【摘要】：近幾年來,國內(nèi)外專家對單自由度或單側(cè)剛性約束兩自由度碰撞振動系統(tǒng)周期運(yùn)動的Hopf分岔問題研究已經(jīng)取得了較大進(jìn)展,而對于系統(tǒng)參數(shù)比較復(fù)雜、動態(tài)響應(yīng)式較繁瑣、參數(shù)對系統(tǒng)的穩(wěn)定性影響較敏感的多自由度碰撞振動系統(tǒng)的研究甚少,研究方法也主要為數(shù)值分析。然而,沖擊振動問題在機(jī)械、車輛等工程實(shí)踐中經(jīng)常存在,迫切需要對此類系統(tǒng)的動態(tài)行為有更全面的了解。因此,在工程實(shí)踐中,對含間隙多自由度碰撞振動系統(tǒng)的研究有重要的意義,因而本文就對兩自由度碰撞振動系統(tǒng)和四自由度碰撞振動系統(tǒng)的情況做了全面的分析。本文主要內(nèi)容為： 1.本文全面分析了兩類典型的兩自由度碰撞振動系統(tǒng)和一類四自由度碰撞振動系統(tǒng)的動力學(xué)行為。通過建立碰撞振動系統(tǒng)的物理模型和數(shù)學(xué)模型,利用正則模態(tài)矩陣法對碰撞振動系統(tǒng)進(jìn)行解耦,并用解析法求解了碰撞振動系統(tǒng)周期運(yùn)動的解析解和線性化矩陣和各個系統(tǒng)的Poincare映射。 2.利用Poincare映射理論對平面映射不動點(diǎn)失穩(wěn)和分岔情況進(jìn)行分析。當(dāng)線性化矩陣的某個特征值為1或-1時,系統(tǒng)可能會發(fā)生鞍結(jié)或倍化分岔：當(dāng)線性化矩陣有二重特征值穿越單位圓時,系統(tǒng)會發(fā)生余維二分岔現(xiàn)象。選擇適當(dāng)?shù)南到y(tǒng)參數(shù),結(jié)合線性化矩陣特征值橫截單位圓周的趨勢圖,分析線性化矩陣特征值在上述情況下,系統(tǒng)發(fā)生分岔與混沌演化的動力學(xué)行為。 3.針對具體的多自由度碰撞振動系統(tǒng)的物理模型,研究了系統(tǒng)在何時參數(shù)下發(fā)生Hopf分岔和混沌的復(fù)雜動力學(xué)行為,給出了系統(tǒng)歷經(jīng)概周期運(yùn)動、周期運(yùn)動和環(huán)面倍化向混沌演化的Poincare截面圖。 4.利用數(shù)值仿真的結(jié)果,分析了系統(tǒng)的主要控制參數(shù)對系統(tǒng)周期運(yùn)動的影響,發(fā)現(xiàn)高維碰撞振動系統(tǒng)的敏感性較高,尤其激勵頻率,間隙和恢復(fù)系數(shù)等參數(shù)對系統(tǒng)周期運(yùn)動對系統(tǒng)周期運(yùn)動的影響較大,因此,選取系統(tǒng)的最優(yōu)參數(shù)對機(jī)械碰撞振動系統(tǒng)得優(yōu)化設(shè)計是必要的。
[Abstract]:In recent years, experts at home and abroad have made great progress in the study of the Hopf bifurcation of the periodic motion of the two-degree-of-freedom collision vibration system with one degree of freedom or one side rigid constraint, but the system parameters are more complex and the dynamic response formula is more complicated. There is little research on the multi-degree-of-freedom impact vibration system which is sensitive to the stability of the system, and the research method is mainly numerical analysis. However, the problem of shock vibration often exists in engineering practice, such as machinery, vehicle and so on. It is urgent to understand the dynamic behavior of this kind of system more comprehensively. Therefore, in engineering practice, it is of great significance to study the impact vibration system with multiple degrees of freedom with clearance, so this paper makes a comprehensive analysis of the impact vibration system with two degrees of freedom and the impact vibration system with four degrees of freedom. The main contents of this paper are as follows: 1. In this paper, the dynamic behaviors of two typical two degree of freedom impact vibration systems and a four degree of freedom impact vibration system are analyzed. By establishing the physical and mathematical models of the impact vibration system, the regular mode matrix method is used to decouple the impact vibration system. The analytical solution and linearization matrix of the periodic motion of the collisional vibration system and the Poincare map of each system are obtained by using the analytical method. 2. The instability and bifurcation of fixed point of planar mapping are analyzed by using Poincare mapping theory. When the eigenvalue of the linearization matrix is 1 or -1, the saddle node or doubling bifurcation may occur. When the linear matrix has a double eigenvalue passing through the unit circle, the system will have a codimensional two-bifurcation phenomenon. By selecting appropriate system parameters and combining with the trend diagram of linear matrix eigenvalue traversing unit circle, the dynamical behavior of bifurcation and chaotic evolution of linear matrix eigenvalue in the above cases is analyzed. 3. In this paper, the complex dynamical behavior of Hopf bifurcation and chaos is studied for the physical model of a specific multi-degree-of-freedom collisional vibration system, and the ergodic almost periodic motion of the system is given. Poincare section of periodic motion and torus doubling to chaos. 4. Based on the results of numerical simulation, the influence of the main control parameters on the periodic motion of the system is analyzed. It is found that the high dimensional impact vibration system has a high sensitivity, especially the excitation frequency. The parameters such as clearance and recovery coefficient have great influence on the periodic motion of the system. Therefore, it is necessary to select the optimal parameters of the system for the optimal design of the mechanical impact vibration system.
【學(xué)位授予單位】：蘭州交通大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：TH113.1

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本文編號：2270614