Simulation of axisymmetric piezoelectric devices

摘要

A numerical model for axisymmetric piezoelectric devices recently was developed and used to simulate various bimorph capsules. These capsules are made of a layered, composite material, one layer made of brass or aluminum, and the other made of a piezoelectric ceramic. An inbound pressure field produces a mechanical deformation of the capsule inducing an electrical field, which in turn reduces the mechanical deformation that would take place in absence of the electrical field. Conductive elements or electrodes are installed on the upper and lower surfaces of the ceramic thus determining the boundary conditions for the electrical field. The analysis includes both static and dynamic problems. The numerical model uses the classical finite element method to solve the coupled differential equations for different boundary conditions involved after having included the piezoelectrical-related terms into an equivalent purely-mechanical set of equations without loss in the simulation of the coupled system. The paper discusses the differential equations, the boundary conditions, the numerical model, and results obtained. The numerical model computes the mechanical displacements and electrical potential, and subsequently the strains, stresses, electrical field, and electrical displacements over the domain. The model determined, for the device simulated, a strong dependency of the resulting natural frequencies of vibration upon the conditions at the support on the outer rim of the device