Vibration analysis of layered film bulk acoustic resonators

Based on Mindlin elastic plate theory, the displacements in layered film bulk acoustic resonators (FBAR) are expanded in power series along the thickness direction. The strain and stress components are obtained with the basic equations of elasticity theory. The variational equations of motion are then derived by Hamilton principle. Next, for the rectangular plate with finite size, the displacements are assumed in the form of trigonometric function. Thus, the vibration equation for layered FBAR can be deduced from the variational equations of motion, through which we are able to analyze the vibration frequency and the dispersion relations.