Nonlinear Resonances of Chains of Thin Elastic Beams With Intermittent Contact
Nonlinear Resonances of Chains of Thin Elastic Beams With Intermittent Contact
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间歇接触薄弹性梁链的非线性共振
DOI：
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发表时间：
2018
影响因子：
2
通讯作者：
A. Saito
中科院分区：
文献类型：
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作者：
A. Saito
本文讨论了弹性薄梁链在周期性外载荷作用下的强迫响应分析，梁与梁之间为无摩擦间歇接触。研究表明，当梁的刚度相同时，梁会发生非线性共振，其频率与线性共振频率相同。此外，它也表明，梁之间的小间隙和小偏差或失调的刚度，每个梁可以引起系统动力学的非线性共振频率的急剧变化。该系统被建模为一个半离散系统的分段线性振荡器与多个自由度（DOF），受到单边约束，这是来自有限元离散的梁。由此产生的运动方程求解的二阶数值积分方案，并寻求各种驱动频率的稳态解决方案。参数研究的结果相对于梁之间的间隙和梁的数量，讨论这些参数如何影响系统的谐振行为。
This paper deals with the forced response analysis of chains of thin elastic beams that are subject to periodic external loading and frictionless intermittent contact between the beams. Our study shows that the beams show nonlinear resonances whose frequencies are the same as the linear resonant frequencies if all the beams have the same stiffness. Furthermore, it is also shown that small gaps between the beams and small deviation or mistuning in the stiffness of each beam can cause drastic changes in the nonlinear resonant frequencies of the system dynamics. The system is modeled as a semidiscrete system of piecewise-linear oscillators with multiple degrees-of-freedom (DOF) that are subject to unilateral constraints, which is derived from a finite element discretization of the beams. The resulting equations of motions are solved by a second-order numerical integration scheme, and steady-state solutions are sought for various driving frequencies. Results of parametric studies with respect to the gaps between the beams and the number of beams are presented to discuss how these parameters affect the resonant behavior of the system.