Nonlinear dynamic analysis of a sandwich plate with S-FGM face sheets and homogeneous core subjected to harmonic excitation

Abstract

In the present paper, for a sandwich plate with homogeneous core, the nonlinear dynamic response is analyzed in which material properties of functionally graded facesheets are varied in accordance with sigmoid law. The sandwich plate of various configurations is presumed to be built on Pasternak foundation and subjected to harmonic load. Equilibrium and compatibility equations are derived by taking into consideration the geometrical non-linearity in von Karman sense. The Airy’s stress function and Galerkin method are used to solve geometric nonlinearity and implement the different edge conditions, respectively, for sandwich sigmoid function plate. A few numerical examples validate the accuracy of the present formulation with the results of available theory for different geometric parameters, elastic foundation, and plate configuration. A convergence study is performed to determine the number of terms in order to converge the solution, and it is deduced that considering the first four terms provides sufficient accuracy with average error less than 0.22% which is acceptable for any computation. The present paper is the first proposal to analyze the nonlinear dynamic characteristics of sandwich sigmoid function plate with homogeneous core and functionally graded material face sheets in ambient conditions. This article is also new in its assessment of the plate behavior in terms of predicting the periodicity such as periodic, quasi-periodic, chaotic, etc. and analyzing the frequency-amplitude relation. The aforementioned prediction aids researchers in active control of plates and shells under dynamic loading. It is found that core thickness in the sandwich plate reduces the effect of the nonlinearity. Also, the plate configurations 1-0-1 and 1-8-1 show the sensitive features in the dynamic response with varying aspect factors and span-to-thickness ratios.