Free vibration analysis of Mindlin plates partially resting on Pasternak foundation

• Natural frequencies of plates on various types of partially elastic foundations are studied.
• The governing equations, boundary conditions and solution domain are discretized based on the GDQ method.
• Different boundary conditions in particular full free edges are considered.
• The effect of geometry and shape of elastic foundation on natural frequencies is studied.
• An attempt is made to model offshore platform and study its free vibration behavior.

In this paper, the generalized differential quadrature (GDQ) method is used to study free vibration of moderately thick rectangular plate partially resting on Pasternak foundation. The foundation is considered to support the plate either completely or partially. The governing equations which consist of a system of partial differential equations (PDEs) are obtained based on the first-order shear deformation theory. Various combinations of simply supported, clamped and free boundary conditions are considered. Application of the GDQ method to the governing PDEs resulted in a system of algebraic equations. Solution of this system with accordance to the considered boundary conditions leads to an eigenvalue problem to obtain natural frequencies of the plate. Results of this study are validated with available results in the literature which reveal accuracy and fast convergence rate of the method. Effects of different parameters such as foundation stiffness, foundation geometry, boundary conditions and geometrical parameters on the natural frequencies of the plate are presented.