FINITE-ELEMENTS FOR PIEZOELECTRIC VIBRATIONS WITH OPEN ELECTRIC BOUNDARIES

The problem of a piezoelectric body vibrating in the free space of inf inite extent has been posed as a problem with open electric boundaries . A three-dimensional finite element analysis of piezoelectric vibrati ons has been complemented by the modeling of the external electrostati c field. The infinite exterior region that adheres to Laplace's equati on is represented as a single ''superelement'' obtained by the balloon ing of the outer boundary. The spectral transformation Lanczos method is used to find approximations to some solutions of the generalized ei genvalue problem arising from the finite element discretization of int erior and exterior regions. The proposed approach was tested on simple vibrators with different mesh discretisation and element order. The m ethod produces numerically stable results, and was used to estimate th e influence of the exterior leakage field an electromechanical propert ies of free piezoelectric vibrations. Numerical tests show that for so me materials, vibrator geometries and modes, favorable to the coupling with the exterior field, the resonant frequency and electrical parame ter shifts due to open electric boundaries may be as great as several percent.