Effects of nonlinear piezoelectric coupling on energy harvesters under direct excitation

Abstract

A nonlinear analysis of an energy harvester consisting of a multilayered cantilever beam with a tip mass is performed. The model takes into account geometric, inertia, and piezoelectric nonlinearities. A combination of the Galerkin technique, the extended Hamilton principle, and the Gauss law is used to derive a reduced-order model of the harvester. The method of multiple scales is used to determine analytical expressions for the tip deflection, output voltage, and harvested power near the first global natural frequency. The results show that one-or two-mode approximations are not sufficient to produce accurate estimates of the voltage and harvested power. A parametric study is performed to investigate the effects of the nonlinear piezoelectric coefficients and the excitation amplitude on the system response. The effective nonlinearity may be of the hardening or softening type, depending on the relative magnitudes of the different nonlinearities.

Nonlinear analysis and power improvement of broadband low-frequency piezomagnetoelastic energy harvesters

“…9a-c. This result can be explained by the effects of the electrical load resistance on the imaginary part of the effective nonlinearity [30,31]. We can conclude that the strength of the softening behavior (hysteresis region or bandwidth) is directly related to the value of the electrical load resistance.…”

“…In these systems, a nonlinear restoring force is introduced which can result in a significant change in the potential energy function of the harvester. This nonlinear restoring force can be obtained when considering the piezoelectric coupling in the harvester [29][30][31] or when including an external magnetic force [12,[32][33][34], or when applying an external axial loading force [17]. The presence of these stiffness nonlinearities results in the appearance of softening or hardening behaviors which lead to a wider range of resonant frequencies of the harvester.…”

“…The presence of these stiffness nonlinearities results in the appearance of softening or hardening behaviors which lead to a wider range of resonant frequencies of the harvester. Considering the effects of the piezoelectric coupling, Abdelkefi et al [30,31] showed that broadband regions for the harvester's response can be obtained through hardening or softening responses due to the piezoelectric coupling when the harvester is directly or parametrically excited. An axially loaded piezoelectric clamped-clamped beam was proposed by Masana and Daqaq [17] to tune the natural frequency of the harvester with the excitation frequency.…”

Aeroelastic energy harvesting: A review

“…The nonlinear effects of the piezoelectric material (Abdelkefi, Nayfeh, & Hajj, 2011b;2011c;Stanton et al, 2010;Triplett & Quinn, 2009) as well as the beam's inertia and geometric nonlinearities were not considered in all previous studies in this topic. This can be explained by the presence of the aerodynamic force which is the dominant nonlinearity in the system.…”

Nonlinear analysis of piezoelectric energy harvesters from ambient and galloping vibrations

“…The third eigenvalue λ 3 is a result of the electromechanical coupling and it is always real and negative. 6,7 It is noted that the stability of the trivial solution depends only on the real part of the first two eigenvalues because λ 3 is always real and negative. The speed U g for which the real part of λ 1 is zero corresponds to the onset of instability or galloping and then self-excited oscillations takes place for higher values of wind speeds.…”