Structural Engineering and Mechanics

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Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories

  • Yahia, Sihame Ait (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Atmane, Hassen Ait (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Houari, Mohammed Sid Ahmed (Advanced Materials and Structures 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 : 2014.04.30
  • Accepted : 2014.10.29
  • Published : 2015.03.25
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Abstract

In this work, various higher-order shear deformation plate theories for wave propagation in functionally graded plates are developed. Due to porosities, possibly occurring inside functionally graded materials (FGMs) during fabrication, it is therefore necessary to consider the wave propagation in plates having porosities in this study. The developed refined plate theories have fewer number of unknowns and equations of motion than the first-order shear deformation theory, but accounts for the transverse shear deformation effects without requiring shear correction factors. The rule of mixture is modified to describe and approximate material properties of the functionally graded plates with porosity phases. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton's principle. The analytic dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions and porosity volume fraction on wave propagation of functionally graded plate are discussed in detail. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.

Keywords

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  197. Free vibration analysis of a piezoelectric curved sandwich nano-beam with FG-CNTRCs face-sheets based on various high-order shear deformation and nonlocal elasticity theories vol.133, pp.5, 2018, https://doi.org/10.1140/epjp/i2018-12015-1
  198. Smart electrical and magnetic stability analysis of exponentially graded shear deformable three-layered nanoplate based on nonlocal piezo-magneto-elasticity theory pp.1530-7972, 2018, https://doi.org/10.1177/1099636218760667
  199. Thermal and Small-Scale Effects on Vibration of Embedded Armchair Single-Walled Carbon Nanotubes vol.51, pp.1661-9897, 2018, https://doi.org/10.4028/www.scientific.net/JNanoR.51.24
  200. Effect of rotation on Rayleigh waves in a fiber-reinforced solid anisotropic magneto-thermo-viscoelastic media pp.1537-6532, 2018, https://doi.org/10.1080/15376494.2018.1445322
  201. Wave dispersion characteristics of embedded graphene platelets-reinforced composite microplates vol.133, pp.4, 2018, https://doi.org/10.1140/epjp/i2018-11956-5
  202. 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
  203. Accumulative Bayesian detection of displacement constants of a hybrid indeterminate box girder with variable scale gradient theory vol.11, pp.2, 2019, https://doi.org/10.1177/1687814018824164
  204. An analytical approach for buckling of functionally graded plates vol.5, pp.3, 2015, https://doi.org/10.12989/amr.2016.5.3.141
  205. A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates vol.22, pp.5, 2015, https://doi.org/10.12989/scs.2016.22.5.975
  206. Dynamic instability analysis for S-FGM plates embedded in Pasternak elastic medium using the modified couple stress theory vol.22, pp.6, 2015, https://doi.org/10.12989/scs.2016.22.6.1239
  207. Hygrothermal effects on buckling of composite shell-experimental and FEM results vol.22, pp.6, 2016, https://doi.org/10.12989/scs.2016.22.6.1445
  208. A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation vol.12, pp.1, 2015, https://doi.org/10.12989/gae.2017.12.1.009
  209. 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
  210. 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
  211. 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
  212. 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
  213. 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
  214. 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
  215. Wave propagation in functionally graded beams using various higher-order shear deformation beams theories vol.62, pp.2, 2015, https://doi.org/10.12989/sem.2017.62.2.143
  216. 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
  217. Bending analysis of functionally graded plates using new eight-unknown higher order shear deformation theory vol.62, pp.3, 2017, https://doi.org/10.12989/sem.2017.62.3.311
  218. 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
  219. Displacement Analytical Solution of a Circular Hole in Layered Composite Materials considering Shear Stress Effect vol.26, pp.3, 2015, https://doi.org/10.1177/096369351702600303
  220. 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
  221. 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
  222. 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
  223. 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
  224. 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
  225. 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
  226. Rotating effects on hygro-mechanical vibration analysis of FG beams based on Euler-Bernoulli beam theory vol.63, pp.4, 2015, https://doi.org/10.12989/sem.2017.63.4.471
  227. 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
  228. 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
  229. 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
  230. 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
  231. 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
  232. Vibro-acoustic analysis of un-baffled curved composite panels with experimental validation vol.64, pp.1, 2015, https://doi.org/10.12989/sem.2017.64.1.093
  233. Dynamic characteristics of curved inhomogeneous nonlocal porous beams in thermal environment vol.64, pp.1, 2015, https://doi.org/10.12989/sem.2017.64.1.121
  234. 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
  235. 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
  236. An analytical solution for bending and vibration responses of functionally graded beams with porosities vol.25, pp.4, 2015, https://doi.org/10.12989/was.2017.25.4.329
  237. 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
  238. 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
  239. 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
  240. 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
  241. 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
  242. Investigating vibration behavior of smart imperfect functionally graded beam subjected to magnetic-electric fields based on refined shear deformation theory vol.5, pp.4, 2017, https://doi.org/10.12989/anr.2017.5.4.281
  243. 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
  244. Nonlocal strain gradient-based vibration analysis of embedded curved porous piezoelectric nano-beams in thermal environment vol.20, pp.6, 2015, https://doi.org/10.12989/sss.2017.20.6.709
  245. 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
  246. 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
  247. 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
  248. 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
  249. A high-order gradient model for wave propagation analysis of porous FG nanoplates vol.29, pp.1, 2018, https://doi.org/10.12989/scs.2018.29.1.053
  250. 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
  251. Vibration characteristics of advanced nanoplates in humid-thermal environment incorporating surface elasticity effects via differential quadrature method vol.68, pp.1, 2015, https://doi.org/10.12989/sem.2018.68.1.131
  252. Earthquake induced dynamic deflection of submerged viscoelastic cylindrical shell reinforced by agglomerated CNTs considering thermal and moisture effects vol.187, pp.None, 2018, https://doi.org/10.1016/j.compstruct.2017.12.004
  253. 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
  254. Forced vibration analysis of cracked functionally graded microbeams vol.6, pp.1, 2015, https://doi.org/10.12989/anr.2018.6.1.039
  255. 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
  256. Development of super convergent Euler finite elements for the analysis of sandwich beams with soft core vol.65, pp.6, 2015, https://doi.org/10.12989/sem.2018.65.6.657
  257. 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
  258. Geometrically nonlinear analysis of a laminated composite beam vol.66, pp.1, 2015, https://doi.org/10.12989/sem.2018.66.1.027
  259. 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
  260. 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
  261. 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
  262. 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
  263. 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
  264. 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
  265. 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
  266. 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
  267. 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
  268. 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
  269. Large deflection analysis of a fiber reinforced composite beam vol.27, pp.5, 2015, https://doi.org/10.12989/scs.2018.27.5.567
  270. 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
  271. 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
  272. Thermal buckling of FGM beams having parabolic thickness variation and temperature dependent materials vol.27, pp.6, 2015, https://doi.org/10.12989/scs.2018.27.6.777
  273. 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
  274. 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
  275. Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter vol.28, pp.1, 2015, https://doi.org/10.12989/scs.2018.28.1.013
  276. 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
  277. The critical buckling load of reinforced nanocomposite porous plates vol.67, pp.2, 2015, https://doi.org/10.12989/sem.2018.67.2.115
  278. Geometrically nonlinear analysis of functionally graded porous beams vol.27, pp.1, 2015, https://doi.org/10.12989/was.2018.27.1.059
  279. 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
  280. 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
  281. 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
  282. 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
  283. 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
  284. Nonlinear Performance of Concrete Beam Reinforced with Prestressed Hybrid Cfrp/Gfrp Composite Sheet vol.27, pp.5, 2015, https://doi.org/10.1177/096369351802700505
  285. 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
  286. 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
  287. 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
  288. Thermal buckling of smart porous functionally graded nanobeam rested on Kerr foundation vol.29, pp.3, 2015, https://doi.org/10.12989/scs.2018.29.3.349
  289. 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
  290. Updated Bayes identification of displacement constants of curve indeterminate box girder with variable scale theory vol.10, pp.12, 2015, https://doi.org/10.1177/1687814018817635
  291. Wave Propagation of Porous Nanoshells vol.9, pp.1, 2019, https://doi.org/10.3390/nano9010022
  292. Three-dimensional vibration analysis of beams with axial functionally graded materials and variable thickness vol.207, pp.None, 2015, https://doi.org/10.1016/j.compstruct.2018.09.029
  293. 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
  294. 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
  295. Finite element solution of stress and flexural strength of functionally graded doubly curved sandwich shell panel vol.16, pp.1, 2015, https://doi.org/10.12989/eas.2019.16.1.055
  296. 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
  297. 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
  298. 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
  299. 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
  300. 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
  301. 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
  302. Experimental method for obtaining the elastic properties of components of a laminated composite vol.12, pp.None, 2019, https://doi.org/10.1016/j.rinp.2019.01.016
  303. Application of the nonlocal strain gradient elasticity on the wave dispersion behaviors of inhomogeneous nanosize beams vol.134, pp.3, 2015, https://doi.org/10.1140/epjp/i2019-12464-x
  304. 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
  305. 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
  306. 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
  307. 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
  308. 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
  309. Static and Dynamic Behavior of Nanotubes-Reinforced Sandwich Plates Using (FSDT) vol.57, pp.None, 2015, https://doi.org/10.4028/www.scientific.net/jnanor.57.117
  310. 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
  311. 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
  312. 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
  313. Wave propagation characteristics of the electrically GNP-reinforced nanocomposite cylindrical shell vol.41, pp.5, 2015, https://doi.org/10.1007/s40430-019-1715-x
  314. Dynamic response of metal foam FG porous cylindrical micro-shells due to moving loads with strain gradient size-dependency vol.134, pp.5, 2015, https://doi.org/10.1140/epjp/i2019-12540-3
  315. Vibration analysis of graphene oxide powder-/carbon fiber-reinforced multi-scale porous nanocomposite beams: A finite-element study vol.134, pp.5, 2015, https://doi.org/10.1140/epjp/i2019-12594-1
  316. 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
  317. Hygro-thermal effects on wave dispersion responses of magnetostrictive sandwich nanoplates vol.7, pp.3, 2015, https://doi.org/10.12989/anr.2019.7.3.157
  318. 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
  319. 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
  320. 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
  321. 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
  322. 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
  323. Forced vibration analysis of functionally graded sandwich deep beams vol.8, pp.3, 2015, https://doi.org/10.12989/csm.2019.8.3.259
  324. 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
  325. Dynamic response of functionally graded graphene nanoplatelet reinforced shells with porosity distributions under transverse dynamic loads vol.6, pp.7, 2019, https://doi.org/10.1088/2053-1591/ab1552
  326. A Numerical Evaluation of SIFs of 2-D Functionally Graded Materials by Enriched Natural Element Method vol.9, pp.17, 2015, https://doi.org/10.3390/app9173581
  327. Static analysis of functionally graded sandwich plates with porosities vol.8, pp.3, 2015, https://doi.org/10.12989/amr.2019.8.3.155
  328. 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
  329. Influence of the distribution shape of porosity on the bending FGM new plate model resting on elastic foundations vol.72, pp.1, 2015, https://doi.org/10.12989/sem.2019.72.1.061
  330. 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
  331. 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
  332. 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
  333. Effect of variable elastic foundations on static behavior of functionally graded plates using sinusoidal shear deformation vol.12, pp.24, 2019, https://doi.org/10.1007/s12517-019-4871-5
  334. 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
  335. 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
  336. 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
  337. Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle vol.8, pp.1, 2020, https://doi.org/10.12989/anr.2020.8.1.037
  338. Thermal buckling analysis of magneto-electro-elastic porous FG beam in thermal environment vol.8, pp.1, 2015, https://doi.org/10.12989/anr.2020.8.1.083
  339. 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
  340. Free vibration analysis of FG nanoplate with poriferous imperfection in hygrothermal environment vol.73, pp.2, 2020, https://doi.org/10.12989/sem.2020.73.2.191
  341. Dynamic characteristics of multi-phase crystalline porous shells with using strain gradient elasticity vol.8, pp.2, 2015, https://doi.org/10.12989/anr.2020.8.2.157
  342. 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
  343. Bending and free vibration analysis of functionally graded beams on elastic foundations with analytical validation vol.9, pp.1, 2015, https://doi.org/10.12989/amr.2020.9.1.063
  344. 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
  345. A refined HSDT for bending and dynamic analysis of FGM plates vol.74, pp.1, 2020, https://doi.org/10.12989/sem.2020.74.1.105
  346. 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
  347. 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
  348. Improved crack analysis of two-dimensional functionally graded materials by enriched natural element method vol.234, pp.10, 2015, https://doi.org/10.1177/0954406220903742
  349. A comprehensive review on the modeling of smart piezoelectric nanostructures vol.74, pp.5, 2015, https://doi.org/10.12989/sem.2020.74.5.611
  350. Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures vol.36, pp.3, 2015, https://doi.org/10.1007/s00366-019-00742-z
  351. Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models vol.36, pp.3, 2015, https://doi.org/10.12989/scs.2020.36.3.293
  352. Size-dependent free vibration and buckling analysis of sigmoid and power law functionally graded sandwich nanobeams with microstructural defects vol.234, pp.18, 2015, https://doi.org/10.1177/0954406220916481
  353. On scale-dependent stability analysis of functionally graded magneto-electro-thermo-elastic cylindrical nanoshells vol.75, pp.6, 2015, https://doi.org/10.12989/sem.2020.75.6.659
  354. Wave dispersion characteristics of fluid-conveying magneto-electro-elastic nanotubes vol.36, pp.4, 2015, https://doi.org/10.1007/s00366-019-00790-5
  355. Influence of geometric discontinuities and geometric/microstructural defects on the temperature-dependent vibration response of functionally graded plates on elastic foundation vol.42, pp.10, 2015, https://doi.org/10.1007/s40430-020-02619-5
  356. 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
  357. Static analysis of functionally graded plates with a porous middle layer based on higher order shear deformation theory with linear/quadratic transverse displacement vol.234, pp.24, 2020, https://doi.org/10.1177/0954406220928369
  358. Effect of porosity distribution rate for bending analysis of imperfect FGM plates resting on Winkler-Pasternak foundations under various boundary conditions vol.9, pp.6, 2020, https://doi.org/10.12989/csm.2020.9.6.575
  359. A compressive study for porous FG curved nanobeam under various boundary conditions via a nonlocal strain gradient theory vol.136, pp.2, 2015, https://doi.org/10.1140/epjp/s13360-021-01238-w
  360. Bending and free vibration analysis of functionally graded sandwich plates: An assessment of the Refined Zigzag Theory vol.23, pp.3, 2021, https://doi.org/10.1177/1099636219843970
  361. Dynamic response of functionally graded plates with a porous middle layer under time-dependent load vol.27, pp.3, 2021, https://doi.org/10.12989/cac.2021.27.3.269
  362. Wave propagation analysis of a rectangular sandwich composite plate with tunable magneto-rheological fluid core vol.27, pp.11, 2015, https://doi.org/10.1177/1077546320938189
  363. Wave propagation analysis of the laminated cylindrical nanoshell coupled with a piezoelectric actuator vol.49, pp.5, 2015, https://doi.org/10.1080/15397734.2019.1697932
  364. Analytic solution for transient responses of viscoelastic FG plates subjected to various asymmetrically loads vol.22, pp.4, 2021, https://doi.org/10.1080/15502287.2020.1861129
  365. Modeling of memory-dependent derivative in a functionally graded plate vol.31, pp.4, 2015, https://doi.org/10.1080/17455030.2019.1606962
  366. Wave dispersion of nanobeams incorporating stretching effect vol.31, pp.4, 2015, https://doi.org/10.1080/17455030.2019.1607623
  367. Higher-Order Free Vibration Analysis of Porous Functionally Graded Plates vol.5, pp.11, 2015, https://doi.org/10.3390/jcs5110305
  368. Wave propagation analysis of a spinning porous graphene nanoplatelet-reinforced nanoshell vol.31, pp.6, 2015, https://doi.org/10.1080/17455030.2019.1694729