Abstract: The present study is concerned with the optimal design of functionally graded plates using particle swarm optimization (PSO) algorithm. In this study, meshless local Petrov-Galerkin (MLPG) method is employed to obtain the functionally graded (FG) plate’s natural frequencies. Effects of two parameters including thickness to height ratio and volume fraction index on the natural frequencies and total mass of plate are studied by using the MLPG results. Then the first natural frequency of the plate, for different conditions where MLPG data are not available, is predicted by an artificial neural network (ANN) approach which is trained by back-error propagation (BEP) technique. The ANN results show that the predicted data are in good agreement with the actual one. To maximize the first natural frequency and minimize the mass of FG plate simultaneously, the weighted sum optimization approach and PSO algorithm are used. However, the proposed optimization process of this study can provide the designers of FG plates with useful data.
Abstract: Analytical investigation of the free vibration behavior
of circular functionally graded (FG) plates integrated with two
uniformly distributed actuator layers made of piezoelectric (PZT4)
material on the top and bottom surfaces of the circular FG plate
based on the classical plate theory (CPT) is presented in this paper.
The material properties of the functionally graded substrate plate are
assumed to be graded in the thickness direction according to the
power-law distribution in terms of the volume fractions of the
constituents and the distribution of electric potential field along the
thickness direction of piezoelectric layers is simulated by a quadratic
function. The differential equations of motion are solved analytically
for clamped edge boundary condition of the plate. The detailed
mathematical derivations are presented and Numerical investigations
are performed for FG plates with two surface-bonded piezoelectric
layers. Emphasis is placed on investigating the effect of varying the
gradient index of FG plate on the free vibration characteristics of the
structure. The results are verified by those obtained from threedimensional
finite element analyses.