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通过谐波平衡法,研究了由Iwan模型和1个质量块构成的干摩擦振子系统的自由振动和受迫振动问题.对于自由振动,推导了系统卸载和加载过程中各自对应的非线性运动方程;通过谐波平衡法,求得了各方程的1阶谐波解;为了得到方程正确的数值解,提出了确定零速度时刻的策略;数值算例结果表明:谐波平衡法与数值方法得到结果吻合较好,从而验证了谐波平衡法求解此类问题的有效性.对于系统微滑移下的受迫振动,采用谐波平衡法求得了系统的幅频关系.最后,对Iwan模型阻尼特性的研究发现,模型等效黏性阻尼比与其振幅存在非线性关系.
The problem of free vibration and forced vibration of a dry friction oscillator system composed of Iwan model and a mass is studied by the harmonic balance method. For the free vibration, the corresponding nonlinear equations of motion in the process of unloading and loading are derived In order to get the correct numerical solution of the equations, the strategy of determining the zero-speed moment is proposed. The numerical example shows that the result of the harmonic balance method and the numerical method The results show that the harmonic balance method is effective in solving this kind of problem.For the forced vibration under the micro-slip system, the amplitude-frequency relationship of the system is obtained by harmonic balance method.Finally, the damping characteristics of Iwan model The study found that there is a nonlinear relationship between the equivalent viscous damping ratio and its amplitude.