Dynamic modeling of a galloping structure equipped with piezoelectric wafers and energy harvesting

Abstract

This study presents the analytical solution and experimental investigation of the galloping energy harvesting from oscillating elastic cantilever beam with a rigid mass. A piezoelectric wafer was attached to galloping cantilever beam to harvest vibrational energy in electric charge form. Based on Euler-Bernoulli beam assumption and piezoelectric constitutive equation, kinetic energy and potential energy of system were obtained for the proposed structure. Virtual work by generated charge and galloping force applied onto the rigid mass was obtained based on Kirchhoff's law and quasistatic assumption. Nonlinear governing electro-mechanical equations were then obtained using Hamilton's principle. As the system vibrates by self-exciting force, the fundamental mode is the only one excited by galloping. Hence, multi-degreeof-freedom equation of motion is simplified to one-degree-of-freedom model. In this study, closed-form solutions for electro-mechanical equations were obtained by using multi-scale method. Using these solutions, we can predict galloping amplitude, voltage amplitude and harvested power level. Numerical and experimental results are presented and discrepancies between experimental and numerical results are fully discussed.