Equivalent damping coefficient of a bistable piezoelectric cantilever beam energy harvester via experimental-analytical balanced energy method

This study shed light on the simultaneous effects of bistability and electrical resistor on the equivalent damping of a piezoelectric cantilever beam energy harvester. Damping coefficient has a direct effect on the frequency bandwidth of an oscillating system. This paper, extends the experimental-analytical balanced energy (BE) method to obtain the damping change due to bistability of a piezoelectric energy harvester. By using extended Hamilton principle and Euler-Lagrange formulation with nonlinear magnetic field relations, the governing equations of the system are derived. Then the equivalent BE viscous damping model was adopted and the equivalent damping term is achieved. In BE method, the test signals are registered into the proposed BE algorithm, then the equivalent viscous damping coefficient of the system will be obtained. In the end, the effects of bistability and electrical resistor of the power circuit of piezoelectric patch is discussed. According to the results, by increasing the bistability of the system, the equivalent damping of the system will also increase. Besides by escalation the value of electrical load in piezoelectric power circuit, the value of the equivalent damping coefficient reaches a maximum value. This behavior is originated from the extracted power of the system.