Summary
This study investigates linear and geometrically nonlinear vibrations of the sandwich plate with auxetic honeycomb core and functionally graded material (FGM) face sheets. The first order shear deformation theory (FSDT) is applied to construct mathematical model. The R-functions theory, variational Ritz method, procedure by Bubnov-Galerkin and Runge-Kutta method are used to solve the given problem for plates with a complex form and different boundary conditions. The effective material properties of the FGM plates made of mixture metal and ceramics are determined by Voight power law. The reliability and accuracy of the proposed method have been validated via comparisons of the present results with known ones for the case of simply supported rectangular plates. Solution structures are constructed for the plates with mixed boundary conditions. The effect of geometric parameters of auxetic material, volume fraction index of FGMs, the thickness ratio of layers, the parameters of the elastic foundation on linear and nonlinear frequencies was investigated for plates with the mixed boundary conditions.
