Periodic Oscillations to Chaos: Nonlinear Dynamics of a Tristable Piezoelectric Flutter System

Piezoelectric flutter systems exhibit rich nonlinear dynamics under aerodynamic excitation. Alongside their beneficial effects in terms of energy harvesting, nonlinearities may also induce chaotic responses, potentially compromising system performance. Unlike bistable energy harvesters in which chaotic behaviors have not been reported, tristable flutter systems exhibit experimentally observed aperiodic oscillations; yet, the underlying chaos mechanisms remain theoretically unexplored. This paper investigates the nonlinear dynamics of a tristable piezoelectric flutter system, elucidating the transition from periodic oscillations to chaos for the first time. Using a harmonic balance method, Lyapunov exponent analysis, and bifurcation mapping, the complete evolutionary pathway is revealed. Originating from the central potential well, the system undergoes Hopf bifurcations followed by a symmetry-breaking bifurcation that triggers period-doubling cascades, which are fundamentally different from classical flutter instabilities. The chaotic regime features positive Lyapunov exponents and fractal basin boundaries, representing unique dynamical behavior. Analyses reveal that chaotic responses reduce power output by up to 80%. Parametric studies show that reducing cubic pitching stiffness substantially lowers the critical wind speed for interwell limit cycles, effectively suppressing pure chaotic regions. This work provides the theoretical foundation for chaos phenomena in tristable piezoelectric flutter systems and actionable design guidelines for performance enhancement.