Performance analysis of nonlinear piezoelectric energy harvesting system under bidirectional excitations

[Display omitted] •A piezoelectric energy harvesting system model is proposed based on parametric excitation and direct excitation.•An accurate theoretical model is established considering the influence of complex nonlinear factors of piezoelectric energy harvesting system excited by parametric excitation and direct excitation.•The energy harvesting bandwidth of the distributed parameter model is larger than that of the lumped parameter model.•Combining parametric excitation with direct excitation for compensation and complementarity purposes can be an ideal solution for vibration energy harvesting. In this paper, a cantilever beam piezoelectric energy harvester model of nonlinear partial differential equation based on Hamilton's Principle is established. A piezoelectric device using a bimorph cantilever beam with a fixed is subjected to horizontal and vertical excitation. Based on the Euler-Bernoulli thin beam model assumptions and inextensible deformation, the analysis further includes the effects of geometric nonlinearity and damping nonlinearity. The reduced-order nonlinear partial differential equations of motion with electro-mechanical coupling distributed parameter are derived by using Galerkin method. By using the method of multiple scales and solving the equations of motion, the energy harvester in its fundamental first-order resonance response is analyzed and the amplitudes of fundamental transverse deflection, output voltage and output power are determined. The major influence aspects of excitation amplitude, linear damping coefficient, nonlinear damping coefficient, impedance, nonlinear electro-mechanical coupling coefficient on transverse deflection, voltage and power are analyzed. The result shows that the linear damping coefficient and resistance affect the initial threshold of parametric excitation. The combination of parametric excitation and direct excitation gives full play to the advantages of parametric excitation and improve the energy conversion efficiency of the energy harvesting system.