Model losses of piezoelectric devices using finite element and complex material constants

A methodology to model mechanical losses of piezoelectric devices by the finite element analysis is presented. Complex parts of the material constants are extracted using an iterative method. Mechanical losses of piezoelectric devices are taken into account through these complex constants. A scheme using the QR factorization is developed to decompose mechanical losses of an arbitrary-shaped device into fundamental modes. These losses are then transformed into an equivalent viscous damping ratio in a standard finite element dynamics analysis. The proposed method enables us to obtain a reliable mechanical loss factor. Numerical results demonstrate that the proposed method can predict measured admittance spectra reasonably well.