Finite element computation of nonlinear normal modes of nonconservative systems
Finite element computation of nonlinear normal modes of nonconservative systems
复制标题
非保守系统非线性简正模态的有限元计算
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
G. Kerschen
中科院分区：
文献类型：
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作者：
L. Renson;G. Deliége;G. Kerschen
模态分析，即，线性系统振动模式的计算，确实是相当复杂和先进的。尽管模态分析服务于，并且仍然服务于，从桥梁到卫星的应用的结构动力学社区，但人们普遍认为非线性在工程结构中经常发生。由于模态分析失败的非线性动力学现象的存在下，一个实用的非线性模拟模态分析的发展是本研究的目标。最近，随着非线性简正模（NNM）计算的数值技术（谐波平衡、周期解的延拓）的发展，在这一方向上取得了进展。由于这些方法考虑保守系统，本研究的目标是计算非保守系统的NNM，即定义为相空间中的不变流形。具体而言，提出了一种新的有限元技术来解决一组偏微分方程的流形几何。使用不同的两个自由度系统的算法进行了演示。
Modal analysis, i.e., the computation of vibration modes of linear systems, is really quite sophisticated and advanced. Even though modal analysis served, and is still serving, the structural dynamics community for applications ranging from bridges to satellites, it is commonly accepted that nonlinearity is a frequent occurrence in engineering structures. Because modal analysis fails in the presence of nonlinear dynamical phenomena, the development of a practical nonlinear analog of modal analysis is the objective of this research. Progress in this direction has been made recently with the development of numerical techniques (harmonic balance, continuation of periodic solutions) for the computation of nonlinear normal modes (NNMs). Because these methods consider the conservative system, this study targets the computation of NNMs for nonconservative systems, i.e. defined as invariant manifolds in phase space. Specifically, a new finite element technique is proposed to solve the set of partial differential equations governing the manifold geometry. The algorithm is demonstrated using different two-degree-of-freedom systems.