Efficient energy harvesting from nonlinear vibrations of PZT beam under simultaneous resonances

The present research aims to analyze a piezoelectric energy harvester under simultaneous effects of two hard excitations. The system consists of a unimorph cantilever beam carrying a tip mass; excited by two simultaneous hard base accelerations. The governing distributed-parameters partial differential equations (PDEs) of motion are obtained based on Euler-Bernoulli beam assumption accounting for geometric nonlinearity. Galerkin scheme is exploited to discretize the PDEs into a set of nonlinear ordinary differential equations (ODEs). The convergence analysis is carried out to obtain the minimum required number of modes. To generalize the further results, the dimensionless forms of ODEs are obtained. Then, the approximate-analytical solutions are derived based on multiple scales method (MSM) for the case of simultaneous occurrence of superharmonic and combination resonances. Frequency response curves of the displacement and voltage are plotted. Moreover, the harvester response is studied for the case of primary resonance. The results disclose that, the level of the generated voltage and power are amplified when the superharmonic and combinations resonances coexist in the system response. Furthermore, the system dynamics are investigated in the time domain, showing good agreement with the frequency domain findings. (C) 2019 Elsevier Ltd. All rights reserved.