Wave-based analysis of jointed elastic bars: stability of nonlinear solutions
Wave-based analysis of jointed elastic bars: stability of nonlinear solutions
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DOI：
10.1007/s11071-022-07969-4
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发表时间：
2022-10-21
影响因子：
5.6
通讯作者：
Leamy, Michael J.
中科院分区：
文献类型：
--
作者：
Balaji, Nidish Narayanaa;Brake, Matthew R. W.;Leamy, Michael J.
在本文中，我们开发了两种新的方法，直接评估非线性波为基础的解决方案的稳定性，应用于联合弹性杆。在第一种稳定性方法中，我们应变的刚度参数，并使用基于波的方法构建分析稳定性边界。这不仅准确地确定了两个杆连接的非线性关节的例子中发现的周期解的稳定性，但它直接支配的参数强迫连续系统的响应和稳定性，而不诉诸离散化，一个新的发展本身。在第二种稳定性方法中，我们提出了一个扰动本征问题残留（PER），并表明PER的符号的变化位于临界点，稳定性从稳定到不稳定的变化，反之亦然。最后，我们讨论了后续的研究使用发达的稳定性方法。特别是，我们确定了一个机会，研究内部共振周围的稳定性，然后确定需要进一步发展和解释PER的方法来直接预测稳定性。
In this paper we develop two new approaches for directly assessing stability of nonlinear wave-based solutions, with application to jointed elastic bars. In the first stability approach, we strain a stiffness parameter and construct analytical stability boundaries using a wave-based method. Not only does this accurately determine stability of the periodic solutions found in the example case of two bars connected by a nonlinear joint, but it directly governs the response and stability of parametrically forced continuous systems without resorting to discretization, a new development in of itself. In the second stability approach, we pose a perturbation eigenproblem residue (PER) and show that changes in the sign of the PER locate critical points where stability changes from stable to unstable, and vice-versa. Lastly, we discuss follow-on research using the developed stability approaches. In particular, we identify an opportunity to study stability around internal resonance, and then identify a need to further develop and interpret the PER approach to directly predict stability.