多稳态压电振动能量采集器的动力学模型及其特性分析

Dynamical model and characteristics of a multi-stable piezoelectric vibration energy harvester

提出了一种双线性弹性元件耦合的多稳态压电振动能量采集器,利用线性弹性元件的大变形引起采集器结构几何构型的变化,使采集器产生单稳态、双稳态和三稳态等非线性振动特性,达到提高能量采集器输出性能的目的。建立了双线性弹性元件耦合压电振动能量采集器的非线性恢复力模型,基于该模型,利用Rayleigh-Ritz模态分析法和能量守恒原理建立了能量采集器的集总参数机电耦合动力学模型,通过对动力学模型无量纲化处理后,仿真分析了系统参数对能量采集器的静力学特性(如非线性恢复力、势能、静态平衡点及其分岔)和动力学特性(振动位移、速度、相图、采集电压等)的影响。有限元计算结果验证了该仿真分析结果的正确性。研究结果表明:系统参数α=β≠0时能量采集器表现出光滑连续的单稳态、双稳态和三稳态等动力学特性,其中双稳态和三稳态振动时的能量采集输出功率比线性能量采集器高。

To improve the output performances of the piezoelectric vibration energy harvester, a multi-stable nonlinear piezoelectric vibration energy harvester (MPVEH) coupled with two linear elastic elements at the tip is presented. In this novel harvester, the large deformation of the two linear elastic elements can change the configuration of the energy harvester, which leads to a mono-stable, bi-stable and tri-stable motion, respectively. The nonlinear restoring force model caused by the deformation of the two linear elastic elements is derived at first, and then the lumped parameter electromechanical model of the new energy harvester is established based on the Rayleigh-Ritz method and energy conversation principle. The effects of the system parameters α and β on the nonlinear restoring force, the potential energy, the equilibriums, the bifurcation characteristics and the dynamics of the novel energy harvester are numerically analyzed. The research results are testified by the finite element model. It is shown that the nonlinear dynamics highly depend on the system parameters α and β. The energy harvester exhibits smooth continuous and non-smooth discontinuous mono-stable, bi-stable and tri-stable dynamics with α=β≠0. The research results are helpful to investigate the dynamical behaviors of the new harvester.