SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 2, Page 908-940, January 2021.
The paper deals with a nonlinear evolution equation describing the dynamics of a nonhomogeneous multiply hinged beam, subject to a nonlocal restoring force of displacement type. First, a spectral analysis for the associated weighted stationary problem is performed, providing a complete system of eigenfunctions. Then, a linear stability analysis for bimodal solutions of the evolution problem is carried out, with the final goal of suggesting optimal choices of the density and of the position of the internal hinged points in order to improve the stability of the beam. The analysis exploits both analytical and numerical methods; the main conclusion of the investigation is that nonhomogeneous density functions improve the stability of the structure.

中文翻译：

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非线性非均质多层铰接梁的稳定性

SIAM应用动力系统杂志，第20卷，第2期，第908-940页，2021年1月。
本文讨论了非线性演化方程，该方程描述了非均质多重铰接梁在位移类型的非局部恢复力作用下的动力学。首先，对相关的加权平稳问题进行频谱分析，从而提供完整的特征函数系统。然后，对演化问题的双峰解进行了线性稳定性分析，其最终目的是提出密度和内部铰接点位置的最佳选择，以提高梁的稳定性。分析利用了分析和数值方法。研究的主要结论是非均匀密度函数提高了结构的稳定性。