本文選題：孤子 + β-FPU鏈�。� 參考：《聲學(xué)技術(shù)》2017年03期

【摘要】：作為非線性領(lǐng)域的重要內(nèi)容,孤子自從被發(fā)現(xiàn)以來就得到了廣泛的關(guān)注。雖然目前關(guān)于孤子的傳播及其相互作用性質(zhì)等方面的研究已經(jīng)相當(dāng)成熟,但是對(duì)于孤子的產(chǎn)生問題仍然沒有系統(tǒng)的認(rèn)識(shí)。孤子產(chǎn)生問題的深入研究,不僅對(duì)于理解自然界及物理系統(tǒng)中的非線性現(xiàn)象十分重要,對(duì)孤子現(xiàn)象的工程應(yīng)用也極為重要�；谶@些原因,一些孤子激發(fā)方法的研究不斷被提出。在非線性陣列帶隙中的能量超透射現(xiàn)象激發(fā)孤子理論的基礎(chǔ)上,局域共振孤子激發(fā)的方法被提出。該方法通過在半無限長β-FPU鏈中加入缺陷來引入局域共振機(jī)制,不僅有效降低了孤子激發(fā)的臨界驅(qū)動(dòng)振幅,還實(shí)現(xiàn)了孤子激發(fā)的可控操作。然而,雖然理論分析與數(shù)值模擬都證明了這一方法的可行性,但關(guān)于該方法的相關(guān)實(shí)驗(yàn)驗(yàn)證還是空白。為了進(jìn)一步將該方法推向?qū)嶋H實(shí)驗(yàn),提出了一種簡易可行的實(shí)驗(yàn)方案,并做了深入的理論分析與大量的數(shù)值模擬。該方案給出一種物理模型,該模型以線性彈簧為基本元件,利用結(jié)構(gòu)的幾何非線性來構(gòu)建β-FPU鏈,并以耦合擺陣列來實(shí)現(xiàn)。通過大量數(shù)值模擬證明了該方法的可行,同時(shí)研究了孤子釋放周期與驅(qū)動(dòng)頻率、振幅的關(guān)系,結(jié)果與前述理論一致。此外,還通過數(shù)值模擬研究了孤子的激發(fā)周期與缺陷處阻尼大小的關(guān)系,以及單元質(zhì)量不均勻性對(duì)孤子激發(fā)與傳播的影響,為進(jìn)一步實(shí)驗(yàn)提供依據(jù)。
[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.
【作者單位】： 南京大學(xué)聲學(xué)研究所;中國海洋大學(xué)信息科學(xué)與工程學(xué)院;
【基金】：國家自然科學(xué)基金資助項(xiàng)目(11174140) 國家973項(xiàng)目(2013CB632904)
【分類號(hào)】：O32

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