Summary
Linear and geometrically nonlinear vibrations of functionally graded sandwich porous shallow shells and plates are studied using the R-functions theory and methods by Ritz, Bubnov-Galerkin and Runge-Kutta. The first order shear deformation theory (FSDT) is applied to construct mathematical model. The power- and sigmoid law models are employed to determine the effective material properties of the functionally graded materials made of mixture of metal and ceramics. Effect of the boundary conditions, shape of the plan, type of constituent materials, the layup of layers and porosity on behaviour of linear and nonlinear frequencies is analysed. Analytical expressions for elements of the matrices, which determine force resultant in-plane, bending and twisting moments resultant and transverse shear force resultants are obtained. New results for plates and shallow shells with a complex shape including cut-out are reported.
