Free Vibrations of Three-Parameter Functionally Graded Plates Resting on Pasternak Foundations

Abstract

In this research work, first, based on the three-dimensional elasticity theory and by means of the Generalized Differential Quadrature Method (GDQM), free vibration characteristics of functionally graded (FG) rectangular plates resting on Pasternak foundation are focused. The two-constituent functionally graded plate consists of ceramic and metal grading through the thickness. A three-parameter power-law distribution is considered for the ceramic volume fraction. The benefit of using a three-parameter power-law distribution is to illustrate and present useful results arising from symmetric, asymmetric and classic profiles. A detailed parametric study is carried out to highlight the influences of different profiles of fiber volume fraction, three parameters of power-law distribution and two-parameter elastic foundation modulus on the vibration characteristics of the FG plates. The main goal of the structural optimization is to minimize the weight of structures while satisfying all design requirements imposed. Thus, for the second aim of this paper, volume fraction optimization of FG plates with objective of minimizing the density to achieve a specified fundamental frequency is presented. The primary optimization variables are the three parameters of the volume fraction of ceramic. Since the optimization processes is complicated and too much time consuming, a novel meta–heuristic called Imperialist Competitive Algorithm (ICA) which is a socio-politically motivated global search strategy and Artificial Neural Networks (ANNs) are applied to obtain the best material profile through the thickness. The performance of ICA is evaluated in comparison with other nature inspired technique Genetic Algorithm (GA). Comparison shows the success of combination of ANN and ICA for design of material profile of FG plates. Finally the optimized material profile for the considered optimization problem is presented.