论文标题
关于非线性非均匀多重铰链梁的稳定性
On the stability of a nonlinear non homogeneous multiply hinged beam
论文作者
论文摘要
本文处理了一个非线性演化方程，描述了非均匀多重铰链光束的动力学，但要受到位移类型的非本地恢复力。首先，对相关的加权固定问题进行了光谱分析，提供了完整的本征函数系统。然后，进行了进化问题的双模式溶液的线性稳定性分析，最终目标是提出最佳的密度选择和内部铰链点的位置，以提高光束的稳定性。该分析利用分析方法和数值方法。研究的主要结论是，非均匀密度函数可改善结构的稳定性。
The paper deals with a nonlinear evolution equation describing the dynamics of a non homogeneous 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 bi-modal 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 non homogeneous density functions improve the stability of the structure.
