Dynamic analysis of functional gradient porous sigmoidal sandwich plates

Analysis of free vibrations of functionally graded (FG) porous sigmoid sandwich plates, is considered in this paper. The plate can have a complex geometric shape and various types of fastening. To solve the problem, we used the variational-structural method (RFM), which combines the theory of R-functions and variational method of Rayleigh-Ritz. The mathematical statement of the problem is carried out within the framework of the deformation theory of plates of the first order (FSDT). Plates are considered, the outer layers of which are made of functionally graded materials (FGM), and the core is isotropic. For different models of porosity distribution (sigmoid uniform and nonuniform), analytical expressions were obtained to calculate the effective properties of FGM. For rectangular plates, a comparison of the obtained results with known results obtained using other approaches is shown. Calculations for plates with a complex shape are presented in the form of tables and graphs. The influence of the volume fraction of ceramics, the different types Of FGM  and the coefficient of porosity on the natural frequencies of the plate is analyzed.