时滞反馈作用下压电梁的参数共振分析

基于Hamilton原理建立了受控压电梁的参数振动方程,研究了轴向激励压电梁时滞速度反馈控制的主参数共振.采用非线性振动的多尺度法研究了压电梁的亚谐波主参数共振,并对其稳定域进行分析.通过算例分析得到了不同时滞,控制增益,轴力影响下压电梁参数共振的稳定域和时程曲线.结果表明:时滞值增大,系统承受轴向力减小,相对于控制增益则反之.同时,随着轴向力增大,在一定范围内主动阻尼增加,时滞反馈能有效降低响应幅值.随着时滞值增大,减振效果变差.

Parametric resonance of piezoelectric beams with time delayed feedback

The primary parametric resonance of the time delayed velocity feedback control on piezoelectric beams under axial excitation is studied. Based on Hamilton principle, the parameter vibration equations of the controlled piezoelectric beam are obtained. The multi scale method of the nonlinear vibration is used to study the subharmonic primary parameter resonance on the piezoelectric beam, and its stability regions are examined. The numerical example is given to investigate the effects of time delays, control gain and axial force on the stability region and obtain the time history curves of the primary parametric resonance on piezoelectric beams. The results show that the increase of time delay leads to the reduction of the axial force of the system, while the control gain exhibits opposite effect. Moreover, with the increase of the axial force, the active damping increases in a certain range, and the time delayed feedback can effectively reduce the response amplitude.