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Free vibration analysis of porous functionally graded piezoelectric microplates resting on an elastic medium subjected to electric voltages

Wu C.-P., Lin E.-L.

Archives of Mechanics

2022

Vol. 74, nr 6

463--511

Basing on the consistent couple stress theory (CCST), we develop a unified size-dependent shear deformation theory to analyze the free vibration characteristics of simply supported, porous functionally graded (FG) piezoelectric microplates which resting on the Winkler-Pasternak foundation are subjected to electric voltages. Various CCST-based shear deformation theories can be reproduced by incorporating their corresponding shape functions, which characterize the through-thickness distributions of the shear deformations, into the unified size-dependent theory. The reproduced CCST-based plate theories include the classical plate theory (CPT), the first-order shear deformation plate theory (SDPT), Reddy’s refined SDPT, the sinusoidal SDPT, the exponential SDPT, and the hyperbolic SDPT. The unified size-dependent theory is subsequently used to determine the natural frequencies of simply supported, porous FG piezoelectric microplates and their corresponding vibration mode shapes. The effects of the material length scale parameter, the length-to-thickness ratio, the material-property gradient index, different values of the applied voltages, the porosity parameter, different porosity distribution patterns, the Winkler spring coefficient, and the shear modulus of the surrounding medium on the natural frequencies of the porous FG piezoelectric microplates are examined and appear to be significant.

Static behaviour of functionally graded plates resting on elastic foundations using neutral surface concept

Van-Loi Nguyen, Minh-Tu Tran, Van-Long Nguyen, Quang-Huy Le

Archive of Mechanical Engineering

2021

LXVIII, nr 1

5--22

In this study, static behaviors of functionally graded plates resting on Winkler-Pasternak elastic foundation using the four-variable refined theory and the physical neutral surface concept is reported. The four-variable refined theory assumes that the transverse shear strain has a parabolic distribution across the plate’s thickness, thus, there is no need to use the shear correction factor. The material properties of the plate vary continuously and smoothly according to the thickness direction by a power-law distribution. The geometrical middle surface of the functionally graded plate selected in computations is very popular in the existing literature. By contrast, in this study, the physical neutral surface of the plate is used. Based on the four-variable refined plate theory and the principle of virtual work, the governing equations of the plate are derived. Next, an analytical solution for the functionally graded plate resting on the Winkler-Pasternak elastic foundation is solved using the Navier’s procedure. In numerical investigations, a comparison of the static behaviors of the functionally graded plate between several models of displacement field using the physical neutral surface is given, and parametric studies are also presented.