Exploring the Dynamics of Nonlinear Models for a Piezoceramic

We analyse the dynamical behaviour of a harmonically excited piezoceramic in dependence on certain design parameters. In particular, we explore its dynamics in dependence on its geometrical shape as well as the influence of nonlinear terms in the associated equations of motion. First we derive a two point boundary value problem whose solutions yield certain eigenfunctions of the linearized model. Based on a Galerkin approach we use the continuation package AUTO2000 in order to compute and analyse families of periodic solutions of an associated nonlinear model for different geometries and excitation frequencies. Finally, we explore the dependence of these solution paths on the magnitude of the nonlinear terms in the equations of motion. Our analysis shows that it may be worthwhile to consider unusually shaped piezoceramics in order to optimize the performance of a certain actuator.