【作者】 刘国英；

【导师】 刘习军；

【作者基本信息】 天津大学 ， 一般力学， 2005， 硕士

【摘要】 非线性科学是当今国内外学术发展的前沿性课题,对于工程中普遍存在的流-固耦合结构,其系统中存在的非线性因素是不可忽略的,研究流-固耦合结构的非线性振动问题有着重大的理论和工程意义。 本文主要研究包括液体自由面运动和壳体弹性位移的流-固耦合系统的非线性振动问题,通过讨论弹性壳与内流体的耦合振动,分析了弹性圆柱壳液耦合系统受高频激励液面出现低频大幅旋转重力波时系统的振动情形,从旋转重力波的产生机制、重力波的运动特性、系统参数对重力波运动特性的影响等相关方面探讨了旋转重力波现象,具体做了以下工作: 1.针对弹性圆柱壳液耦合系统受高频激励而出现低频大幅非轴对称旋转重力波的实验现象,应用流体力学和弹性力学的知识,依据系统的边界条件和壳液耦合条件,建立了壳液耦合系统的非线性振动方程组。 2.采用Runge-Kutta法对系统的非线性振动方程组进行了数值计算,得到了系统振动的时间历程及频谱特性曲线,改变激励力的幅值和频率,得到旋转重力波响应随外加激励的变化关系,从而分析了系统的非线性动力学特性。 3.运用平均法理论对耦合系统四个自由度的非线性振动方程组进行了解析求解,根据方程组的一次近似定常解,分析了系统的振动特性及各参数对振动响应的影响,从理论上进一步解释了弹性圆柱壳液耦合系统受高频激励出现低频大幅旋转重力波的振动机理,得到了与数值解和实验现象基本吻合的结论。 4.运用奇异性理论,分别以激励力频率和幅值为分岔参数,得到了系统的转迁集和多种分岔模式,统一而全面的分析了系统的分岔特性,建立了系统参数与拓扑分岔解之间的联系,为分析系统的振动特性提供了理论依据。 通过讨论弹性壳与内流体的耦合非线性振动,解释了低频大幅旋转重力波的产生机理,得到了与实验现象基本吻合的结论。更多还原

【Abstract】 In the recent years, nonlinear science is the important research project in domestic and international academic. As far as the liquid-solid coupled system which lies in engineering structure widely, the nonlinear factor in the system is not be ignored. It is of great value to study the nonlinear vibration of the liquid-solid coupled system.The nonlinear vibration of the liquid-elastic shell coupled system is studied in the paper;the free surface motion and the elastic shell displacement are considered. Analyze the vibration of the liquid-elastic shell coupled system subjected to the high-frequency excitation with the revolving gravity waves appearing. The phenomenon of the revolving gravity waves is discussed from the aspect of the vibration mechanism、 the dynamical character、 the change of the system parameter, and so on. The concrete work is showed in the following text.1. Based on the experimental phenomenon that the low-frequency and large-amplitude traveling gravity waves may be generated by the high-frequency external excitation in the liquid-elastic shell coupled system, according as the boundary conditions at the fluid-structure interface, a set of nonlinear equations for the multi-degree of freedom system is constructed with the use of the knowledge of hydromechanics and elasticity.2. The numerical computation is carried out by means of the Runge-Kutta method. The time history curves and frequency spectrum curves are obtained, and amplitude-frequency characteristic curves are obtained by changing the amplitude and frequency of the exciting force. Sequentially analyze the dynamical character of the liquid-elastic shell coupled system.3. The theoretical analysis is carried out by the means of averaging method. A set of nonlinear differential equations for the four-degree of freedom system is solved. According to the steady state solution of the first order approximation obtained, the relationship between the amplitude and the frequency of the external excitation and the response of the revolvinggravity waves is established, which makes the vibration mechanism more clear. The results show good agreement with the numerical results. 4. The frequency and the amplitude of the excitation are considered to be the bifurcation parameter respectively. The bifurcation behaviors are discussed according to singularity theory, and many bifurcation models and transition sets are also obtained. The relationship between the system parameter and the bifurcation behavior is constituted, which supplies the theoretical reference for the analysis of the system.On the basis of the numerical computation and the theoretical analysis, an in-depth study is given to explain the vibration mechanism of the low-frequency and high-amplitude revolving gravity wave in the liquid-elastic shell coupled system. The results agree generally with the experimental results.更多还原