论文标题
Melnikov分析中强制阻尼反应的稳定性
Stability of Forced-Damped Response in Mechanical Systems from a Melnikov Analysis
论文作者
论文摘要
可以从其保守的极限中研究具有弱强迫和阻尼的多度机械系统的频率响应。具体而言，最近的结果表明，如何从周期性轨道的保守家族（非线性正常模式）分析地预测附近的共振。但是，通常通过数值模拟确定强制抑制运动的稳定性。在本文中，我们介绍了从保守非线性正常模式扰动的周期性轨道稳定性的分析结果。与先前解决相同问题的方法相反，我们的方法可以解决强烈的非线性振荡，高阶共振和影响系统的非保守力的任意类型，正如我们在特定示例中所显示的那样。
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be predicted analytically from conservative families of periodic orbits (nonlinear normal modes). However, the stability of forced-damped motions is generally determined a posteriori via numerical simulations. In this paper, we present analytic results on the stability of periodic orbits that perturb from conservative nonlinear normal modes. In contrast with prior approaches to the same problem, our method can tackle strongly nonlinear oscillations, high-order resonances and arbitrary types of non-conservative forces affecting the system, as we show with specific examples.
