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为获得机械连接处微滑移对结构动力学行为的影响,以一自由端存在迟滞力约束的悬臂梁为研究对象,分析了其在基础激励下的主共振。约束端的迟滞力用Iwan模型描述,用多尺度法求得了此非线性边界条件下梁方程主共振过程中的稳态响应。通过可解性条件确定了稳态响应的幅频关系,并基于Lyapunov线性化稳定理论对稳态响应进行了稳定性分析。算例结果表明,主共振幅频曲线的共振峰均向左弯曲,表现出“软化”特征;当方程参数取值在特定范围时,幅频曲线以及响应振幅与激励幅值关系曲线均出现了不稳定部分,幅频曲线中不稳定部分的存在范围受激励幅值、黏性阻尼和约束刚度等参数影响。
In order to obtain the influence of micro-slip at the mechanical connection on the structural dynamic behavior, a cantilever beam with a hysteresis constraint at the free end is taken as the research object, and the main resonance under its fundamental excitation is analyzed. The hysteresis at the restraining end is described by the Iwan model. The steady-state response of the beam equation under the nonlinear boundary conditions is obtained by the multi-scale method. The amplitude-frequency relationship of steady-state response was determined by the conditions of solvability, and the stability of steady-state response was analyzed based on Lyapunov linearization stability theory. The results of the example show that the resonance peaks of the main resonance amplitude curve all bend to the left, showing the characteristic of softening. When the equation parameters are in a specific range, the amplitude-frequency curve and the response amplitude to the excitation amplitude curve The unstable part appeared. The existence range of the unstable part in the amplitude-frequency curve was affected by parameters such as excitation amplitude, viscous damping and constraint stiffness.