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On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model

  • Belkorissat, Ismahene (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Houari, Mohammed Sid Ahmed (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil) ;
  • 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 : 2014.07.17
  • Accepted : 2014.11.06
  • Published : 2015.04.25
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Abstract

In this paper, a new nonlocal hyperbolic refined plate model is presented for free vibration properties of functionally graded (FG) plates. This nonlocal nano-plate model incorporates the length scale parameter which can capture the small scale effect. The displacement field of the present theory is chosen based on a hyperbolic variation in the in-plane displacements through the thickness of the nano-plate. By dividing the transverse displacement into the bending and shear parts, the number of unknowns and equations of motion of the present theory is reduced, significantly facilitating structural analysis. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG nano-plate are computed using Mori-Tanaka homogenization scheme. The governing equations of motion are derived based on the nonlocal differential constitutive relations of Eringen in conjunction with the refined four variable plate theory via Hamilton's principle. Analytical solution for the simply supported FG nano-plates is obtained to verify the theory by comparing its results with other available solutions in the open literature. The effects of nonlocal parameter, the plate thickness, the plate aspect ratio, and various material compositions on the dynamic response of the FG nano-plate are discussed.

Keywords

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  46. Critical Buckling Load of Chiral Double-Walled Carbon Nanotubes Embedded in an Elastic Medium vol.53, pp.6, 2018, https://doi.org/10.1007/s11029-018-9708-x
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  49. Influence of various temperature distributions on critical speed and vibrational characteristics of rotating cylindrical microshells with modified lengthscale parameter vol.132, pp.6, 2017, https://doi.org/10.1140/epjp/i2017-11551-4
  50. Buckling and free vibration of shallow curved micro/nano-beam based on strain gradient theory under thermal loading with temperature-dependent properties vol.123, pp.1, 2017, https://doi.org/10.1007/s00339-016-0591-9
  51. Electro-magnetic effects on nonlocal dynamic behavior of embedded piezoelectric nanoscale beams vol.28, pp.15, 2017, https://doi.org/10.1177/1045389X16682850
  52. An analytical method for free vibration analysis of functionally graded sandwich beams vol.23, pp.1, 2016, https://doi.org/10.12989/was.2016.23.1.059
  53. Nonlinear vibration of nonlocal four-variable graded plates with porosities implementing homotopy perturbation and Hamiltonian methods vol.229, pp.1, 2018, https://doi.org/10.1007/s00707-017-1952-y
  54. 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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  58. A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates vol.22, pp.2, 2016, https://doi.org/10.12989/scs.2016.22.2.257
  59. 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
  60. A novel four variable refined plate theory for laminated composite plates vol.22, pp.4, 2016, https://doi.org/10.12989/scs.2016.22.4.713
  61. Thermal stability analysis of solar functionally graded plates on elastic foundation using an efficient hyperbolic shear deformation theory vol.10, pp.3, 2016, https://doi.org/10.12989/gae.2016.10.3.357
  62. Small scale effect on the vibration of non-uniform nanoplates vol.55, pp.3, 2015, https://doi.org/10.12989/sem.2015.55.3.495
  63. A nonlocal quasi-3D trigonometric plate model for free vibration behaviour of micro/nanoscale plates vol.56, pp.2, 2015, https://doi.org/10.12989/sem.2015.56.2.223
  64. Dynamic behavior of FGM beam using a new first shear deformation theory vol.10, pp.2, 2016, https://doi.org/10.12989/eas.2016.10.2.451
  65. Investigating physical field effects on the size-dependent dynamic behavior of inhomogeneous nanoscale plates vol.132, pp.2, 2017, https://doi.org/10.1140/epjp/i2017-11357-4
  66. Frequency analysis of nanoporous mass sensors based on a vibrating heterogeneous nanoplate and nonlocal strain gradient theory 2017, https://doi.org/10.1007/s00542-017-3531-5
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  69. On the bending and stability of nanowire using various HSDTs vol.3, pp.4, 2015, https://doi.org/10.12989/anr.2015.3.4.177
  70. Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes vol.514, 2017, https://doi.org/10.1016/j.physb.2017.03.030
  71. Nonlocal Timoshenko Beam for Vibrations of Magnetically Affected Inclined Single-Walled Carbon Nanotubes as Nanofluidic Conveyors vol.131, pp.6, 2017, https://doi.org/10.12693/APhysPolA.131.1439
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  73. A general nonlocal stress-strain gradient theory for forced vibration analysis of heterogeneous porous nanoplates vol.67, 2018, https://doi.org/10.1016/j.euromechsol.2017.09.001
  74. A new higher-order shear and normal deformation theory for functionally graded sandwich beams vol.19, pp.3, 2015, https://doi.org/10.12989/scs.2015.19.3.521
  75. Wave propagation analysis of a size-dependent magneto-electro-elastic heterogeneous nanoplate vol.131, pp.12, 2016, https://doi.org/10.1140/epjp/i2016-16433-7
  76. Thermomechanical effects on the bending of antisymmetric cross-ply composite plates using a four variable sinusoidal theory vol.19, pp.1, 2015, https://doi.org/10.12989/scs.2015.19.1.093
  77. Application of nonlocal strain gradient theory and various shear deformation theories to nonlinear vibration analysis of sandwich nano-beam with FG-CNTRCs face-sheets in electro-thermal environment vol.123, pp.5, 2017, https://doi.org/10.1007/s00339-017-0922-5
  78. Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory vol.57, pp.4, 2016, https://doi.org/10.12989/sem.2016.57.4.617
  79. Bending analysis of FGM plates using a sinusoidal shear deformation theory vol.23, pp.6, 2016, https://doi.org/10.12989/was.2016.23.6.543
  80. A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate vol.60, pp.4, 2016, https://doi.org/10.12989/sem.2016.60.4.547
  81. Buckling analysis of nonuniform nonlocal strain gradient beams using generalized differential quadrature method 2018, https://doi.org/10.1016/j.aej.2017.06.001
  82. Effect of porosity on vibrational characteristics of non-homogeneous plates using hyperbolic shear deformation theory vol.22, pp.4, 2016, https://doi.org/10.12989/was.2016.22.4.429
  83. Parametric excitation analysis of a piezoelectric-nanotube conveying fluid under multi-physics field 2017, https://doi.org/10.1007/s00542-017-3670-8
  84. Vibration analysis of bonded double-FGM viscoelastic nanoplate systems based on a modified strain gradient theory incorporating surface effects vol.123, pp.3, 2017, https://doi.org/10.1007/s00339-017-0784-x
  85. Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept vol.20, pp.5, 2016, https://doi.org/10.12989/scs.2016.20.5.963
  86. Size-dependent thermally affected wave propagation analysis in nonlocal strain gradient functionally graded nanoplates via a quasi-3D plate theory vol.232, pp.1, 2018, https://doi.org/10.1177/0954406216674243
  87. Analytical solution for bending analysis of functionally graded beam vol.19, pp.4, 2015, https://doi.org/10.12989/scs.2015.19.4.829
  88. Thermo-mechanical analysis of FG nanobeam with attached tip mass: an exact solution vol.122, pp.12, 2016, https://doi.org/10.1007/s00339-016-0542-5
  89. Nonlocal microstructure-dependent dynamic stability of refined porous FG nanoplates in hygro-thermal environments vol.132, pp.10, 2017, https://doi.org/10.1140/epjp/i2017-11686-2
  90. Static and dynamic behavior of FGM plate using a new first shear deformation plate theory vol.57, pp.1, 2016, https://doi.org/10.12989/sem.2016.57.1.127
  91. Nonlinear atomic vibrations and structural phase transitions in strained carbon chains vol.138, 2017, https://doi.org/10.1016/j.commatsci.2017.07.004
  92. On thermal stability of plates with functionally graded coefficient of thermal expansion vol.60, pp.2, 2016, https://doi.org/10.12989/sem.2016.60.2.313
  93. Dynamic response of a single-walled carbon nanotube under a moving harmonic load by considering modified nonlocal elasticity theory vol.133, pp.2, 2018, https://doi.org/10.1140/epjp/i2018-11868-4
  94. Size-dependent vibration analysis of viscoelastic nanocrystalline silicon nanobeams with porosities based on a higher order refined beam theory vol.166, 2017, https://doi.org/10.1016/j.compstruct.2017.01.036
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  97. Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory vol.18, pp.4, 2016, https://doi.org/10.12989/sss.2016.18.4.755
  98. Nonlinear thermal vibration analysis of refined shear deformable FG nanoplates: two semi-analytical solutions vol.40, pp.2, 2018, https://doi.org/10.1007/s40430-018-0968-0
  99. Non-Local Buckling Analysis of Functionally Graded Nanoporous Metal Foam Nanoplates vol.8, pp.11, 2018, https://doi.org/10.3390/coatings8110389
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  102. Stabilities and electronic properties of nanowires made of single atomic sulfur chains encapsulated in zigzag carbon nanotubes vol.29, pp.41, 2018, https://doi.org/10.1088/1361-6528/aad67a
  103. Forced vibration analysis of cracked nanobeams vol.40, pp.8, 2018, https://doi.org/10.1007/s40430-018-1315-1
  104. Vibration and buckling analysis of a rotary functionally graded piezomagnetic nanoshell embedded in viscoelastic media vol.29, pp.11, 2018, https://doi.org/10.1177/1045389X18770856
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  106. Hygrothermal wave characteristic of nanobeam-type inhomogeneous materials with porosity under magnetic field pp.2041-2983, 2018, https://doi.org/10.1177/0954406218781680
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  110. A novel approach for nonlinear bending response of macro- and nanoplates with irregular variable thickness under nonuniform loading in thermal environment pp.1539-7742, 2019, https://doi.org/10.1080/15397734.2018.1557529
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  112. Electro-mechanical vibration of nanoshells using consistent size-dependent piezoelectric theory vol.22, pp.6, 2015, https://doi.org/10.12989/scs.2016.22.6.1301
  113. 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
  114. A non-polynomial four variable refined plate theory for free vibration of functionally graded thick rectangular plates on elastic foundation vol.23, pp.3, 2015, https://doi.org/10.12989/scs.2017.23.3.317
  115. Static deflection and dynamic behavior of higher-order hyperbolic shear deformable compositionally graded beams vol.6, pp.1, 2015, https://doi.org/10.12989/amr.2017.6.1.013
  116. 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
  117. 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
  118. Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT vol.19, pp.3, 2015, https://doi.org/10.12989/sss.2017.19.3.289
  119. Analysis of functionally graded plates using a sinusoidal shear deformation theory vol.19, pp.4, 2017, https://doi.org/10.12989/sss.2017.19.4.441
  120. 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
  121. 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
  122. Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory vol.19, pp.6, 2015, https://doi.org/10.12989/sss.2017.19.6.601
  123. A new shear deformation plate theory with stretching effect for buckling analysis of functionally graded sandwich plates vol.24, pp.5, 2017, https://doi.org/10.12989/scs.2017.24.5.569
  124. 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
  125. Hygro-thermo-mechanical vibration and buckling of exponentially graded nanoplates resting on elastic foundations via nonlocal elasticity theory vol.63, pp.3, 2015, https://doi.org/10.12989/sem.2017.63.3.401
  126. Dynamic bending response of SWCNT reinforced composite plates subjected to hygro-thermo-mechanical loading vol.20, pp.2, 2015, https://doi.org/10.12989/cac.2017.20.2.229
  127. 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
  128. A simple analytical approach for thermal buckling of thick functionally graded sandwich plates vol.63, pp.5, 2015, https://doi.org/10.12989/sem.2017.63.5.585
  129. Vibration analysis of FG nanobeams based on third-order shear deformation theory under various boundary conditions vol.25, pp.1, 2017, https://doi.org/10.12989/scs.2017.25.1.067
  130. An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities vol.13, pp.3, 2015, https://doi.org/10.12989/eas.2017.13.3.255
  131. A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates vol.13, pp.3, 2015, https://doi.org/10.12989/gae.2017.13.3.385
  132. Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory vol.20, pp.3, 2015, https://doi.org/10.12989/sss.2017.20.3.369
  133. Analytical solutions for sandwich plates considering permeation effect by 3-D elasticity theory vol.25, pp.2, 2015, https://doi.org/10.12989/scs.2017.25.2.127
  134. A new and simple HSDT for thermal stability analysis of FG sandwich plates vol.25, pp.2, 2015, https://doi.org/10.12989/scs.2017.25.2.157
  135. A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams vol.64, pp.2, 2015, https://doi.org/10.12989/sem.2017.64.2.145
  136. 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
  137. An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates vol.25, pp.3, 2015, https://doi.org/10.12989/scs.2017.25.3.257
  138. Effects of triaxial magnetic field on the anisotropic nanoplates vol.25, pp.3, 2017, https://doi.org/10.12989/scs.2017.25.3.361
  139. 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
  140. Thermal vibration of two-dimensional functionally graded (2D-FG) porous Timoshenko nanobeams vol.25, pp.4, 2015, https://doi.org/10.12989/scs.2017.25.4.415
  141. 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, 2015, https://doi.org/10.12989/eas.2017.13.5.509
  142. A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates vol.64, pp.4, 2015, https://doi.org/10.12989/sem.2017.64.4.391
  143. Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermo-mechanical loading using nonlocal strain gradient theory vol.64, pp.6, 2015, https://doi.org/10.12989/sem.2017.64.6.683
  144. A new quasi-3D HSDT for buckling and vibration of FG plate vol.64, pp.6, 2015, https://doi.org/10.12989/sem.2017.64.6.737
  145. An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions vol.25, pp.6, 2015, https://doi.org/10.12989/scs.2017.25.6.693
  146. A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations vol.25, pp.6, 2015, https://doi.org/10.12989/scs.2017.25.6.717
  147. An original HSDT for free vibration analysis of functionally graded plates vol.25, pp.6, 2015, https://doi.org/10.12989/scs.2017.25.6.735
  148. Vibration analysis of thick orthotropic plates using quasi 3D sinusoidal shear deformation theory vol.16, pp.2, 2015, https://doi.org/10.12989/gae.2018.16.2.141
  149. Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory vol.65, pp.5, 2015, https://doi.org/10.12989/sem.2018.65.5.621
  150. Forced vibration analysis of cracked functionally graded microbeams vol.6, pp.1, 2015, https://doi.org/10.12989/anr.2018.6.1.039
  151. Buckling analysis of FGM Euler-Bernoulli nano-beams with 3D-varying properties based on consistent couple-stress theory vol.26, pp.6, 2015, https://doi.org/10.12989/scs.2018.26.6.663
  152. 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
  153. Improved HSDT accounting for effect of thickness stretching in advanced composite plates vol.66, pp.1, 2015, https://doi.org/10.12989/sem.2018.66.1.061
  154. 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
  155. Three dimensional dynamic response of functionally graded nanoplates under a moving load vol.66, pp.2, 2015, https://doi.org/10.12989/sem.2018.66.2.249
  156. A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory vol.21, pp.4, 2015, https://doi.org/10.12989/sss.2018.21.4.397
  157. Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates vol.14, pp.6, 2015, https://doi.org/10.12989/gae.2018.14.6.519
  158. 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
  159. 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
  160. Free vibration of FGM plates with porosity by a shear deformation theory with four variables vol.66, pp.3, 2015, https://doi.org/10.12989/sem.2018.66.3.353
  161. Free vibration and buckling analysis of orthotropic plates using a new two variable refined plate theory vol.15, pp.1, 2015, https://doi.org/10.12989/gae.2018.15.1.711
  162. 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
  163. 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
  164. 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
  165. 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
  166. 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
  167. A new nonlocal HSDT for analysis of stability of single layer graphene sheet vol.6, pp.2, 2015, https://doi.org/10.12989/anr.2018.6.2.147
  168. 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
  169. 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
  170. 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
  171. 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
  172. 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
  173. 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
  174. 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
  175. 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
  176. Analysis of boundary conditions effects on vibration of nanobeam in a polymeric matrix vol.67, pp.5, 2015, https://doi.org/10.12989/sem.2018.67.5.517
  177. 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
  178. 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
  179. 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
  180. 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
  181. 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
  182. 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
  183. 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
  184. 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
  185. 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
  186. 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
  187. Critical buckling loads of carbon nanotube embedded in Kerr's medium vol.6, pp.4, 2015, https://doi.org/10.12989/anr.2018.6.4.339
  188. A novel hyperbolic shear deformation theory for the mechanical buckling analysis of advanced composite plates resting on elastic foundations vol.30, pp.1, 2015, https://doi.org/10.12989/scs.2019.30.1.013
  189. 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
  190. Nonlinear vibration of functionally graded nano-tubes using nonlocal strain gradient theory and a two-steps perturbation method vol.69, pp.2, 2015, https://doi.org/10.12989/sem.2019.69.2.205
  191. 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
  192. 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
  193. Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections vol.17, pp.2, 2019, https://doi.org/10.12989/gae.2019.17.2.175
  194. 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
  195. 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
  196. 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, 2015, https://doi.org/10.12989/sss.2019.23.2.141
  197. 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
  198. 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
  199. Free vibration of an annular sandwich plate with CNTRC facesheets and FG porous cores using Ritz method vol.7, pp.2, 2015, https://doi.org/10.12989/anr.2019.7.2.109
  200. Vibration analysis of different material distributions of functionally graded microbeam vol.69, pp.6, 2015, https://doi.org/10.12989/sem.2019.69.6.637
  201. Nonlocal strain gradient model for thermal stability of FG nanoplates integrated with piezoelectric layers vol.23, pp.3, 2015, https://doi.org/10.12989/sss.2019.23.3.215
  202. Postbuckling of Curved Carbon Nanotubes Using Energy Equivalent Model vol.57, pp.None, 2015, https://doi.org/10.4028/www.scientific.net/jnanor.57.136
  203. Participation Factor and Vibration of Carbon Nanotube with Vacancies vol.57, pp.None, 2015, https://doi.org/10.4028/www.scientific.net/jnanor.57.158
  204. 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
  205. 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
  206. 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
  207. 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
  208. Influence of shear preload on wave propagation in small-scale plates with nanofibers vol.70, pp.4, 2015, https://doi.org/10.12989/sem.2019.70.4.407
  209. 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
  210. 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
  211. Nonlocal strain gradient thermal vibration analysis of double-coupled metal foam plate system with uniform and non-uniform porosities vol.8, pp.3, 2015, https://doi.org/10.12989/csm.2019.8.3.247
  212. Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities vol.6, pp.2, 2015, https://doi.org/10.12989/smm.2019.6.2.147
  213. h-p finite element vibration analysis of side cracked rectangular nano-plates based on nonlocal elasticity theory vol.134, pp.7, 2015, https://doi.org/10.1140/epjp/i2019-12724-9
  214. Vibration characteristics of zigzag and chiral functionally graded material rotating carbon nanotubes sandwich with ring supports vol.233, pp.16, 2015, https://doi.org/10.1177/0954406219855095
  215. Investigating Instability Regions of Harmonically Loaded Refined Shear Deformable Inhomogeneous Nanoplates vol.43, pp.3, 2015, https://doi.org/10.1007/s40997-018-0215-4
  216. 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
  217. Buckling analysis of porous FGM sandwich nanoplates due to heat conduction via nonlocal strain gradient theory vol.1, pp.1, 2015, https://doi.org/10.1088/2631-8695/ab38f9
  218. 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
  219. Nonlinear forced vibrations of sandwich smart nanobeams with two-phase piezo-magnetic face sheets vol.134, pp.10, 2019, https://doi.org/10.1140/epjp/i2019-12806-8
  220. Effect of nonlocal parameter on nonlocal thermoelastic solid due to inclined load vol.33, pp.1, 2015, https://doi.org/10.12989/scs.2019.33.1.123
  221. Static stability analysis of axially functionally graded tapered micro columns with different boundary conditions vol.33, pp.1, 2019, https://doi.org/10.12989/scs.2019.33.1.133
  222. Frequency response of initially deflected nanotubes conveying fluid via a nonlinear NSGT model vol.72, pp.1, 2015, https://doi.org/10.12989/sem.2019.72.1.071
  223. 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
  224. On axial buckling and post-buckling of geometrically imperfect single-layer graphene sheets vol.33, pp.2, 2015, https://doi.org/10.12989/scs.2019.33.2.261
  225. A Non-Linear Spring Model for Predicting Modal Behavior of Oscillators Built from Double Walled Carbon Nanotubes vol.60, pp.None, 2015, https://doi.org/10.4028/www.scientific.net/jnanor.60.21
  226. Effect of nano glass cenosphere filler on hybrid composite eigenfrequency responses - An FEM approach and experimental verification vol.7, pp.6, 2015, https://doi.org/10.12989/anr.2019.7.6.419
  227. 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
  228. Dynamic modeling of a multi-scale sandwich composite panel containing flexible core and MR smart layer vol.134, pp.12, 2015, https://doi.org/10.1140/epjp/i2019-12662-6
  229. Free Vibration Analysis of Simply Supported P-FGM Nanoplate Using a Nonlocal Four Variables Shear Deformation Plate Theory vol.69, pp.4, 2015, https://doi.org/10.2478/scjme-2019-0039
  230. 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
  231. Effect of grading pattern and porosity on the eigen characteristics of porous functionally graded structure vol.33, pp.6, 2015, https://doi.org/10.12989/scs.2019.33.6.865
  232. 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
  233. Transfer matrix formulations and single variable shear deformation theory for crack detection in beam-like structures vol.73, pp.2, 2020, https://doi.org/10.12989/sem.2020.73.2.109
  234. Hygrothermal postbuckling analysis of smart multiscale piezoelectric composite shells vol.135, pp.2, 2015, https://doi.org/10.1140/epjp/s13360-020-00137-w
  235. 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
  236. Three dimensional free vibration analysis of functionally graded nano cylindrical shell considering thickness stretching effect vol.34, pp.5, 2020, https://doi.org/10.12989/scs.2020.34.5.657
  237. Mechanical-hygro-thermal vibrations of functionally graded porous plates with nonlocal and strain gradient effects vol.7, pp.2, 2015, https://doi.org/10.12989/aas.2020.7.2.169
  238. A review of effects of partial dynamic loading on dynamic response of nonlocal functionally graded material beams vol.9, pp.1, 2015, https://doi.org/10.12989/amr.2020.9.1.033
  239. A numerical method for dynamic characteristics of nonlocal porous metal-ceramic plates under periodic dynamic loads vol.7, pp.1, 2020, https://doi.org/10.12989/smm.2020.7.1.027
  240. Critical Buckling Load of Triple-Walled Carbon Nanotube Based on Nonlocal Elasticity Theory vol.62, pp.None, 2020, https://doi.org/10.4028/www.scientific.net/jnanor.62.108
  241. Bending analysis of magneto-electro piezoelectric nanobeams system under hygro-thermal loading vol.8, pp.3, 2015, https://doi.org/10.12989/anr.2020.8.3.203
  242. 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
  243. 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
  244. Time harmonic interactions in non local thermoelastic solid with two temperatures vol.74, pp.3, 2015, https://doi.org/10.12989/sem.2020.74.3.341
  245. Vibration analysis of nonlocal strain gradient porous FG composite plates coupled by visco-elastic foundation based on DQM vol.9, pp.3, 2020, https://doi.org/10.12989/csm.2020.9.3.201
  246. 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
  247. Thermal vibration analysis of embedded graphene oxide powder-reinforced nanocomposite plates vol.36, pp.3, 2015, https://doi.org/10.1007/s00366-019-00737-w
  248. 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, 2015, https://doi.org/10.1080/15397734.2019.1642766
  249. Static analysis of multiple graphene sheet systems in cylindrical bending and resting on an elastic medium vol.75, pp.1, 2015, https://doi.org/10.12989/sem.2020.75.1.109
  250. Nonlocal vibration analysis of the three-layered FG nanoplates subjected to applied electric potential considering thickness stretching effect vol.234, pp.9, 2015, https://doi.org/10.1177/1464420720928378
  251. Wave dispersion characteristics of fluid-conveying magneto-electro-elastic nanotubes vol.36, pp.4, 2015, https://doi.org/10.1007/s00366-019-00790-5
  252. Thermomechanical interactions in a non local thermoelastic model with two temperature and memory dependent derivatives vol.9, pp.5, 2020, https://doi.org/10.12989/csm.2020.9.5.397
  253. 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
  254. Size dependent vibration of embedded functionally graded nanoplate in hygrothermal environment by Rayleigh-Ritz method vol.10, pp.1, 2015, https://doi.org/10.12989/anr.2021.10.1.025
  255. Buckling treatment of piezoelectric functionally graded graphene platelets micro plates vol.38, pp.3, 2021, https://doi.org/10.12989/scs.2021.38.3.337
  256. State of the art in functionally graded materials vol.262, pp.None, 2015, https://doi.org/10.1016/j.compstruct.2021.113596
  257. Wave dispersion of nanobeams incorporating stretching effect vol.31, pp.4, 2015, https://doi.org/10.1080/17455030.2019.1607623
  258. Size-dependent vibration response of porous graded nanostructure with FEM and nonlocal continuum model vol.11, pp.1, 2021, https://doi.org/10.12989/anr.2021.11.1.001
  259. On vibration of functionally graded sandwich nanoplates in the thermal environment vol.23, pp.6, 2015, https://doi.org/10.1177/1099636220909790