[4D7] Free vibration analysis of FGM plates and shallow shells by the R-functions method
A Zippo¹, T Shmatko², F Pellicano¹ and L Kurpa²
¹University of Modena and Reggio Emilia, Italy
²National Technical University, Ukraine
Research on the free vibration of porous functionally graded material (FGM) plates with complex shape is carried out. It is supposed that the thickness of the plate changes in the direction of one of the axes. Two types of porosity distributions through the thickness are considered: even and uneven. Elastic foundation is two parameters (Winkler and Pasternak). To obtain the mathematical model of the given problem the first-order shear deformation theory (FSDT) of the plate is used. The effective material properties in the thickness direction are modelled by the power law. Variational Ritz’s method joined with the R-functions theory is used as the solution for 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. A demonstration of the efficiency of the proposed approach is fulfilled for FGM plates with complex shape and various boundary conditions. The effect of the different parameters on vibration characteristics such as porosity, volume exponent, elastic foundation, types of FGM and boundary conditions is studied.
