Electromechanical decoupled model for cantilever-beam piezoelectric energy harvesters with inductive-resistive circuits and its application in galloping mode

The electromechanical decoupled distributed parameter model for cantilever-beam piezoelectric energy harvesters with inductive-resistive circuits is proposed. The modified natural frequency and electrical damping for series and parallel inductive-resistive cases are derived, which are functions of the first natural frequency of the cantilever beam, capacitance of the piezoelectric layers, load resistance, inductance and electromechanical coupling term. As a demonstration, we apply the decoupled model to cantilever-beam piezoelectric energy harvesters operated in the galloping mode. The average harvested power is derived as an algebraic expression of the electrical damping in addition to the wind speed, aerodynamic parameters of the bluff body and mechanical properties of the cantilever beam. Besides these impacts, the amplitude of the tip displacement also depends on its modified natural frequency. The electromechanical decoupled model and its analytical solutions are confirmed by the numerical solutions of the coupled model for the galloping mode. The theoretical expressions for the maximal harvested power and corresponding tip displacement at the optimal electrical damping are then developed. The cantilever-beam piezoelectric energy harvester with the inductive-resistive circuit has multiple solution sets of the modified natural frequency and electrical damping. Any optimal electrical damping can be realized by series or parallel inductive-resistive circuit, which cannot be accomplished by pure resistive circuit. By introducing the inductance to the circuit of the galloping piezoelectric energy harvester, the performance of such a system is improved with larger maximal harvested power at high wind speed and smaller amplitude of the tip displacement. This study provides a theoretical approach to capture the intrinsic effects of the inductance in addition to the load resistance on the performance of cantilever-beam piezoelectric energy harvesters.