Equivalent electrical circuit framework for nonlinear and high quality factor piezoelectric structures

Abstract Equivalent electrical circuits are useful simulation tools to emulate and investigate the behavior of electromechanically coupled systems and structures as well as to develop energy harvesting or control circuits, among other configurations with two-way coupling. The existing efforts in this context have mostly considered linear structural (mechanical) domain, occasionally with nonlinear circuit for signal process and control. Typically, resonant circuits are employed to represent the mechanical domain of single- or multi-degree-of-freedom systems, while ideal transformers or current- and voltage-dependent sources are employed to model the electromechanical coupling. However, practical limitations of ideal transformers and dependent sources are challenges for experimental implementations of equivalent circuits. Furthermore, the internal resistance of equivalent resonant circuits limits the representation of high quality factor systems. This paper introduces equivalent electrical circuits for linear and nonlinear electromechanically coupled systems with high quality factor and various types of nonlinearities. The focus is placed on piezoelectric structures that exhibit stiffness and damping nonlinearities. An alternative to the existing models for the electromechanical coupling is also presented for convenient simulation of coupled system dynamics using standard electronic simulation programs. The equivalent circuit framework given here for high quality factor electromechanical systems is validated against both linear and nonlinear case studies, including published data for a nonlinear piezoelectric energy harvester. The proposed framework paves the way for the design of circuits emulating nonlinear structures, such as nonlinear vibration absorbers and sinks.