A Plate on Winkler Foundation with Variable Coecient

Plates on elastic foundations have attracted the attention of many researchers. Some elementary models have been introduced to consider interactions between the plate and its foundation. Other improved models have been proposed to develop basic models. In this work, a model based on the Winkler-foundation theory is proposed, while the constant parameter of Winkler is assumed to be variable; such as non-uniform springs with the functionality of the domain position, along with the plate and beam span in order to consider the non-uniform behavior of the foundation. The governing equation on the system is solved by using the Galerkin method and e ects such as the presence of rigid points in the foundation are considered. Keywords: Plate theory; Kirchho plate; Winkler elastic foundation; Galerkin''s method.