Energy harvesting from the secondary resonances of a nonlinear piezoelectric beam under hard harmonic excitation

Abstract

This paper investigates the dynamical response of a nonlinear piezoelectric (PZT) energy harvester under a hard harmonic excitation and assesses its output power. The system is composed of a unimorph cantilever beam with a tip mass and exposed to an harmonic tip excitation with a hard forcing amplitude. First, the governing dimensionless nonlinear electromechanical ordinary differential equations (ODEs) are obtained. Next, the multiple scales method (MSM) is exploited to provide an approximate-analytical solution for the ODEs in hard and soft forcing scenarios. It is observed that, the hard force results in suband super-harmonic resonances. The MSM-based solutions are then validated by a numerical integration method and a good agreement is observed between the approximate-analytical and numerical results. Furthermore, utilizing the MSM-based solutions for the subharmonic, superharmonic, and soft primary resonances cases, the associated frequency and force response curves are constructed. It is revealed that the hard excitation leads to a remarkable voltage generation in the secondary resonances; this leads to a broadband energy harvesting. In addition, the time-domain electrical responses of the secondary resonances are also obtained and compared with each other. Finally, the three-dimensional graphs of the electrical power versus detuning parameter and time constant ratio in the cases of the secondary resonances are plotted. The results show that the optimum output power of the superharmonic resonance is considerably larger than the maximum power of the subharmonic resonance case.

Multimodal analysis of generic cantilever-based piezoelectric nanogenerators with offset-proof mass

“…To ascertain a better understanding of the harvester's working principles and performance dynamics, the way of polarization and polling conditions must keep in mind for a given PZT vibration-based nanogenerator. The mostly d 33 , d 31 , and sometimes d 15 modes of polarization for operation have been discussed in [31][32][33][34] depending upon how the force and the electric potential are related and the choice of one of these modes influences the maximum output voltage and power. Due to base and axial excitations, the power and voltage are increased because the device's natural frequency coincides with ambient frequencies while the energy of ambient vibration is distributed over a wide frequency spectrum.…”

“…The research showed that the power is produced of 16.3 mW at 219 Hz for 0.3N Stress. In [31], mechanically excited uni-morph piezoelectric membranes and electromechanical modeling are also studied. The maximum power produces for 80 N at 47 KΩ around 1.7 mW.…”

“…The maximum power produces for 80 N at 47 KΩ around 1.7 mW. In [31][32][33][34], authors described the voltage amplitude increases with frequency. In [31], figures 7(a) and (b) showed that the excitation amplitude increases the resonance region expands and generates high voltage amplitude over large frequency.…”

“…In [31][32][33][34], authors described the voltage amplitude increases with frequency. In [31], figures 7(a) and (b) showed that the excitation amplitude increases the resonance region expands and generates high voltage amplitude over large frequency. In figure 9 [31] forcing amplitude increases the deflection and voltage over the large frequency range.…”

Nonlinear electromechanical modeling and robustness of soft robotic fish-like energy harvester: insights and possible issues

“…The parametric resonance frequency is taken at the peak of the resonance as well. Figure 5(a) demonstrates that the superharmonic is moving with two frequencies [32,33]. The parametric resonance time history shows that the response is of similar frequency as the primary resonance, shown in figure 5(b).…”