Misalignment-induced bending-torsional coupling vibrations of doubly-clamped nonlinear piezoelectric energy harvesters

This article presents a theoretical and experimental study on the unique bending-torsional coupling vibration of a doubly-clamped nonlinear piezoelectric energy harvester due to the misalignment of the centroid and the torsional axis in vibration environments. Based on the Euler-Bernoulli beam theory, the extended Hamilton's principle, and the Galerkin discretization, a distributed-parameter model considering the misalignment is developed, and the corresponding governing equations are formulated. The developed model is validated against experimental data and Finite Element Analysis, where good agreements are achieved. Effects of the key parameters on the system's responses, and the characteristics and the causes of the bending-torsional coupling vibration are studied numerically based on the developed model. The results show that the torsion-induced chaotic motion can activate the jump-down phenomenon, largely reducing the electrical output of the harvester. Additionally, the occurrence of the torsion-induced jump-down phenomenon is sensitive to the system's initial state in some cases and can be reduced or even avoided by effectively tuning parameters that have slight effects on the bending resonance, such as the preloaded axial force and the distance between the torsional axis and the centroid.