Multidomain modeling of acoustical transducers and arrays using electrical network theory

Abstract

Modeling of piezoceramic acoustic transducers involves the transformation of energy in the electrical, mechanical, acoustical radiation domains. By using generalized coordinates and Lagrangian mechanics, in which principle of least action is applied in each domain, the electrical, piezoelectric, mechanical and sound radiation problems can be solved separately and then combined in a multi-contour equivalent electro-mechanical circuit with each mechanical vibrational resonant modes representing separate degrees of freedom in the coupled electrical circuit. This energy approach involves the calculation of the potential and kinetic energies of each practical mode of vibration, which can be determined analytically, experimentally, or by finite-element-analysis. This is an alternative to the use of Newtonian mechanics which requires an accurate description of the real boundary conditions in the device and is common in many FEA modeling approaches. The availability of software (e.g., Matlab, Python, LTSpice, etc.) to model electrical circuits (networks in the case of multi-resonant devices) makes for a powerful and efficient modeling approach. The historical emergence of this approach stems from adapting the Rayleigh-Ritz method for mechanical and electrical domains with the advent of piezoelectric and magnetostrictive bodies. Several example of piezoceramic transducers are presented.