Free vibration and buckling characteristics of compressed non-homogeneous rectangular plates on Winkler foundation with variable stiffness

Based on the classical thin plate theory, the governing differential equation of free vibration and buckling of a compressed non-homogeneous rectangular plate on Winkler foundation with variable stiffness was established by using Hamilton's principle, and then its dimensionless form was obtained. The characteristics of the plate's dimensionless natural frequencies and buckling critical loads were studied with a semi-analytical method called the differential transformation method (DTM). DTM was used to convert dimensionless governing differential equation and boundary conditions into equivalent algebraic equations, and derive characteristic equations of frequencies and buckling loads. Then, the problem was degenerated into the case of an in-plane variable stiffness rectangular plate, and its DTM solution was compared with the analytical solution. The results showed that DTM have very higher accuracy and stronger applicability. Finally, the buckling critical loads were calculated under different boundary conditions, and the effects of foundation stiffness parameters, elastic modulus parameters, density parameter, in-plane loads and length-width ratio on the plate's dimensionless natural frequencies were analyzed. The first three modal shapes of the compressed non-homogeneous rectangular plate on Winkler foundations with variable stiffness were deduced under different boundary conditions. © 2019, Editorial Office of Journal of Vibration and Shock. All right reserved.