Nonlinear Dissipative Electroelastic Dynamics of an M-Shaped Broadband Piezoelectric Energy Harvester

The use of nonlinear dynamic phenomena for frequency bandwidth enhancement in vibration-based energy harvesting has received growing attention over the last few years. Various designs have been studied to create Duffing oscillators usually by introducing magnetoelastic coupling. In such devices, magnetic forces are typically coupled with elastic beams involving ferromagnetic components to achieve a nonlinear restoring force of the monostable or bistable Duffing type. Other than the increased volume and structural complexity due to additional magnets and discrete components, these magnetoelastic piezoelectric energy harvesters are not suitable to use in various compact applications and in systems that are sensitive to magnetic fields. The M-shaped structural configuration studied in this work overcomes these issues due to the asymmetric stiffness nonlinearity created by a simple structural configuration composed of a bent spring steel beam with piezoelectric patches. The electroelastic dynamics of the M-shaped broadband piezoelectric energy harvester is governed by various interacting nonlinearities, such as the deliberately introduced stiffness nonlinearity of hardening type resulting from the substrate geometry, inherent elastic nonlinearities of softening type as well as hysteretic losses associated with piezoelectric patches, and other dissipative effects due to large velocities experienced in response to base excitation. A recently developed nonlinear non-conservative electroelastic modeling framework for the piezoelectric patches is combined with geometric nonlinearities of the M-shaped energy harvester to establish a nonlinear dissipative model of the electromechanically coupled system. Energy harvesting experiments for a set of resistors and base excitation levels are then performed to experimentally characterize the bandwidth enhancement using the M-shaped broadband piezoelectric energy harvester.