Free vibration analysis of homogeneous and FGM skew plates resting on variable Winkler-Pasternak elastic foundation

In this research study, free vibration of homogeneous and functionally graded skew plates resting on Winkler-Pasternak elastic foundation is investigated. The elastic foundation is assumed to be a combination of Winkler and Pasternak elastic support with linearly or parabolically variable stiffness coefficients along the directions. Plate skewness is obtained by using a transformation from Cartesian coordinate to oblique coordinate system. The energy of the functionally graded skew plate and the elastic foundation is derived, and the natural frequency of the plate is calculated by the Rayleigh-Ritz method. The results are compared with available results in the literature, showing an excellent agreement. Furthermore, a parametric study is carried out to thoroughly investigate the effects of different boundary conditions, skew angles, inhomogeneity factors, and variable elastic foundation stiffness on the free vibration of skew plates