基于完善双线性迟滞模型的干摩擦阻尼系统动力学分析

Dynamic analysis of dry friction system based on improved bilinear hysteretic model

针对接触正压力较大时干摩擦力主要表现出刚度特性的情况,结合已有文献的实验研究结论,对双线性迟滞模型进行完善。通过龙格库塔方法计算干摩擦阻尼系统的动力响应,结合傅里叶变换、庞加莱图及相图分析系统的非线性动力学特性。仿真结果表明,在干摩擦接触不脱离的情况下,系统没有出现分叉与混沌现象,稳态响应与摩擦力没有出现次谐波响应且高次谐波分量很小,证明了基于一次谐波平衡的等效线性化方法求解接触不脱离的干摩擦阻尼系统是较为精确的;得到了接触刚度、外激励幅值、正压力对干摩擦阻尼系统减振效果影响的规律,与相关实验结果基本相符。相关结论可为工程中干摩擦阻尼器的设计提供参考。

Considering that the dry friction force only shows stiffness characteristic when the normal contact force is high and combining with the existing conclusions of experimental research,the bilinear hysteresis model is improved.Runge kutta method is adapted to calculate the dynamic response of the dry friction damping system,the nonlinear characteristics of the system are analyzed by means of Fourier transform,Poincare diagram and phase diagram.Simulation results show that the system has no bifurcation and chaotic phenomenon when separation of dry friction contact is not considered,steady-state response and the friction force don＇t have sub-harmonic response and higher harmonic component is very small,which proves that using the equivalent linearization method which is based on the first order harmonic balance method to solve the dry friction damping sys-tem is accurate when separation is not considered;vibration reduction effect of the contact stiffness,excitation amplitude and normal load of dry friction damping system is obtained,and it is almost consistent with the related test results.The relevant conclusions can provide references for the design of dry friction damper in engineering.