Nonlinear dynamics of magnetically coupled double beam based piezoelectric energy harvester under galloping excitation

Abstract

This paper presents a magnetically coupled double cantilever beam-based piezoelectric energy harvester. Two square-shaped bluff bodies are attached to the tip of the beams to induce galloping-based oscillation in the proposed system. Spatio-temporal electro-mechanical equations of motion are developed using the Lagrange principle and discretized to their temporal form using generalized Galerkin’s method. 4th order Runge-Kutta method-based MATLAB solver (ode45) is used to solve these equations of motion and obtain numerical results. A prototype of the system is developed and experimented in a wind tunnel to support the numerical findings. Three wind speed regions (light air, light breeze, and gentle breeze) based on the Beaufort wind force scale are considered for getting a detailed insight into the system dynamics. Periodic, quasi-periodic, and chaotic oscillations are observed depending on different coupling conditions and wind speeds. Typical hopf bifurcation, Torus 3 bifurcations occur in the system due to galloping and magnetic repulsive force. Parametric studies are conducted for each wind speed region considering the load resistances and distance between the permanent magnets. Significant improvement in power output can be found for light air and gentle breeze regions with the magnetically coupled system than the uncoupled system (without magnetic interaction), whereas the uncoupled system performs better in the light breeze region.