Investigating the performance of piezoelectric energy harvester including geometrical, damping and material nonlinearities with the method of multiple scales

Employing piezoelectric systems is one of the suitable methods for harvesting energy from mechanical vibrations available in the environment. In this work,single degree of freedom model for cantilever beam with piezoelectric layer is considered. Simulation contains nonlinear coefficients like: stiffness, damping and coupling coefficient. Governing system of equations is solved by multiple scales method. First with assuming one term in approximate response, the effects of all nonlinear parameters on frequency curve are investigated. Results show that assuming only one term in response evaluates the effect of nonlinear damping correctly. Increasing this coefficient leads to reduce the range of excitation frequency and maximum harvested power. But one term assumption couldn’t assess the effects of nonlinear stiffness and coupling coefficient logically. In this case, the peak of frequency response curve is independent of nonlinear coefficients. So for obtaining accurate results assuming at least two terms of response is necessary. Results show increasing nonlinear stiffness coefficient increase the maximum harvested power and the range of excitation frequency. The effect of nonlinear coupling coefficient is decreasing the maximum power because this coefficient increases the stiffness of the system.