Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators
Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators
复制标题
DOI：
10.1016/j.jsv.2018.10.028
复制
发表时间：
2018-10
影响因子：
4.7
通讯作者：
A. Papangelo;F. Fontanela;A. Grolet;M. Ciavarella;N. Hoffmann
中科院分区：
文献类型：
--
作者：
A. Papangelo;F. Fontanela;A. Grolet;M. Ciavarella;N. Hoffmann
许多工程结构是由弱耦合扇区组成的，这些扇区以循环和理想对称的形式组装，可以简化为强制Duffing振子。本文研究了弱非线性区域中局域态的出现。我们表明可能存在多个空间局部解，并且由此产生的分岔图非常类似于在光学和流体动力学等物理领域中观察到的蛇形图案。此外，在从线性行为到非线性行为的过渡中，还确定了解的孤立分支。局部化是由非线性刚度引入的硬化效应引起的，并发生在较大的激励水平上。与失谐的情况相反，所提出的局部化机制是由非线性触发的，并且出现在完全齐次系统中。
Many engineering structures are composed of weakly coupled sectors assembled in a cyclic and ideally symmetric configuration, which can be simplified as forced Duffing oscillators. In this paper, we study the emergence of localized states in the weakly nonlinear regime. We show that multiple spatially localized solutions may exist, and the resulting bifurcation diagram strongly resembles the snaking pattern observed in a variety of fields in physics, such as optics and fluid dynamics. Moreover, in the transition from the linear to the nonlinear behaviour isolated branches of solutions are identified. Localization is caused by the hardening effect introduced by the nonlinear stiffness, and occurs at large excitation levels. Contrary to the case of mistuning, the presented localization mechanism is triggered by the nonlinearities and arises in perfectly homogeneous systems.