考虑几何非线性时双稳态压电悬臂梁响应分析

针对双稳态压电振子产生大挠度振动现象,利用哈密顿原理建立了其大变形动力学方程,再用Galerkin法将其离散为模态坐标方程。对无量纲化方程进行数值分析可知:在激励一定下,存在最优阻抗使输出功率最大;在相同的激励水平下,大幅周期运动发电能力优于大幅混沌运动;通过对比发现几何非线性使系统产生更多的混沌窗口,改变梁长可使系统处在大幅周期运动中,从而提升压电发电能力。

Response Analysis of Bistable Piezoelectric Cantilever Beam Considering Geometric Nonlinearity

According to the large deflection vibration properties of the bistable piezoelectric vibrator,dynamic equation of piezoelectric bistable system is established by using Hamilton principle, and the Galerkin method is used to discrete the motion equation for modal coordinate equation.The numerical results of the dimensionless equations are as follows. In case of certain excitation,there exists optimal impedance,in which the output power of the system is the maximum. Under the same excitation level,the power generation ability of a periodic motion is better than a chaotic motion. Comparing the simulation results before and after adding the geometric nonlinearity, more chaos windows are acquired. By changing the beam length,a periodic motion expected can be obtained, which can enhance the power generation capacity.