孤子局域共振激发的一种物理模型

发布时间：2018-05-04 15:07

本文选题：孤子 + β-FPU链　；参考：《声学技术》2017年03期

【摘要】：作为非线性领域的重要内容,孤子自从被发现以来就得到了广泛的关注。虽然目前关于孤子的传播及其相互作用性质等方面的研究已经相当成熟,但是对于孤子的产生问题仍然没有系统的认识。孤子产生问题的深入研究,不仅对于理解自然界及物理系统中的非线性现象十分重要,对孤子现象的工程应用也极为重要。基于这些原因,一些孤子激发方法的研究不断被提出。在非线性阵列带隙中的能量超透射现象激发孤子理论的基础上,局域共振孤子激发的方法被提出。该方法通过在半无限长β-FPU链中加入缺陷来引入局域共振机制,不仅有效降低了孤子激发的临界驱动振幅,还实现了孤子激发的可控操作。然而,虽然理论分析与数值模拟都证明了这一方法的可行性,但关于该方法的相关实验验证还是空白。为了进一步将该方法推向实际实验,提出了一种简易可行的实验方案,并做了深入的理论分析与大量的数值模拟。该方案给出一种物理模型,该模型以线性弹簧为基本元件,利用结构的几何非线性来构建β-FPU链,并以耦合摆阵列来实现。通过大量数值模拟证明了该方法的可行,同时研究了孤子释放周期与驱动频率、振幅的关系,结果与前述理论一致。此外,还通过数值模拟研究了孤子的激发周期与缺陷处阻尼大小的关系,以及单元质量不均匀性对孤子激发与传播的影响,为进一步实验提供依据。
[Abstract]:As an important part of nonlinear field, soliton has been paid more and more attention since it was discovered. Although the studies on the propagation and interaction properties of solitons are quite mature, there is still no systematic understanding of the generation of solitons. The study of soliton generation is not only very important for understanding the nonlinear phenomena in nature and physical systems, but also very important for the engineering application of soliton phenomena. For these reasons, some soliton excitation methods have been proposed. Based on the theory of excitatory soliton excited by energy hypertransmission phenomenon in the band gap of nonlinear array, the method of local resonance soliton excitation is proposed. The local resonance mechanism is introduced by adding defects to the semi-infinite 尾 -FPU chain, which not only effectively reduces the critical driving amplitude of the soliton excitation, but also realizes the controllable operation of the soliton excitation. However, although both theoretical analysis and numerical simulation have proved the feasibility of this method, the experimental verification of the method is still blank. In order to further apply the method to practical experiments, a simple and feasible experimental scheme is proposed, and a deep theoretical analysis and a large number of numerical simulations are made. In this scheme, a physical model is presented, in which the linear spring is used as the basic element to construct the 尾 -FPU chain using the geometric nonlinearity of the structure, and the coupled pendulum array is used to realize the model. The feasibility of the method is proved by a large number of numerical simulations. At the same time, the relationship between the soliton release period and the driving frequency and amplitude is studied. The results are in agreement with the previous theory. In addition, the relationship between the excitation period of soliton and the damping at the defect is studied by numerical simulation, and the influence of element mass inhomogeneity on the excitation and propagation of soliton is also studied, which provides the basis for further experiments.
【作者单位】：南京大学声学研究所;中国海洋大学信息科学与工程学院;
【基金】：国家自然科学基金资助项目(11174140) 国家973项目(2013CB632904)
【分类号】：O32

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