Finite element analysis using trigonometric interpolations for quasi-thickness piezoelectric resonators

Although it is a successful method for general purposes, FEM still remains difficult to handle when applied to the simulation of resonant modes in bulk acoustic wave resonators. Because standard elements available in commercial packages usually take low degree polynomial interpolations, many layers of such elements are required to account for the fast variations of mechanical displacement along the thickness. This results into a loss of efficiency and very large matrixes requiring much computational power. To address these problems, we propose an original analysis built upon specific volume elements which use trigonometric interpolations along the thickness, while sticking to classical parabolic interpolations along the in-plane directions of the thin plate. Piezoelectricity is introduced in the framework of a variational formalism according to a Lagrangian formulation. This will facilitate further inclusion of static temperature influence in the modal analysis