Dynamic Analysis of Piezoelectric Based Energy Harvester under Periodic Excitation

In the present work, a vertical cantilever beam fixed with a torsional spring at one end and a tip mass at free end is analyzed as an energy harvester using piezoelectric patch for super-harmonic resonance condition. This model is non-linear dynamical system; it is exhibit super-harmonic resonances that can activate large amplitude motions at fraction integers of the fundamental frequency of the system. Such resonances offer a unique and untapped opportunity for harnessing vibratory energy from excitation sources with low frequency components. The nonlinear temporal differential equation of motion having periodic excitation is solved by using method of multiple scales. The closed form expressions for super-harmonic resonance condition are determined. The generated voltage is estimated for a wide range of system parameters.