On the free vibration response of rectangular plates, partially supported on elastic foundation

Rectangular plates on distributed elastic foundations are widely employed in footings and raft foundations of variety of structures. In particular, mounted columns and single footings may partially occupy the rectangular plate of any kind.This study deals with free vibration problem of thin rectangular plates on Winkler and Pasternak elastic foundation model which is distributed over a particular arbitrary area of the plate. Closed form solutions are developed through solving the governing differential equations of plates. Moreover, a novel mathematical approach is proposed to find the exact analytical solution of free vibration of plates with mixed or fully-clamped boundary conditions. Results are discussed in detail thorough parametric and verification studies. It was concluded that proposed mathematical method can successfully obtain the exact solution to free vibration problems of plates on partial elastic foundations with clamped and/or simply-supported boundary conditions.