本文選題：切換系統(tǒng)　切入點(diǎn)：廣義BVP振子　出處：《力學(xué)學(xué)報(bào)》2016年04期 　論文類型：期刊論文

【摘要】：非線性切換系統(tǒng)具有廣泛的工程背景,而傳統(tǒng)的非線性理論不能直接用來(lái)解決其中的問題,因而成為當(dāng)前國(guó)內(nèi)外熱點(diǎn)和前沿課題之一.目前相關(guān)工作大都是圍繞固定時(shí)間或單狀態(tài)切換開展的,而實(shí)際工程系統(tǒng)大都屬于多狀態(tài)切換問題,同時(shí)多狀態(tài)切換涉及到更為豐富的動(dòng)力學(xué)行為.本文基于兩廣義BVP振子,通過引入雙向切換開關(guān),構(gòu)建了雙狀態(tài)切換下的非線性動(dòng)力學(xué)模型,進(jìn)而研究狀態(tài)切換導(dǎo)致的各種運(yùn)動(dòng)模式及其相應(yīng)的產(chǎn)生機(jī)制.應(yīng)用非光滑系統(tǒng)的Poincar′e映射理論,推導(dǎo)了雙狀態(tài)切換下的Lyapunov指數(shù)的計(jì)算公式,結(jié)合子系統(tǒng)的分岔分析,得到了切換系統(tǒng)隨分岔參數(shù)變化的動(dòng)力學(xué)演化過程及其相應(yīng)的最大Lyapunov指數(shù)的變化情況.得到了雙狀態(tài)切換條件下系統(tǒng)存在著各種形式的振蕩行為,分析了諸如周期突變等現(xiàn)象及通往混沌的倍周期分岔道路,揭示了不同運(yùn)動(dòng)模式的產(chǎn)生機(jī)制及倍周期序列的本質(zhì).與固定時(shí)間切換和單狀態(tài)切換系統(tǒng)不同,雙臨界狀態(tài)切換系統(tǒng)存在著更為豐富的非線性現(xiàn)象,其主要原因在于雙狀態(tài)切換會(huì)產(chǎn)生更多的切換點(diǎn),且切換點(diǎn)的位置更加多變.同時(shí)切換系統(tǒng)的倍周期分岔序列與光滑系統(tǒng)中的倍周期分岔序列不同,切換系統(tǒng)的倍周期分岔序列只對(duì)應(yīng)于切換點(diǎn)數(shù)目的成倍增加,而其相應(yīng)的周期一般不對(duì)應(yīng)于嚴(yán)格的周期倍化過程.
[Abstract]:Nonlinear switched systems have a wide engineering background, but the traditional nonlinear theory can not be directly used to solve the problems. Therefore, it has become one of the hot and frontier topics at home and abroad. At present, most of the related work is carried out around fixed time or single state switching, but the practical engineering systems are mostly multi-state switching problems. At the same time, multi-state switching involves a richer dynamic behavior. Based on two generalized BVP oscillators, a nonlinear dynamic model with two-state switching is constructed by introducing bi-directional switching switches. Based on the Poincar'e mapping theory of non-smooth systems, the calculation formula of Lyapunov exponent under two-state switching is derived, and the bifurcation analysis of subsystems is combined with the analysis of the bifurcation of subsystems. The dynamic evolution process of switched systems with bifurcation parameters and the corresponding maximum Lyapunov exponents are obtained. The phenomena such as periodic mutation and the path of periodic doubling bifurcation to chaos are analyzed. The generation mechanism of different motion modes and the nature of periodic doubling sequence are revealed, which are different from those of fixed time switching and single state switching systems. There are more nonlinear phenomena in the double critical state switched system, the main reason is that the double state switching will produce more switching points. Moreover, the position of the switching point is more changeable. At the same time, the period doubling bifurcation sequence of the switched system is different from that of the smooth system, and the double period bifurcation sequence of the switched system only corresponds to the multiple increase of the number of switching points. However, the corresponding period does not correspond to the strict periodic doubling process.
【作者單位】： 江蘇大學(xué)土木工程與力學(xué)學(xué)院;
【基金】：國(guó)家自然科學(xué)基金(11472115,11572141,1150209) 鎮(zhèn)江市科技攻關(guān)基金(GY2013032,GY2013052)資助項(xiàng)目
【分類號(hào)】：O322
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本文編號(hào)：1637448