Nonlinear Dynamic Behavior of Cantilever Piezoelectric Energy Harvesters: Numerical and Experimental Investigation

Abstract

It is known that the best performance of a given piezoelectric energy harvester is usually limited to excitation at its fundamental resonance frequency. If the ambient vibration frequency deviates slightly from this resonance condition then the electrical power delivered is drastically reduced. One possible way to increase the frequency range of operation of the harvester is to design vibration harvesters that operate in the nonlinear regime. The main goal of this article is to discuss the potential advantages of introducing nonlinearities in the dynamics of a beam type piezoelectric vibration energy harvester. The device is a cantilever beam partially covered by piezoelectric material with a magnet tip mass at the beam’s free end. Governing equations of motion are derived for the harvester considering the excitation applied at its fixed boundary. Also, we consider the nonlinear constitutive piezoelectric equations in the formulation of the harvester’s electromechanical model. This model is then used in numerical simulations and the results are compared to experimental data from tests on a prototype. Numerical as well as experimental results obtained support the general trend that structural nonlinearities can improve the harvester’s performance.

Appendix

The following expressions were used in Eqs. (4.6) and (4.11) [18, 20]

$$ {W}_0^{2L}={\displaystyle \underset{0}{\overset{L}{\int }}{W}^2(x) dx}\quad\quad {D}^2{W}_0^{2 Lp}={\displaystyle \underset{0}{\overset{ Lp}{\int }}{W}^{{\prime\prime} }{(x)}^2 dx}$$

$$ {W}_0^L={\displaystyle \underset{0}{\overset{L}{\int }}W(x) dx}{D}^2{W}_0^{2L}={\displaystyle \underset{0}{\overset{L}{\int }}{W}^{{\prime\prime} }{(x)}^2 dx} $$

$$ {W}_0^{2 Lp}={\displaystyle \underset{0}{\overset{L_p}{\int }}{W}^2(x) dx}{D}^2{W}_0^{Lp}={\displaystyle \underset{0}{\overset{ Lp}{\int }}{W}^{{\prime\prime} }(x) dx}$$

$$ {W}_0^{Lp}={\displaystyle \underset{0}{\overset{L_p}{\int }}W(x) dx}{D}^2{W}_0^{4 Lp}={\displaystyle \underset{0}{\overset{ Lp}{\int }}{W}^{{\prime\prime} }{(x)}^4 dx} $$

$$ {D}^2{W}_0^{3 Lp}={\displaystyle \underset{0}{\overset{ Lp}{\int }}{W}^{{\prime\prime} }{(x)}^3 dx} $$