Dynamic Analysis and Performance Comparison of a Geometrically Nonlinear Piezoelectric Energy Harvester in Bistable Versus Quad-Stable Configurations

This study investigates a piezoelectric energy harvester with three hinged springs, in which bistable or quad-stable potential wells are configured by adjusting spring assembly distances under equivalent potential barrier constraints. Static bifurcation analysis reveals the formation mechanisms of multistable topologies, while dynamic analysis characterizes intra-well and inter-well resonant responses. A multiobjective framework integrating Root Mean Square (RMS) voltage, effective bandwidth, and Basin of Attraction (BA) area is established to quantify the performance of the bistable and quad-stable energy harvesting systems. Numerical simulations using the cell-mapping approach with fourth-order Runge–Kutta integration demonstrate the superior practical performance of the bistable configuration under low-to-moderate base vibration amplitudes, resulting from its significantly larger BAs that ensure reliable high-energy responses. Conversely, a reversal in performance dominance occurs at higher amplitudes, where the quad-stable system prevails due to its broader BAs that enable robust inter-well oscillations. The core innovation of this work lies in establishing a direct link between the geometrically parameterized potential wells of the system and the resulting amplitude-dependent basin stability, offering a deterministic design principle for selecting and optimizing nonlinear energy harvesters according to anticipated environmental vibrations.