Chaos Threshold of a Multistable Piezoelectric Energy Harvester Subjected to Wake-Galloping

In order to extend the working range of the energy harvester, a nonlinear spring with multistable property is usually introduced to realize the structural design optimization. The nonlinear multistability property might increase the chance of inter-well chaotic responses, which leads to low-power output and unpredictability in motions. Quantitative determination of the parameter space in which chaos occurs is important. We investigated the chaos threshold of a multistable piezoelectric energy harvester subjected to wake-galloping in this paper. The homoclinic-like and heteroclinic-like orbits are obtained analytically for this system. This allows us to employ the Melnikov method to obtain chaos criterion from the breaking of the homoclinic-like and heteroclinic-like orbits in the presence of viscous damping and an external wake-galloping. The threshold of the excitation amplitude for snap-through motion is verified by numerical calculation. We observed that the nonlinear parameter can be effectively used to control the dynamical behavior of the system. The normalized voltage increases significantly when an inter-well chaotic response occurs. The results provide a guideline for the design and optimization of the multistable energy harvester subjected to wake-galloping.