Numerical and experimental investigation of the energy harvesting performance of electromechanically coupled piezoelectric prestressed beams subjected to nonlinear vibrations

Abstract

Τhe piezoelectric energy harvesting from nonlinear vibrating structures has greatly attracted the attention of scientific community over the last decades, as it seems to provide one of the more promising ways for high electromechanical energy conversion. Current study deals with the development of a robust and accurate numerical tool capable of modelling and designing piezoelectric structures undergoing severe nonlinear vibrations. Specifically, a coupled multi-field generalized nonlinear mechanics framework for piezoelectric beams and plates subjected to initial stresses and large rotations, extended to include passive external electric circuits in order to predict the dynamic response of the structure and the power generated at the external resistive load. An experimental setup was also developed providing great correlations with the numerical results in case of a vibrating axially prestressed composite beam under the prebuckling regime. At the end, a computational investigation was performed studying the complex dynamic behavior of the piezoelectric beam, in the postbuckling regime. The model successfully captures the measured energy harvesting response of the beam including additional effects induced by the asymmetric configuration of the piezoelectric film.

Predictive lumped model for a tunable bistable piezoelectric energy harvester architecture

“…The value of P lim is higher when the value of the elasticity factor κ is lower. This can be concluded by observing the formula given by (41) since the value of the resonant pulsation ω 0 is lower when the elasticity factor κ decreases, as shown by equation (32). The expression given by (41) can therefore be rewritten as a function of the elasticity factor κ to highlight this further, by considering the variable ω 0PRJ which is equal to ε √ 4K M and corresponds to the resonant pulsation of the BPEH when the perfect revolute joint model is considered.…”

“…For the condition described by (43) to be satisfied, the coupling coefficient k 2 m must be high enough, since the quality factor Q m is assumed to be independent of κ. A decrease in the value of the elasticity factor κ implies a decrease in the value of the coupling coefficient k 2 m , as shown by the expressions given by (32). Consequently, in order for the harvested power to reach P lim at the cut-off frequency the elasticity factor κ must be equal to the lowest value that guarantees that the criterion given by ( 43) is satisfied.…”

“…Moreover, we notice in figure 10(a) that the harvested power at the cut-off frequency increases as κ decreases provided k 2 m Q m is high enough and β equal to 1 is reached. This is because P lim is inversely proportional to ω 0 (see equation ( 41)) and ω 0 is proportional to the square root of κ (see equation (32)).…”

“…Consequently, the non-linear terms of the proposed lumped model described by (31) can be neglected, leading to a linearized version of the electromechanical equations. The linearized version of the normalized equations is given by (34), with ū = x − ε (see equation (32)) and considering low values of normalized displacement as described in equation ( 35)…”

“…The one proposed by Cottone et al in 2012 [30] comes to mind as it describes the effect of the beams in the electromechanical equations for an architecture that uses piezoelectric patches laminated on the bistable beams of the BPEH [31]. More recently, a more detailed model for BPEH using post-buckled beams with piezoelectric patches has been proposed by Karadarakos et al [32]. The latter proposes a more intricate model to account for a wider range of mechanical deformations and conversion modes in the piezoelectric element, which allows for more accurate predictions, but also requires more computational power and a longer computation time.…”