Reduced-order models for piezoelectric systems

Abstract

Large-scale analysis of transducer arrays usually requires detailed, high-resolution modeling to represent the coupling effects of piezoelectric, elastic, and fluid media. However, reduced-order models, in the form of low-DOF lumped-parameter engineering models remain essential for system design. Here, we show how to bridge the gap between these model classes by deriving a simple means to compute the modes of an arbitrary piezoelectric system. Our approach exploits the intrinsic disparity in time scale between the electric and elastic fields to reduce the coupled problem into an augmented, elastic-only, system of equations. This system is shown to have the same mathematical characteristics as the elastic system, insofar as no new singularities appear. The piezoelectric-elastic modal system is fully general, and compatible with large-scale finite element representations of complex transducer designs. Numerical examples are shown to demonstrate the efficiency and practicality of the modal analysis.