考虑界面微观滑移的连接非线性系统多尺度分析

Multiple time scale analysis of a lap-jointed structural system considering micro-slip

振动环境下,连接界面上存在着复杂的多尺度粘滑摩擦行为,进而造成含连接系统复杂的非线性振动现象。本文针对机械结构中的搭接连接系统,采用改进的Iwan迟滞非线性模型建模连接界面的多尺度粘滑行为,建立了连接系统的非线性运动方程,利用多尺度摄动分析方法研究了系统在初始条件下的自由振动,获得了系统响应的近似解析解并与直接数值积分解进行了对比;研究了粘性阻尼系数、刚度比等参数对系统动力学响应的影响。结果表明,Iwan迟滞非线性模型能够复现界面多尺度的微观粘滑行为;多尺度近似解析解和数值解吻合很好;连接系统的自由振动过程中,系统相轨迹以螺线收敛,但平衡位置可能发生偏移;界面切向刚度表现出随振幅增大而减小的软化非线性特点,系统瞬时固有频率随振幅减小而增大;振动过程中连接界面单位周期的能量耗散随振动幅值的减小而减小。研究结果为进一步探索含连接复杂装配结构的非线性动力学行为提供了基础。

There exists complex multiple stick-slip behavior on joint surface when subject to vibration excitation. This paper used the adjusted Iwan model to simulate the multiple stick-slips behavior on joint surface and built the dynamic motion equation for a lap-jointed system. Free vibration with different initial conditions was solved by multiple time scale method. The approximate analytical solution was compared with direct numerical integration solution to validate the precision. Parametric analysis was performed to investigate the effect of visco-damping factor and residual stiffness ration on the system response. The results show that Iwan model can model the multiple scale stick-slip behaviors on surface and the approximate analytical solution solved by multiple scale method agrees well with numeric solution. The joint stiffness and instantaneous normal frequency increase as the response amplitude decrease. The equivalent visco-damping factor and energy dissipation increase with the increasing of the response amplitude.