We investigate the dynamical characteristics of a two degrees of freedom friction oscillator with constrained spring cushions. Based on the discontinuity resulted from the rough contact surface and the nonsmoothness resulted from fixed spring, different boundaries and domains are given in phase space. The G-functions are introduced to determine whether the passable, grazing, sliding and stick motions occur on separation boundaries. The periodic orbits in such a system are predicted by using mapping dynamical theory after introducing four-dimension switching sets and basic mappings. The passable, grazing, stick, sliding and periodic motions of system are studied numerically by the velocity, displacement and G-functions responses in order to better illustrate the switching conditions of different motions. This investigation can provide effective technical support for the optimization design of system with fixed spring cushions.

我们研究了带有约束弹簧垫的两自由度摩擦振荡器的动力学特性。根据粗糙的接触表面产生的不连续性和固定弹簧产生的不光滑性，在相空间中给出了不同的边界和区域。引入了G功能以确定是否在分隔边界上发生可通过，掠过，滑动和粘滞运动。在引入四维切换集和基本映射之后，通过使用映射动力学理论来预测这种系统中的周期轨道。通过速度，位移和G函数响应，对系统的可通过，掠过，粘着，滑动和周期性运动进行了数值研究，以更好地说明不同运动的切换条件。