A high-order gradient model for wave propagation analysis of porous FG nanoplates

Davood Shahsavari , Behrouz Karami , Li Li

Abstract

A high-order nonlocal strain gradient model is developed for wave propagation analysis of porous FG nanoplates resting on a gradient hybrid foundation in thermal environment, for the first time. Material properties are assumed to be temperature-dependent and graded in the nanoplate thickness direction. To consider the thermal effects, uniform, linear, nonlinear, exponential, and sinusoidal temperature distributions are considered for temperature-dependent FG material properties. On the basis of the refined-higher order shear deformation plate theory (R-HSDT) in conjunction with the bi-Helmholtz nonlocal strain gradient theory (B-H NSGT), Hamilton's principle is used to derive the equations of wave motion. Then the dispersion relation between frequency and wave number is solved analytically. The influences of various parameters (such as temperature rise, volume fraction index, porosity volume fraction, lower and higher order nonlocal parameters, material characteristic parameter, foundations components, and wave number) on the wave propagation behaviors of porous FG nanoplates are investigated in detail.

Key Words

nanoporous materials; wave propagation; bi-Helmholtz nonlocal strain gradient theory; higher-order shear deformation plate theory; thermal loadings

Address

(1) Davood Shahsavari, Behrouz Karami — Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
(2) Li Li — State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China.

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