the r-functions theory

Investigation of free vibration of porous power and sigmoid-law sandwich functionally graded (FG) plates with different boundary conditions is presented in this paper. The FG sandwich plate includes three layers. The face layers are fabricated of functionally graded material (FGM) and middle layer (core) is isotropic (ceramic). Imperfect sigmoid FG sandwich plates with even and linear-uneven porosities and nonporous core layer are studied. Developed approach has been realized in the framework of a refined theory of the first-order shear deformation theory (FSDT) using variational methods and the R-functions theory. The analytical expressions are obtained for calculating the elastic characteristics with the assumption that the values of Poisson's ratio are the same for constituent FGM materials. For rectangular plates, the obtained results are compared with known results and a good agreement is obtained. Vibration analysis of a complex-shaped porous sandwich plate made of FGM has been performed. The effect of various parameters on the dynamic behavior of the plate, such as the type and values of porosity coefficients, power index, lay-up scheme, types of FGM, has been studied.