首页> 外文期刊>Communications in Nonlinear Science and Numerical Simulation >Dynamic behavior analysis of a mechanical system with two unstable modes coupled to a single nonlinear energy sink
【24h】

Dynamic behavior analysis of a mechanical system with two unstable modes coupled to a single nonlinear energy sink

机译:具有两种不稳定模式的机械系统的动态行为分析,耦合到单个非线性能量下沉

获取原文
获取原文并翻译 | 示例

摘要

This paper investigates a problem of passive mitigation of vibratory instabilities caused by two unstable modes by means of a single nonlinear energy sink (NES). For this purpose, a linear four-degree-of-freedom (DOF) primary structure having two unstable modes (reproducing the typical dynamic behavior of a friction system) and undergoing, as it is linear, unbounded motions when it is unstable, is coupled to a NES. In this work, the NES involves an essentially cubic restoring force and a linear damping force. We are interested in characterizing analytically the response regimes resulting from the coupling of the two unstable linear modes of the primary structure and the nonlinear mode of the NES. To this end, from a suitable rescaling of the governing equations of the coupled system in which the dynamics of the primary structure is reduced to its unstable modal coordinates, the complexification-averaging method is applied. The resulting averaged system appears to be a fast-slow system with four fast variables and two slow ones related to the two unstable modes of the primary structure. The critical manifold of the averaged dynamics is obtained through the geometric singular perturbation theory and appears as a two-dimensional parametric surface (with respect to two of the four fast variables) which evolves in the whole six-dimensional variable space. The asymptotic analysis reveals that the NES attachment can produce some bounded responses and suggests that the system may have simultaneous stable attractors. Numerical simulations complement the study, highlighting a possible competition between stable attractors and allowing us to investigate their basins of attraction. In each considered situation, a good agreement has been observed between theoretical results and numerical simulations, which validates the proposed asymptotic analysis. (C) 2020 Elsevier B.V. All rights reserved.
机译:本文通过单个非线性能量水槽(NES)调查了由两个不稳定模式引起的振动不稳定性的被动缓解的问题。为此目的,具有两个不稳定模式(再现摩擦系统的典型动态行为)并在不稳定的情况下进行线性,耦合时,具有两种不稳定模式(再现摩擦系统的典型动态行为)。对一个人。在这项工作中,NES涉及基本上立方恢复力和线性阻尼力。我们有兴趣地在分析上表征响应制度,该响应制度是由初级结构的两个不稳定线性模式的耦合和NE的非线性模式的耦合。为此,从耦合系统的控制方程的适当重新求助,其中初级结构的动态减小到其不稳定的模态坐标,施加络合平均方法。由此产生的平均系统似乎是一个快速慢速系统,具有四个快速变量和与主要结构的两个不稳定模式相关的两个慢速变量。通过几何奇异扰动理论获得平均动态的关键歧管,并且看起来作为二维参数表面(相对于四个快速变量中的两个),这在整个六维可变空间中发展。渐近分析表明,NES附件可以产生一些有界响应,并表明系统可以具有同时稳定的吸引子。数值模拟补充了研究,突出了稳定吸引子之间可能的竞争,并使我们能够调查他们的吸引力盆地。在每个考虑的情况下,在理论结果和数值模拟之间观察到良好的一致性,验证了所提出的渐近分析。 (c)2020 Elsevier B.v.保留所有权利。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱:kefu@zhangqiaokeyan.com

京公网安备:11010802029741号 ICP备案号:京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有
  • 客服微信

  • 服务号