Bifurcation study of a bi-directional tunable piezoelectric vibration energy harvester equipped with nonlinear elastic stoppers

Mechanical stoppers are usually incorporated into the piezoelectric harvester design, to absorb momentary overloads and restrict the tip mass displacement within the allowable operating ranges. Employing mechanical stoppers introduces the nonlinearity due to the piecewise contact force. Although nonlinear properties can be used for extending the operational frequency bandwidth of the harvesters, the complexity of their nonlinear responses is the major challenge in designing the rectifier circuits. So, the main purpose of this paper is to explore nonlinear phenomena in the response of a bi-directional tunable piezoelectric vibration energy harvester with the mechanical stoppers. The electromechanical equations are established for the system and solved by the Runge–Kutta method. Then, the bifurcation diagram, phase plane trajectories, power spectrum plot and Poincaré section are employed to describe bifurcation characteristics of system. Vibration experiments are conducted to validate the simulation model. Various nonlinear behaviors such as jumps during frequency sweeps, multi periodic and chaos are detected. Also, the results show that the route to chaos is significantly affected by the stopper stiffness and the gap distance between the stopper and the lumped mass. With the results obtained here, design methodology for determination of system parameters can be more precise.