Vibration of sandwich plates considering elastic foundation, temperature change and FGM faces

Behzad Mohammadzadeh , Eunsoo Choi , Dongkyun Kim

Abstract

This study presents a comprehensive nonlinear dynamic approach to investigate the linear and nonlinear vibration of sandwich plates fabricated from functionally graded materials (FGMs) resting on an elastic foundation. Higher-order shear deformation theory and Hamilton's principle are employed to obtain governing equations. The Runge–Kutta method is employed together with the commercially available mathematical software MAPLE 14 to solve the set of nonlinear dynamic governing equations. Method validity is evaluated by comparing the results of this study and those of previous research. Good agreement is achieved. The effects of temperature change on frequencies are investigated considering various temperatures and various volume fraction index values, N. As the temperature increased, the plate frequency decreased, whereas with increasing N, the plate frequency increased. The effects of the side-to-thickness ratio, c/h, on natural frequencies were investigated. With increasing c/h, the frequencies increased nonlinearly. The effects of foundation stiffness on nonlinear vibration of the sandwich plate were also studied. Backbone curves presenting the variation of maximum displacement with respect to plate frequency are presented to provide insight into the nonlinear vibration and dynamic behavior of FGM sandwich plates.

Key Words

nonlinear vibration; dynamics; sandwich plate; functionally graded materials; frequency analysis; higher order shear deformation theory; Runge-Kutta method

Address

Behzad Mohammadzadeh — 1Department of Landscape Architecture and Rural System Engineering, Seoul National University, Seoul, 08826, South Korea 2Research Institute of Agriculture and Life Sciences, Seoul National University, Seoul 08826, Korea
Eunsoo Choi and Dongkyun Kim — Department of Civil Engineering, Hongik University, Seoul 04066, Republic of Korea

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