019.28.1.019
  125. Dynamic and wave propagation investigation of FGM plates with porosities using a four variable plate theory vol.28, pp.1, 2015, https://doi.org/10.12989/was.2019.28.1.049
  126. A novel refined shear deformation theory for the buckling analysis of thick isotropic plates vol.69, pp.3, 2019, https://doi.org/10.12989/sem.2019.69.3.335
  127. Dynamic analysis of concrete column reinforced with Sio2 nanoparticles subjected to blast load vol.7, pp.1, 2015, https://doi.org/10.12989/acc.2019.7.1.051
  128. Effect of the micromechanical models on the bending of FGM beam using a new hyperbolic shear deformation theory vol.16, pp.2, 2019, https://doi.org/10.12989/eas.2019.16.2.177
  129. Vibration response and wave propagation in FG plates resting on elastic foundations using HSDT vol.69, pp.5, 2015, https://doi.org/10.12989/sem.2019.69.5.511
  130. Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT vol.7, pp.2, 2015, https://doi.org/10.12989/anr.2019.7.2.089
  131. Free vibration of imperfect sigmoid and power law functionally graded beams vol.30, pp.6, 2019, https://doi.org/10.12989/scs.2019.30.6.603
  132. Free Vibration Analysis of Composite Material Plates "Case of a Typical Functionally Graded FG Plates Ceramic/Metal" with Porosities vol.25, pp.None, 2015, https://doi.org/10.4028/www.scientific.net/nhc.25.69
  133. Buckling behavior of rectangular plates under uniaxial and biaxial compression vol.70, pp.1, 2019, https://doi.org/10.12989/sem.2019.70.1.113
  134. Assessing the Effects of Porosity on the Bending, Buckling, and Vibrations of Functionally Graded Beams Resting on an Elastic Foundation by Using a New Refined Quasi-3D Theory vol.55, pp.2, 2015, https://doi.org/10.1007/s11029-019-09805-0
  135. A simple HSDT for bending, buckling and dynamic behavior of laminated composite plates vol.70, pp.3, 2019, https://doi.org/10.12989/sem.2019.70.3.325
  136. A novel first order refined shear-deformation beam theory for vibration and buckling analysis of continuously graded beams vol.6, pp.3, 2015, https://doi.org/10.12989/aas.2019.6.3.189
  137. Improved analytical method for adhesive stresses in plated beam: Effect of shear deformation vol.7, pp.3, 2015, https://doi.org/10.12989/acc.2019.7.3.151
  138. Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT vol.7, pp.3, 2015, https://doi.org/10.12989/anr.2019.7.3.191
  139. Temperature dependent vibration analysis of functionally graded sandwich plates resting on Winkler/Pasternak/Kerr foundation vol.6, pp.6, 2015, https://doi.org/10.1088/2053-1591/ab097b
  140. The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate vol.18, pp.2, 2015, https://doi.org/10.12989/gae.2019.18.2.161
  141. Nonlinear bending of functionally graded porous nanobeam subjected to multiple physical load based on nonlocal strain gradient theory vol.31, pp.5, 2019, https://doi.org/10.12989/scs.2019.31.5.469
  142. A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation vol.31, pp.5, 2015, https://doi.org/10.12989/scs.2019.31.5.503
  143. Post-buckling analysis of honeycomb core sandwich panels with geometrical imperfection and graphene reinforced nano-composite face sheets vol.6, pp.9, 2019, https://doi.org/10.1088/2053-1591/ab2b74
  144. Vibration analysis of nonlocal porous nanobeams made of functionally graded material vol.7, pp.5, 2019, https://doi.org/10.12989/anr.2019.7.5.351
  145. Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT vol.24, pp.4, 2015, https://doi.org/10.12989/cac.2019.24.4.347
  146. The nano scale bending and dynamic properties of isolated protein microtubules based on modified strain gradient theory vol.7, pp.6, 2015, https://doi.org/10.12989/anr.2019.7.6.443
  147. Effect of nonlinear elastic foundations on dynamic behavior of FG plates using four-unknown plate theory vol.17, pp.5, 2015, https://doi.org/10.12989/eas.2019.17.5.447
  148. Wave dispersion properties in imperfect sigmoid plates using various HSDTs vol.33, pp.5, 2015, https://doi.org/10.12989/scs.2019.33.5.699
  149. A new higher-order shear and normal deformation theory for the buckling analysis of new type of FGM sandwich plates vol.72, pp.5, 2019, https://doi.org/10.12989/sem.2019.72.5.653
  150. Investigation of thermal buckling properties of ceramic-metal FGM sandwich plates using 2D integral plate model vol.33, pp.6, 2015, https://doi.org/10.12989/scs.2019.33.6.805
  151. On the modeling of dynamic behavior of composite plates using a simple nth-HSDT vol.29, pp.6, 2015, https://doi.org/10.12989/was.2019.29.6.371
  152. A refined of trigonometric shear deformation plate theory based on neutral surface position is proposed for static analysis of FGM plate. vol.26, pp.None, 2015, https://doi.org/10.1016/j.prostr.2020.06.016
  153. Buckling of carbon nanotube reinforced composite plates supported by Kerr foundation using Hamilton's energy principle vol.73, pp.2, 2015, https://doi.org/10.12989/sem.2020.73.2.209
  154. Mechanical buckling of FG-CNTs reinforced composite plate with parabolic distribution using Hamilton's energy principle vol.8, pp.2, 2015, https://doi.org/10.12989/anr.2020.8.2.135
  155. A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates vol.25, pp.2, 2020, https://doi.org/10.12989/sss.2020.25.2.197
  156. An Amplitude- and Temperature-Dependent Vibration Model of Fiber-Reinforced Composite Thin Plates in a Thermal Environment vol.13, pp.7, 2020, https://doi.org/10.3390/ma13071590
  157. Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory vol.25, pp.4, 2015, https://doi.org/10.12989/sss.2020.25.4.409
  158. Mixture rule for studding the environmental pollution reduction in concrete structures containing nanoparticles vol.9, pp.3, 2015, https://doi.org/10.12989/csm.2020.9.3.281
  159. A novel hyperbolic plate theory including stretching effect for free vibration analysis of advanced composite plates in thermal environments vol.75, pp.2, 2020, https://doi.org/10.12989/sem.2020.75.2.193
  160. Free Vibration Analysis of Functionally Graded FG Nano-Plates with Porosities vol.64, pp.None, 2015, https://doi.org/10.4028/www.scientific.net/jnanor.64.61
  161. Bayesian in-situ parameter estimation of metallic plates using piezoelectric transducers vol.26, pp.6, 2015, https://doi.org/10.12989/sss.2020.26.6.735
  162. Thermal frequency analysis of FG sandwich structure under variable temperature loading vol.77, pp.1, 2015, https://doi.org/10.12989/sem.2021.77.1.057
  163. Free vibration and buckling analysis of FGM plates using inverse trigonometric shear deformation theory vol.93, pp.2, 2021, https://doi.org/10.1108/aeat-01-2020-0001
  164. State of the art in functionally graded materials vol.262, pp.None, 2015, https://doi.org/10.1016/j.compstruct.2021.113596