Geometric nonlinear distributed parameter model for cantilever-beam piezoelectric energy harvesters and structural dimension analysis for galloping mode

To investigate the effects of structural dimension on the performance of cantilever-beam piezoelectric energy harvesters, a novel distributed parameter model considering the geometric nonlinearity of the cantilever beam is proposed using the extended Hamilton’s principle. Electromechanical decoupling method is utilized to simplify the coupling simulation and facilitate the geometric dimension analysis. For such harvesters operated in galloping mode, the effects of the geometric dimension of the cantilever beam on the electromechanical coupling term, modified natural frequency, electrical damping, modal velocity, power, power density, and tip displacement are investigated. The geometric nonlinearity is found to affect the tip displacement and power greatly at high wind speed. Due to subtle changes of the modal velocity with the geometric parameters, the variation of the power with these parameters is found to be approximately predicted from that of the electrical damping, while the variation of the tip displacement with these parameters is detected to be opposite to that of the modified natural frequency. For higher power with smaller tip displacement, shorter narrower thicker substrate layer fully covered with thicker piezoelectric layer is preferred. For higher power density with smaller tip displacement, shorter wider thicker substrate layer covered with shorter thinner piezoelectric layer is recommended.