一种含负刚度元件的新型动力吸振器的参数优化

提出了一种含有负刚度弹簧元件的新型动力吸振器模型,对该模型的最优参数进行了详细研究. 通过拉氏变换得到了系统的解析解,发现该系统存在着两个固定点,利用固定点理论得到了动力吸振器的最优阻尼比和最优频率比. 进一步研究发现接地刚度取负值时能够得到更好的减振效果,根据负刚度的特性得到了在保证系统稳定情况下的最优负刚度比. 通过数值解与解析解的对比证明了解析解的正确性. 通过与两种已有的典型动力吸振器模型在简谐激励和随机激励情况下的对比,说明了负刚度模型在主系统减振方面具有很大的优势,减振效果远优于两种已有动力吸振器模型,从而为设计新型动力吸振器模型提出了理论上的依据. 

PARAMETERS OPTIMIZATION OF A NEW TYPE OF DYNAMIC VIBRATION ABSORBER WITH NEGATIVE STIFFNESS

A new type of dynamic vibration absorber with negative stiffness spring is presented and studied analytically in detail. At first the analytical solution is obtained based on the Laplace transform method, and it could be found that there exist two fixed points independent of the damping ratio in the normalized amplitude-frequency curves. The optimum tuning ratio and damping ratio are obtained based on the fixed-point theory. According to the characteristics of the negative stiffness element, the optimal negative stiffness ratio is obtained and it could keep the system stable. The comparison of the analytical solution with the numerical one verifies the correctness and satisfactory precision of the analytical solution. The comparison with other two traditional dynamic vibration absorbers under the harmonic and random excitation show that the presented dynamic vibration absorber performs better in vibration absorption. The result could provide theoretical basis for the optimal design of similar dynamic vibration absorber.