压电弹性梁主共振响应的时滞加速度反馈控制

摘要

The time-delayed acceleration feedback control method was applied to study the primary resonance response of vibration control of piezoelectric flexible beams.Based on the Hamilton principle and a closed-loop feedback control strategy with delayed acceleration,a piezoelectric coupling nonlinear dynamic model of the elastic beam were established.Utilizing the multiple scale method,the first-order approximate solution and the stability condition of the primary resonance response of controlled beam were obtained.The peak amplitude and the critical excitation amplitude were given.It is shown that using time-delayed acceleration feedback control can reduce vibration effectively,and that the primary resonance response is affected by the delay value periodically.Reasonable selection of control gain and time delay value can avoid the resonance region and improve the effect of vibration control.%应用时滞加速度反馈控制方法研究压电弹性梁主共振响应的减振控制。基于 Hamilton 原理和时滞加速度闭环反馈控制策略，建立了压电耦合弹性梁的非线性动力学模型。采用多尺度方法，得到了受控梁主共振响应的一阶近似解及稳定性条件，进而给出了响应峰值和临界激励幅值的表达式，并给出算例分析。结果表明：采用时滞加速度反馈控制可以有效减振，其主共振响应受时滞值周期性影响，合理选取控制增益和时滞值，可以避免主共振区及多值不稳定解，提高振动控制效果。