Nonlinear Free Vibrations of Functionally Graded Porous Sandwich Plates with Complex Shape

Linear and geometrically nonlinear vibrations of porous FGM sandwich plates of different shape and boundary conditions are studied. Face layers are composed of FGM (mixture of metal and ceramics), and the isotropic core is made of ceramics. A mathematical model accounting for the first-order shear deformation theory (FSDT) is employed. A power-law model is embraced to determine effective material properties of the structure taking into account thickness-wise even and uneven porosity distributions. The R-functions theory combined with variational Ritz’s method is used to study free nonlinear vibrations of these porous sandwich plates. The proposed methodology transforms the initial nonlinear equations of motion in PDE form into a nonlinear system of ODEs. The frequencies of porous FGM sandwich plates of complex shape with a hole are determined. The effects of volume fraction, porosity models, type of FGM, and boundary conditions on the linear and nonlinear frequencies are investigated.