An asymptotic consistent couple stress theory for the three‐dimensional free vibration analysis of functionally graded microplates resting on an elastic medium

Abstract

Based on the three-dimensional (3D) consistent couple stress theory (CCST), we develop an asymptotic theory for the free vibration analysis of functionally graded (FG) microplates resting on an elastic medium. The material properties of the FG microplate are assumed to obey a power-law distribution of the volume fractions of the constituents in the thickness direction, for which the effective material properties are estimated using the rule of mixtures. The interactions between the FG microplate and its foundation medium are simulated using a Winkler-Pasternak foundation. Carrying out the asymptotic expansion method, we obtain recursive sets of motion equations for various order problems. The CCST-based classical plate theory is derived as a firstorder approximation of the 3D CCST. The asymptotic theory is shown to converge rapidly and to be in excellent agreement with the exact solutions for FG macroplates reported in the literature when the value of the material length scale parameter is assigned to be zero.

A Hermitian Cn finite cylindrical layer method for 3D size‐dependent buckling and free vibration analyses of simply supported FG piezoelectric cylindrical sandwich microshells subjected to axial compression and electric voltages

“…For example, Wu and Hu [39] developed a unified size‐dependent SDT and applied it to analyze the static bending and free vibration behaviors of FG elastic microplates. In another study, Wu and Lin [40] developed a unified size‐dependent SDT to explore the free vibration behavior of porous FG piezoelectric microplates. A general function in the unified kinematic model suited to characterizing the through‐thickness distribution of the shear deformations was introduced into the formulations of both unified size‐dependent SDTs.…”

Analysis of wave propagation in multi‐physical environments for double‐layer auxetic FGP sandwich plates resting on Kerr elastic foundation

“…Mitra and his team [21] provided computational and experimental evaluations of guided wave propagation through a tapered HCSS, with the main objective of understanding and further exploiting the modification of local wave characteristics as a result of the shifting thickness. Case studies can be found in the following documents [22][23][24][25][26][27][28][29][30][31][32].…”