2017 # Influence of Winkler-Pasternak Foundation on the Vibrational Behavior of Plates and Shells Reinforced by Agglomerated Carbon Nanotubes

**Abstract:** This paper aims to investigate the effect of the Winkler-Pasternak elastic foundation on the natural frequencies of Carbon Nanotube (CNT)-reinforced laminated composite plates and shells. The micromechanics of reinforcing CNT particles are described by a two-parameter agglomeration model. CNTs are gradually distributed along the thickness direction according to various functionally graded laws. Elastic foundations are modeled according to the Winkler-Pasternak theory. The theoretical model considers several Hi…

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“…Properties of the FGM media are obtained according to the simple rule of mixtures, same as Equation . Here $T={T}_{0}+\mathrm{\Delta}T$, and $\mathrm{\Delta}T$ is the temperature rise from reference temperature T 0 at room temperature (300K).…”

confidence: 99%

“…Properties of the FGM media are obtained according to the simple rule of mixtures, same as Equation . Here $T={T}_{0}+\mathrm{\Delta}T$, and $\mathrm{\Delta}T$ is the temperature rise from reference temperature T 0 at room temperature (300K).…”

confidence: 99%

“…In this study, except for Poisson's ratio which is assumed to be constant, the other temperature-dependent functionally graded material properties are assumed to be nonlinear functions of temperature and may be expressed by the following function [35,36] ( ) = 0 ( . [37][38][39][40][41][42][43][44][45][46][47][48][49][50] Here = 0 + Δ , and Δ is the temperature rise from reference temperature 0 at room temperature (300K). Also, ( = 0, ±1, 2, 3) are temperature-dependent coefficients of the FG material properties given by Table. 1.…”

confidence: 99%

“…The governing differential equations of the bending problem of simply supported shallow spherical shells on Winkler foundation [9,[11][12][13][14][15][16] can be expressed as follows:…”

confidence: 99%

“…Tornabene et al implemented GDQM incorporated with different types of shear deformation theories to analyze the static and vibration behaviors of nanocomposite shells and plates reinforced by agglomerated CNTs. Banić et al utilized Carrera unified formulation, HSDT and GDQM to investigate the effect of Winkler‐Pasternak elastic foundation on the fundamental frequency of FG‐CNTRC plates and shells. Using a multiscale approach, the free vibration behavior of laminated three‐phase nanocomposite shells and plates reinforced with agglomeration of CNTs and fibers were presented by Tornabene et al .…”

confidence: 99%