Effect of piezoelectric layer geometry on the mechanical response of an energy harvester beam under combined vortex and magnetic excitations

This study investigates the influence of various geometrical shapes of piezoelectric layers on the mechanical performance of a piezoelectric energy harvesting (PEH) cantilever beam subjected to simultaneous excitations from vortex-induced vibrations (VIV) and a nonlinear magnetic force. VIV arises from fluid flow over a cylinder mounted at the beam’s free end as a tip mass. The aerodynamic excitation is modeled using a modified Van der Pol oscillator. The nonlinear magnetic force is generated by placing magnets at the cylinder’s base, along with an additional magnet on its surface. Equations of motion for free vibration are derived via Hamilton’s principle and solved using the Galerkin method. The discretized equations governing VIV are obtained through the assumed-modes method and Lagrange’s equations. Numerical solutions enable a comparative analysis of the system’s dynamic behavior with rectangular, trapezoidal, and triangular piezoelectric layer configurations. Results show that the layer’s shape and length, along with magnet placement, significantly affect the lock-in region and the overall performance of the energy harvester under VIV.