A novel numerical approach for the modelling of the square shaped silicon membrane

Abstract

In this paper, we are interested in solving the Lagrange partial differential equation of the fourth order, which governs the deformation of a thin silicon square membrane, perfectly embedded and subjected to a uniform static pressure in the case of the weak disturbances. The proposed approach that consists of using the Galerkin method with trigonometrical basis functions is simple, easy to implement and ensures a good stability of the algorithm and a satisfactory accuracy.