Nonlinear equivalent circuit modeling of bistable piezoelectric energy harvesters

Abstract

Bistable piezoelectric energy harvesters (BPEHs) can efficiently convert low-frequency environmental vibrations into electrical energy. While analytical and finite element (FE) models can be used to estimate the nonlinear dynamics, an accurate circuit-level representation that simultaneously captures mechanical bistability and electromechanical coupling remains unexplored. In this work, a novel nonlinear equivalent circuit modeling (ECM) framework for BPEHs is proposed that directly links FE-derived nonlinear dynamics with circuit-domain simulation. A magneto-elastic clamped-free cantilever beam with piezoelectric transduction is modeled in a FE software to establish the symmetric double-well potential and stable equilibria. A two-step perturbation strategy is developed to identify admittance and charge responses governing local electromechanical dynamics. Next, the identified RLC parameters and equivalent voltage source are implemented in LTspice for time- and frequencydomain responses. Predicted ECM voltage and tip displacement responses are validated against FE simulations and experimentally calibrated measurements, further providing agreement in voltage amplitude, softening behavior, and dominant switching signatures. The ECM reliably captures intra- and cross-well voltage patterns and transition-level responses, despite the inability to replicate the exact chaotic trajectories due to initialcondition sensitivity. This work presents a novel nonlinear ECM capturing bistable piezoelectric energy harvesting dynamics, offering a compact and efficient model for rapid system-level analysis, design exploration, and circuit-domain simulations.