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A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation

  • Bounouara, Fatima (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Benrahou, Kouider Halim (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Belkorissat, Ismahene (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)
  • Received : 2015.03.19
  • Accepted : 2015.09.17
  • Published : 2016.02.10
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Abstract

The objective of this work is to present a zeroth-order shear deformation theory for free vibration analysis of functionally graded (FG) nanoscale plates resting on elastic foundation. The model takes into consideration the influences of small scale and the parabolic variation of the transverse shear strains across the thickness of the nanoscale plate and thus, it avoids the employ use of shear correction factors. Also, in this present theory, the effect of transverse shear deformation is included in the axial displacements by using the shear forces instead of rotational displacements as in available high order plate theories. The material properties are supposed to be graded only in the thickness direction and the effective properties for the FG nanoscale plate are calculated by considering Mori-Tanaka homogenization scheme. The equations of motion are obtained using the nonlocal differential constitutive expressions of Eringen in conjunction with the zeroth-order shear deformation theory via Hamilton's principle. Numerical results for vibration of FG nanoscale plates resting on elastic foundations are presented and compared with the existing solutions. The influences of small scale, shear deformation, gradient index, Winkler modulus parameter and Pasternak shear modulus parameter on the vibration responses of the FG nanoscale plates are investigated.

Keywords

Acknowledgement

Supported by : Algerian National Thematic Agency of Research in Science and Technology (ATRST), university of Sidi Bel Abbes (UDL SBA)

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  26. A new refined nonlocal beam theory accounting for effect of thickness stretching in nanoscale beams vol.4, pp.4, 2016, https://doi.org/10.12989/anr.2016.4.4.251
  27. Large-Amplitude Vibration of Functionally Graded Doubly-Curved Panels Under Heat Conduction vol.55, pp.12, 2017, https://doi.org/10.2514/1.J055878
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  49. Thermal buckling behaviour of shear deformable functionally graded single/doubly curved shell panel with TD and TID properties vol.5, pp.4, 2016, https://doi.org/10.12989/amr.2016.5.4.205
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  51. A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates vol.184, 2018, https://doi.org/10.1016/j.compstruct.2017.10.047
  52. Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories vol.67, 2018, https://doi.org/10.1016/j.euromechsol.2017.09.004
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  57. Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory vol.21, pp.6, 2016, https://doi.org/10.12989/scs.2016.21.6.1287
  58. Influence of size effect on flapwise vibration behavior of rotary microbeam and its analysis through spectral meshless radial point interpolation vol.123, pp.5, 2017, https://doi.org/10.1007/s00339-017-0955-9
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  93. Bending, buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydro-thermo-magneto-mechanical loadings using DQM 2017, https://doi.org/10.1080/19475411.2017.1377312
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  122. A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates vol.22, pp.5, 2016, https://doi.org/10.12989/scs.2016.22.5.975
  123. A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation vol.12, pp.1, 2016, https://doi.org/10.12989/gae.2017.12.1.009
  124. A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams vol.19, pp.2, 2017, https://doi.org/10.12989/sss.2017.19.2.115
  125. Non-linear study of mode II delamination fracture in functionally graded beams vol.23, pp.3, 2016, https://doi.org/10.12989/scs.2017.23.3.263
  126. A non-polynomial four variable refined plate theory for free vibration of functionally graded thick rectangular plates on elastic foundation vol.23, pp.3, 2016, https://doi.org/10.12989/scs.2017.23.3.317
  127. Static deflection and dynamic behavior of higher-order hyperbolic shear deformable compositionally graded beams vol.6, pp.1, 2016, https://doi.org/10.12989/amr.2017.6.1.013
  128. Bending and stability analysis of size-dependent compositionally graded Timoshenko nanobeams with porosities vol.6, pp.1, 2017, https://doi.org/10.12989/amr.2017.6.1.045
  129. Buckling temperature of a single-walled boron nitride nanotubes using a novel nonlocal beam model vol.5, pp.1, 2017, https://doi.org/10.12989/anr.2017.5.1.001
  130. Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT vol.19, pp.3, 2016, https://doi.org/10.12989/sss.2017.19.3.289
  131. Wave propagation in functionally graded beams using various higher-order shear deformation beams theories vol.62, pp.2, 2016, https://doi.org/10.12989/sem.2017.62.2.143
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  133. A novel and simple HSDT for thermal buckling response of functionally graded sandwich plates vol.62, pp.4, 2017, https://doi.org/10.12989/sem.2017.62.4.401
  134. A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams vol.62, pp.6, 2017, https://doi.org/10.12989/sem.2017.62.6.695
  135. Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory vol.19, pp.6, 2016, https://doi.org/10.12989/sss.2017.19.6.601
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  138. Free vibrations of laminated composite plates using a novel four variable refined plate theory vol.24, pp.5, 2017, https://doi.org/10.12989/scs.2017.24.5.603
  139. Hygro-thermo-mechanical vibration and buckling of exponentially graded nanoplates resting on elastic foundations via nonlocal elasticity theory vol.63, pp.3, 2016, https://doi.org/10.12989/sem.2017.63.3.401
  140. Dynamic bending response of SWCNT reinforced composite plates subjected to hygro-thermo-mechanical loading vol.20, pp.2, 2016, https://doi.org/10.12989/cac.2017.20.2.229
  141. An original single variable shear deformation theory for buckling analysis of thick isotropic plates vol.63, pp.4, 2017, https://doi.org/10.12989/sem.2017.63.4.439
  142. A simple analytical approach for thermal buckling of thick functionally graded sandwich plates vol.63, pp.5, 2016, https://doi.org/10.12989/sem.2017.63.5.585
  143. An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities vol.13, pp.3, 2016, https://doi.org/10.12989/eas.2017.13.3.255
  144. A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates vol.13, pp.3, 2016, https://doi.org/10.12989/gae.2017.13.3.385
  145. Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory vol.20, pp.3, 2016, https://doi.org/10.12989/sss.2017.20.3.369
  146. A new and simple HSDT for thermal stability analysis of FG sandwich plates vol.25, pp.2, 2016, https://doi.org/10.12989/scs.2017.25.2.157
  147. A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams vol.64, pp.2, 2016, https://doi.org/10.12989/sem.2017.64.2.145
  148. Free vibration of functionally graded plates resting on elastic foundations based on quasi-3D hybrid-type higher order shear deformation theory vol.20, pp.4, 2017, https://doi.org/10.12989/sss.2017.20.4.509
  149. An analytical solution for bending and vibration responses of functionally graded beams with porosities vol.25, pp.4, 2016, https://doi.org/10.12989/was.2017.25.4.329
  150. An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates vol.25, pp.3, 2016, https://doi.org/10.12989/scs.2017.25.3.257
  151. Effects of triaxial magnetic field on the anisotropic nanoplates vol.25, pp.3, 2017, https://doi.org/10.12989/scs.2017.25.3.361
  152. A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate vol.25, pp.4, 2017, https://doi.org/10.12989/scs.2017.25.4.389
  153. A simple quasi-3D sinusoidal shear deformation theory with stretching effect for carbon nanotube-reinforced composite beams resting on elastic foundation vol.13, pp.5, 2016, https://doi.org/10.12989/eas.2017.13.5.509
  154. A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates vol.64, pp.4, 2016, https://doi.org/10.12989/sem.2017.64.4.391
  155. Vibration analysis of micro composite thin beam based on modified couple stress vol.64, pp.4, 2017, https://doi.org/10.12989/sem.2017.64.4.403
  156. Coupled effects of electrical polarization-strain gradient on vibration behavior of double-layered flexoelectric nanoplates vol.20, pp.5, 2017, https://doi.org/10.12989/sss.2017.20.5.573
  157. A new quasi-3D HSDT for buckling and vibration of FG plate vol.64, pp.6, 2016, https://doi.org/10.12989/sem.2017.64.6.737
  158. Nonlocal strain gradient-based vibration analysis of embedded curved porous piezoelectric nano-beams in thermal environment vol.20, pp.6, 2016, https://doi.org/10.12989/sss.2017.20.6.709
  159. An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.693
  160. A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.717
  161. An original HSDT for free vibration analysis of functionally graded plates vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.735
  162. The role of micromechanical models in the mechanical response of elastic foundation FG sandwich thick beams vol.68, pp.1, 2018, https://doi.org/10.12989/sem.2018.68.1.053
  163. A nonlocal strain gradient theory for nonlinear free and forced vibration of embedded thick FG double layered nanoplates vol.68, pp.1, 2018, https://doi.org/10.12989/sem.2018.68.1.103
  164. Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory vol.65, pp.5, 2016, https://doi.org/10.12989/sem.2018.65.5.621
  165. Forced vibration analysis of cracked functionally graded microbeams vol.6, pp.1, 2016, https://doi.org/10.12989/anr.2018.6.1.039
  166. Vibration analysis of carbon nanotubes with multiple cracks in thermal environment vol.6, pp.1, 2016, https://doi.org/10.12989/anr.2018.6.1.057
  167. Buckling analysis of FGM Euler-Bernoulli nano-beams with 3D-varying properties based on consistent couple-stress theory vol.26, pp.6, 2016, https://doi.org/10.12989/scs.2018.26.6.663
  168. Wave dispersion characteristics of nonlocal strain gradient double-layered graphene sheets in hygro-thermal environments vol.65, pp.6, 2018, https://doi.org/10.12989/sem.2018.65.6.645
  169. Development of super convergent Euler finite elements for the analysis of sandwich beams with soft core vol.65, pp.6, 2016, https://doi.org/10.12989/sem.2018.65.6.657
  170. A novel four variable refined plate theory for wave propagation in functionally graded material plates vol.27, pp.1, 2018, https://doi.org/10.12989/scs.2018.27.1.109
  171. Geometrically nonlinear analysis of a laminated composite beam vol.66, pp.1, 2016, https://doi.org/10.12989/sem.2018.66.1.027
  172. Improved HSDT accounting for effect of thickness stretching in advanced composite plates vol.66, pp.1, 2016, https://doi.org/10.12989/sem.2018.66.1.061
  173. Vibration and instability analysis of pipes reinforced by SiO2 nanoparticles considering agglomeration effects vol.21, pp.4, 2018, https://doi.org/10.12989/cac.2018.21.4.431
  174. Three dimensional dynamic response of functionally graded nanoplates under a moving load vol.66, pp.2, 2016, https://doi.org/10.12989/sem.2018.66.2.249
  175. A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory vol.21, pp.4, 2016, https://doi.org/10.12989/sss.2018.21.4.397
  176. Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates vol.14, pp.6, 2016, https://doi.org/10.12989/gae.2018.14.6.519
  177. Bending of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment using an accurate theory vol.27, pp.3, 2018, https://doi.org/10.12989/scs.2018.27.3.311
  178. Size dependent bending analysis of micro/nano sandwich structures based on a nonlocal high order theory vol.27, pp.3, 2018, https://doi.org/10.12989/scs.2018.27.3.371
  179. Free vibration of FGM plates with porosity by a shear deformation theory with four variables vol.66, pp.3, 2016, https://doi.org/10.12989/sem.2018.66.3.353
  180. Free vibration and buckling analysis of orthotropic plates using a new two variable refined plate theory vol.15, pp.1, 2016, https://doi.org/10.12989/gae.2018.15.1.711
  181. 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
  182. Mathematical modeling of smart nanoparticles-reinforced concrete foundations: Vibration analysis vol.27, pp.4, 2016, https://doi.org/10.12989/scs.2018.27.4.465
  183. 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
  184. Large deflection analysis of a fiber reinforced composite beam vol.27, pp.5, 2016, https://doi.org/10.12989/scs.2018.27.5.567
  185. A novel four-unknown quasi-3D shear deformation theory for functionally graded plates vol.27, pp.5, 2016, https://doi.org/10.12989/scs.2018.27.5.599
  186. A new nonlocal HSDT for analysis of stability of single layer graphene sheet vol.6, pp.2, 2016, https://doi.org/10.12989/anr.2018.6.2.147
  187. Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions vol.66, pp.6, 2018, https://doi.org/10.12989/sem.2018.66.6.761
  188. 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
  189. Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter vol.28, pp.1, 2016, https://doi.org/10.12989/scs.2018.28.1.013
  190. Dynamic stability of nanocomposite Mindlin pipes conveying pulsating fluid flow subjected to magnetic field vol.67, pp.1, 2016, https://doi.org/10.12989/sem.2018.67.1.021
  191. 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
  192. 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, 2016, https://doi.org/10.12989/sss.2018.22.1.027
  193. Forced vibration response in nanocomposite cylindrical shells - Based on strain gradient beam theory vol.28, pp.3, 2016, https://doi.org/10.12989/scs.2018.28.3.381
  194. Single variable shear deformation model for bending analysis of thick beams vol.67, pp.3, 2016, https://doi.org/10.12989/sem.2018.67.3.291
  195. 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
  196. Analysis of boundary conditions effects on vibration of nanobeam in a polymeric matrix vol.67, pp.5, 2016, https://doi.org/10.12989/sem.2018.67.5.517
  197. 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
  198. Dynamic analysis of higher order shear-deformable nanobeams resting on elastic foundation based on nonlocal strain gradient theory vol.6, pp.3, 2018, https://doi.org/10.12989/anr.2018.6.3.279
  199. Seismic analysis of AL2O3 nanoparticles-reinforced concrete plates based on sinusoidal shear deformation theory vol.15, pp.3, 2016, https://doi.org/10.12989/eas.2018.15.3.285
  200. Free axial vibration analysis of axially functionally graded thick nanorods using nonlocal Bishop's theory vol.28, pp.6, 2018, https://doi.org/10.12989/scs.2018.28.6.749
  201. A novel quasi-3D hyperbolic shear deformation theory for vibration analysis of simply supported functionally graded plates vol.22, pp.3, 2016, https://doi.org/10.12989/sss.2018.22.3.303
  202. 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
  203. An analytical solution for free vibration of functionally graded beam using a simple first-order shear deformation theory vol.27, pp.4, 2016, https://doi.org/10.12989/was.2018.27.4.247
  204. 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, 2016, https://doi.org/10.12989/was.2018.27.4.269
  205. Surface effects on nonlinear vibration and buckling analysis of embedded FG nanoplates via refined HOSDPT in hygrothermal environment considering physical neutral surface position vol.5, pp.6, 2016, https://doi.org/10.12989/aas.2018.5.6.691
  206. Size-dependent forced vibration response of embedded micro cylindrical shells reinforced with agglomerated CNTs using strain gradient theory vol.22, pp.5, 2016, https://doi.org/10.12989/sss.2018.22.5.527
  207. 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
  208. Critical buckling loads of carbon nanotube embedded in Kerr's medium vol.6, pp.4, 2016, https://doi.org/10.12989/anr.2018.6.4.339
  209. Small-scale effect on the forced vibration of a nano beam embedded an elastic medium using nonlocal elasticity theory vol.6, pp.1, 2019, https://doi.org/10.12989/aas.2019.6.1.001
  210. Nonlinear vibration of functionally graded nano-tubes using nonlocal strain gradient theory and a two-steps perturbation method vol.69, pp.2, 2016, https://doi.org/10.12989/sem.2019.69.2.205
  211. Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory vol.28, pp.1, 2016, https://doi.org/10.12989/was.2019.28.1.019
  212. Dynamic and wave propagation investigation of FGM plates with porosities using a four variable plate theory vol.28, pp.1, 2016, https://doi.org/10.12989/was.2019.28.1.049
  213. 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
  214. Dynamic analysis of concrete column reinforced with Sio2 nanoparticles subjected to blast load vol.7, pp.1, 2016, https://doi.org/10.12989/acc.2019.7.1.051
  215. 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
  216. Application of nonlocal elasticity theory on the wave propagation of flexoelectric functionally graded (FG) timoshenko nano-beams considering surface effects and residual surface stress vol.23, pp.2, 2016, https://doi.org/10.12989/sss.2019.23.2.141
  217. On exact wave propagation analysis of triclinic material using three-dimensional bi-Helmholtz gradient plate model vol.69, pp.5, 2016, https://doi.org/10.12989/sem.2019.69.5.487
  218. Vibration response and wave propagation in FG plates resting on elastic foundations using HSDT vol.69, pp.5, 2016, https://doi.org/10.12989/sem.2019.69.5.511
  219. Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT vol.7, pp.2, 2016, https://doi.org/10.12989/anr.2019.7.2.089
  220. Free vibration of an annular sandwich plate with CNTRC facesheets and FG porous cores using Ritz method vol.7, pp.2, 2016, https://doi.org/10.12989/anr.2019.7.2.109
  221. Vibration analysis of different material distributions of functionally graded microbeam vol.69, pp.6, 2016, https://doi.org/10.12989/sem.2019.69.6.637
  222. Nonlocal strain gradient model for thermal stability of FG nanoplates integrated with piezoelectric layers vol.23, pp.3, 2016, https://doi.org/10.12989/sss.2019.23.3.215
  223. Static and Dynamic Behavior of Nanotubes-Reinforced Sandwich Plates Using (FSDT) vol.57, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.57.117
  224. Postbuckling of Curved Carbon Nanotubes Using Energy Equivalent Model vol.57, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.57.136
  225. Participation Factor and Vibration of Carbon Nanotube with Vacancies vol.57, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.57.158
  226. A New Hyperbolic Two-Unknown Beam Model for Bending and Buckling Analysis of a Nonlocal Strain Gradient Nanobeams vol.57, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.57.175
  227. Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation vol.70, pp.1, 2019, https://doi.org/10.12989/sem.2019.70.1.055
  228. 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
  229. Dynamic response of metal foam FG porous cylindrical micro-shells due to moving loads with strain gradient size-dependency vol.134, pp.5, 2016, https://doi.org/10.1140/epjp/i2019-12540-3
  230. 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
  231. Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT vol.7, pp.3, 2016, https://doi.org/10.12989/anr.2019.7.3.191
  232. Effect of distribution shape of the porosity on the interfacial stresses of the FGM beam strengthened with FRP plate vol.16, pp.5, 2016, https://doi.org/10.12989/eas.2019.16.5.601
  233. Influence of shear preload on wave propagation in small-scale plates with nanofibers vol.70, pp.4, 2016, https://doi.org/10.12989/sem.2019.70.4.407
  234. A Novel Refined Plate Theory for Free Vibration Analyses of Single-Layered Graphene Sheets Lying on Winkler-Pasternak Elastic Foundations vol.58, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.58.151
  235. The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate vol.18, pp.2, 2016, https://doi.org/10.12989/gae.2019.18.2.161
  236. A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation vol.31, pp.5, 2016, https://doi.org/10.12989/scs.2019.31.5.503
  237. Numerical analysis for free vibration of hybrid laminated composite plates for different boundary conditions vol.70, pp.5, 2019, https://doi.org/10.12989/sem.2019.70.5.535
  238. Nonlocal strain gradient thermal vibration analysis of double-coupled metal foam plate system with uniform and non-uniform porosities vol.8, pp.3, 2016, https://doi.org/10.12989/csm.2019.8.3.247
  239. Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities vol.6, pp.2, 2016, https://doi.org/10.12989/smm.2019.6.2.147
  240. Conformable solution of fractional vibration problem of plate subjected to in-plane loads vol.28, pp.6, 2019, https://doi.org/10.12989/was.2019.28.6.347
  241. Chaotic dynamics of a non-autonomous nonlinear system for a smart composite shell subjected to the hygro-thermal environment vol.25, pp.7, 2019, https://doi.org/10.1007/s00542-018-4206-6
  242. Stability analysis of embedded graphene platelets reinforced composite plates in thermal environment vol.134, pp.7, 2019, https://doi.org/10.1140/epjp/i2019-12581-6
  243. Vibration characteristics of zigzag and chiral functionally graded material rotating carbon nanotubes sandwich with ring supports vol.233, pp.16, 2016, https://doi.org/10.1177/0954406219855095
  244. Elastic guided waves in fully-clamped functionally graded carbon nanotube-reinforced composite plates vol.6, pp.9, 2019, https://doi.org/10.1088/2053-1591/ab3474
  245. Analysis of static and dynamic characteristics of strain gradient shell structures made of porous nano-crystalline materials vol.8, pp.3, 2016, https://doi.org/10.12989/amr.2019.8.3.179
  246. Analyzing large-amplitude vibration of nonlocal beams made of different piezo-electric materials in thermal environment vol.8, pp.3, 2019, https://doi.org/10.12989/amr.2019.8.3.237
  247. 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
  248. Frequency response of initially deflected nanotubes conveying fluid via a nonlinear NSGT model vol.72, pp.1, 2016, https://doi.org/10.12989/sem.2019.72.1.071
  249. Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT vol.24, pp.4, 2016, https://doi.org/10.12989/cac.2019.24.4.347
  250. A Non-Linear Spring Model for Predicting Modal Behavior of Oscillators Built from Double Walled Carbon Nanotubes vol.60, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.60.21
  251. The nano scale bending and dynamic properties of isolated protein microtubules based on modified strain gradient theory vol.7, pp.6, 2016, https://doi.org/10.12989/anr.2019.7.6.443
  252. Effect of nonlinear elastic foundations on dynamic behavior of FG plates using four-unknown plate theory vol.17, pp.5, 2016, https://doi.org/10.12989/eas.2019.17.5.447
  253. Dynamic modeling of a multi-scale sandwich composite panel containing flexible core and MR smart layer vol.134, pp.12, 2016, https://doi.org/10.1140/epjp/i2019-12662-6
  254. Wave dispersion properties in imperfect sigmoid plates using various HSDTs vol.33, pp.5, 2016, https://doi.org/10.12989/scs.2019.33.5.699
  255. 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
  256. Investigation of thermal buckling properties of ceramic-metal FGM sandwich plates using 2D integral plate model vol.33, pp.6, 2016, https://doi.org/10.12989/scs.2019.33.6.805
  257. On the modeling of dynamic behavior of composite plates using a simple nth-HSDT vol.29, pp.6, 2016, https://doi.org/10.12989/was.2019.29.6.371
  258. Finite element forced vibration analysis of refined shear deformable nanocomposite graphene platelet-reinforced beams vol.42, pp.1, 2016, https://doi.org/10.1007/s40430-019-2118-8
  259. Buckling of carbon nanotube reinforced composite plates supported by Kerr foundation using Hamilton's energy principle vol.73, pp.2, 2016, https://doi.org/10.12989/sem.2020.73.2.209
  260. Hygrothermal postbuckling analysis of smart multiscale piezoelectric composite shells vol.135, pp.2, 2016, https://doi.org/10.1140/epjp/s13360-020-00137-w
  261. Effect of Microstructure and Surface Energy on the Static and Dynamic Characteristics of FG Timoshenko Nanobeam Embedded in an Elastic Medium vol.61, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.61.97
  262. Mechanical buckling of FG-CNTs reinforced composite plate with parabolic distribution using Hamilton's energy principle vol.8, pp.2, 2016, https://doi.org/10.12989/anr.2020.8.2.135
  263. Dynamic characteristics of multi-phase crystalline porous shells with using strain gradient elasticity vol.8, pp.2, 2016, https://doi.org/10.12989/anr.2020.8.2.157
  264. Free vibration analysis of sandwich FGM shells using isogeometric B-spline finite strip method vol.34, pp.3, 2020, https://doi.org/10.12989/scs.2020.34.3.361
  265. 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
  266. Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory vol.35, pp.1, 2020, https://doi.org/10.12989/scs.2020.35.1.147
  267. Analysis of post-buckling of higher-order graphene oxide reinforced concrete plates with geometrical imperfection vol.9, pp.4, 2016, https://doi.org/10.12989/acc.2020.9.4.397
  268. Finite element based modeling and thermal dynamic analysis of functionally graded graphene reinforced beams vol.5, pp.2, 2016, https://doi.org/10.12989/acd.2020.5.2.177
  269. Bending analysis of magneto-electro piezoelectric nanobeams system under hygro-thermal loading vol.8, pp.3, 2016, https://doi.org/10.12989/anr.2020.8.3.203
  270. Buckling and free vibration analyses of nanobeams with surface effects via various higher-order shear deformation theories vol.74, pp.2, 2020, https://doi.org/10.12989/sem.2020.74.2.175
  271. Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory vol.25, pp.4, 2016, https://doi.org/10.12989/sss.2020.25.4.409
  272. Nonlocal nonlinear dynamic behavior of composite piezo-magnetic beams using a refined higher-order beam theory vol.35, pp.4, 2016, https://doi.org/10.12989/scs.2020.35.4.545
  273. Nonlinear vibration of smart nonlocal magneto-electro-elastic beams resting on nonlinear elastic substrate with geometrical imperfection and various piezoelectric effects vol.25, pp.5, 2016, https://doi.org/10.12989/sss.2020.25.5.619
  274. Mixture rule for studding the environmental pollution reduction in concrete structures containing nanoparticles vol.9, pp.3, 2016, https://doi.org/10.12989/csm.2020.9.3.281
  275. Elastic wave characteristics of graphene nanoplatelets reinforced composite nanoplates vol.74, pp.6, 2020, https://doi.org/10.12989/sem.2020.74.6.809
  276. Nonlinear stability of smart nonlocal magneto-electro-thermo-elastic beams with geometric imperfection and piezoelectric phase effects vol.25, pp.6, 2020, https://doi.org/10.12989/sss.2020.25.6.707
  277. Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT vol.36, pp.3, 2016, https://doi.org/10.1007/s00366-019-00732-1
  278. Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory vol.48, pp.4, 2016, https://doi.org/10.1080/15397734.2019.1642766
  279. Static analysis of multiple graphene sheet systems in cylindrical bending and resting on an elastic medium vol.75, pp.1, 2016, https://doi.org/10.12989/sem.2020.75.1.109
  280. Analyzing exact nonlinear forced vibrations of two-phase magneto-electro-elastic nanobeams under an elliptic-type force vol.9, pp.1, 2016, https://doi.org/10.12989/anr.2020.9.1.047
  281. Post-buckling analysis of geometrically imperfect nanoparticle reinforced annular sector plates under radial compression vol.26, pp.1, 2020, https://doi.org/10.12989/cac.2020.26.1.021
  282. Strain gradient based static stability analysis of composite crystalline shell structures having porosities vol.36, pp.6, 2016, https://doi.org/10.12989/scs.2020.36.6.631
  283. Dynamics of graphene-nanoplatelets reinforced composite nanoplates including different boundary conditions vol.36, pp.6, 2016, https://doi.org/10.12989/scs.2020.36.6.689
  284. Wave dispersion characteristics of fluid-conveying magneto-electro-elastic nanotubes vol.36, pp.4, 2016, https://doi.org/10.1007/s00366-019-00790-5
  285. Analyzing nonlocal nonlinear vibrations of two-phase geometrically imperfect piezo-magnetic beams considering piezoelectric reinforcement scheme vol.55, pp.7, 2020, https://doi.org/10.1177/0309324720917285
  286. Thermal postbuckling behavior of CNT-reinforced composite sandwich plate models resting on elastic foundations with tangentially restrained edges and temperature-dependent properties vol.33, pp.10, 2016, https://doi.org/10.1177/0892705719828789
  287. A Critical Review of Recent Research of Free Vibration and Stability of Functionally Graded Materials of Sandwich Plate vol.1094, pp.1, 2021, https://doi.org/10.1088/1757-899x/1094/1/012081
  288. A boundary integral investigation for unsteady modified Helmholtz problems of some other classes of anisotropic functionally graded materials vol.10, pp.1, 2016, https://doi.org/10.1142/s2047684121500056
  289. On the mechanics of nanocomposites reinforced by wavy/defected/aggregated nanotubes vol.38, pp.5, 2016, https://doi.org/10.12989/scs.2021.38.5.533
  290. State of the art in functionally graded materials vol.262, pp.None, 2016, https://doi.org/10.1016/j.compstruct.2021.113596
  291. Wave dispersion of nanobeams incorporating stretching effect vol.31, pp.4, 2016, https://doi.org/10.1080/17455030.2019.1607623
  292. Mass density effect on vibration of zigzag and chiral SWCNTs: A theoretical study vol.23, pp.6, 2016, https://doi.org/10.1177/1099636220906257
  293. On vibration of functionally graded sandwich nanoplates in the thermal environment vol.23, pp.6, 2016, https://doi.org/10.1177/1099636220909790