Free vibration analysis of FGM plates and shallow shells by the R-functions method

Abstract

Research of free vibration of porous functionally graded material (FGM) plates with complex shape is carried out. It is supposed that thickness of the plate changes in direction of one of the axes. Two types of porosity distributions through the thickness even and uneven are considered. Elastic foundation is two parameters (Winkler and Pasternak). To obtain the mathematical model of the given problem the first order shear deformation theory of the plate (FSDT) is used. The effective material properties in the thickness direction is modelled by the power law. Variational Ritz’s method joined with the R-functions theory is used for solution of the formulated problem. The developed approach is tested on a lot of problems. Comparative analysis of the obtained results for rectangular plates confirms their verification. Demonstration of the efficiency of the proposed approach is fulfilled for FGM plate with complex shape and various boundary conditions. Effect of the different parameters on vibration characteristics such as porosity, volume exponent, elastic foundation, types of FGM, boundary conditions is studied.