VIBRO-IMPACT DYNAMICS OF PIPE CONVEYING FLUID SUBJECTED TO RIGID CLEARANCE CONSTRAINT 1)

管道与间隙约束间的碰撞振动是工程输流管结构的一个重要动力学现象. 迄今,人们通常采用光滑的非线性弹簧来模拟管道与间隙约束之间的碰撞力,但这种光滑的碰撞力无法真实反映碰撞前后管道状态向量的非光滑传递特征. 本文基于非光滑理论建立了具有刚性间隙约束简支输流管的非线性碰撞振动模型,利用 Galerkin 法离散了无穷维的管道模型, 并引入恢复系数构造了碰撞前后管道各处状态向量的传递矩阵,运用四阶龙格库塔法分析了脉动内流激励下管道与刚性间隙约束的非光滑碰撞振动现象,着重讨论了刚性间隙约束参数对管道动态响应随流速脉动频率变化的影响规律,特别是碰撞振动的周期性运动规律. 研究结果表明,刚性约束间隙值对管道碰撞振动行为的影响较大,在某些脉动频率下管道会出现多周期和非周期性的运动形态,还可出现非光滑系统特有的黏滑现象. 此外,碰撞恢复系数对管道振动的影响也比较显著,较小的恢复系数值更容易使管道在大范围脉动频率区间出现复杂的非周期碰撞振动.     

一类单侧碰撞悬臂振动系统的擦边分岔分析

与光滑动力系统不同,擦边分岔是非光滑动力系统中的一种特殊分岔行为.局部不连续映射是研究非光滑动力系统擦边分岔的一种有力工具.对一类单侧弹性碰撞悬臂振动系统进行了擦边分岔分析.首先建立了系统对应的局部不连续映射(ZDM)和全局Poincaré映射,进而在其他参数固定,碰撞间隙9为分岔参数时利用数值仿真的方法分别对原系统和对应的Poincaré映射进行擦边分岔分析,得到了该系统的两种不同类型的擦边分岔行为:周期1到周期2运动和周期1到混沌,这两种擦边分岔与刚性碰撞系统的情况是不相同的.由分析可知,对于含高阶非线性项的非光滑动力系统的擦边分岔,同样可以利用局部不连续映射的方法进行研究.     

存在间隙的多自由度系统的周期运动及Robust稳定性

研究一类存在间隙的多自由度振动系统的动态响应．系统由线性元件构成，但其中一个元件的最大位移不能超过由刚性平面约束所确定的阀值．应用模态矩阵方法将系统解耦，并根据碰撞条件和由碰撞规律所确定的衔接条件求得系统的周期运动及其稳定条件．将Ｌｙａｐｕｎｏｖ方法应用于周期运动的扰动差分方程，导出了含不确定参数的碰撞振动系统周期运动的鲁棒（Ｒｏｂｕｓｔ）稳定性条件．文末用一个二自由度系统阐明了方法的有效性     

分布式运动约束下悬臂输液管的参数共振研究

输液管道结构在航空、航天、机械、海洋、水利和核电等工程领域都有广泛应用,其稳定性、振动与安全评估备受关注.针对具有分布式运动约束悬臂输液管的非线性动力学模型,分别采用立方非线性弹簧和修正三线性弹簧来模拟运动约束的作用力,研究了管道在脉动内流激励下的参数共振行为.首先,从输液管系统的非线性控制方程出发,利用Galerkin方法进行离散化;然后,由Floquet理论得出线性系统在失稳前两个不同平均流速下脉动幅值和脉动频率变化时的共振参数区域;最后,考虑系统的几何非线性项和分布式非线性运动约束力的影响,求解了管道的非线性动力学响应,讨论了非线性项及运动约束力对管道参数共振行为的影响.研究结果表明,系统非线性共振响应的参数区域与线性系统的共振参数区域是一致的,分布式运动约束力对发生参数共振时管道的位移响应有显著影响;立方非线性弹簧和修正三线性弹簧模型所预测的分岔路径存有较大差异,但都可诱发管道在一定的参数激励下出现混沌运动.      

非光滑动力系统Floquet特征乘子的计算方法

对刚性约束的非线性动力系统进行研究 ,得到了该动力系统周期运动稳定性分析的Floquet特征乘子计算的半解析法。同时 ,也给出了刚性约束的线性动力系统和弹性约束 (分段光滑 )的非线性动力系统的Floquet特征乘子计算的解析法和数值方法。最后 ,针对一刚性约束的非线性动力系统 ,应用上述方法求Floquet特征乘子 ,并基于Floquet理论对周期运动的稳定性和分岔进行分析 ,将所得的结果与用Poincar啨映射方法分析的结果进行比较 ,以验证非光滑动力系统Floquet特征乘子计算方法的正确性     

分布式运动约束下悬臂输液管的参数共振研究

输液管道结构在航空、航天、机械、海洋、水利和核电等工程领域都有广泛应用,其稳定性、振动与安全评估备受关注.针对具有分布式运动约束悬臂输液管的非线性动力学模型,分别采用立方非线性弹簧和修正三线性弹簧来模拟运动约束的作用力,研究了管道在脉动内流激励下的参数共振行为.首先,从输液管系统的非线性控制方程出发,利用Galerkin方法进行离散化;然后,由Floquet理论得出线性系统在失稳前两个不同平均流速下脉动幅值和脉动频率变化时的共振参数区域;最后,考虑系统的几何非线性项和分布式非线性运动约束力的影响,求解了管道的非线性动力学响应,讨论了非线性项及运动约束力对管道参数共振行为的影响.研究结果表明,系统非线性共振响应的参数区域与线性系统的共振参数区域是一致的,分布式运动约束力对发生参数共振时管道的位移响应有显著影响;立方非线性弹簧和修正三线性弹簧模型所预测的分岔路径存有较大差异,但都可诱发管道在一定的参数激励下出现混沌运动.     

Grazing Bifurcation of a Cantilever Vibrating System with One-sided Impact

与光滑动力系统不同,擦边分岔是非光滑动力系统中的一种特殊分岔行为. 局部不连续映射 是研究非光滑动力系统擦边分岔的一种有力工具. 对一类单侧弹性碰撞悬臂振动系统进行了擦边分岔分析. 首先建立了系统对应的局部不连 续映射(ZDM)和全局Poincar\'{e}映射,进而在其他参数固定,碰撞间隙$g$为分 岔参数时利用数值仿真的方法分别对原系统和对应的Poincar\'{e} 映射进行擦边分岔分析,得到了该系统的两种不同类型的擦边分岔行为：周期1到周期2运 动和周期1到混沌,这两种擦边分岔与刚性碰撞系统的情况是不相同的. 由分析可知,对 于含高阶非线性项的非光滑动力系统的擦边分岔,同样可以利用局部不连续映射的方法进行 研究.     

空间可展机构非光滑力学模型和动力学研究

空间可展机构广泛应用于展开和支撑柔性太阳能帆板和航天工程领域中的有效载荷, 包括抛物面天线、平面相控阵雷达和合成孔径雷达等. 非光滑特性及其相应的动力学现象在空间可展机构的设计中有着非常重要的作用. 该文系统地综述了空间可展机构非光滑力学建模与非线性动力学的研究进展. 首先详细描述了含间隙铰链的接触碰撞力和摩擦力等非光滑特点;然后系统地介绍了含间隙机构的动力学建模方法、分析方法和参数设计;进一步简单介绍了含间隙铰链空间可展机构的非线性动力学特性, 如谐波共振、周期运动的稳定性和各类分岔等;最后提出了空间可展机构非光滑动力系统动力学、稳定性与控制中亟待解决的若干问题.     

碰撞振动系统分岔与混沌的研究进展

针对工程实际中普遍存在的碰撞振动系统这种典型的非光滑动力系统, 其研究具有重要的理论意义和工程实用价值. 碰撞振动系统动力学的分析与研究方法主要有理论分析、数值模拟以及应用与实验研究. 为了研究碰撞振动系统的周期运动稳定性、分岔及混沌, 采用的手段有建立Poincar\'{e}映射、中心流形和范式方法, 映射的分岔与混沌理论是碰撞振动系统研究的理论基础. 首先简述了碰撞振动系统的分析与研究方法, 光滑非线性系统动力学的分析方法部分可以推广到碰撞振动系统, 碰撞振动的不连续性导致一些方法的适用性和有效性问题. 进一步综述了碰撞振动系统周期运动稳定性、分岔、混沌及奇异性的理论研究和工程应用现状. 最后着重结合相关离散型映射系统的动力学发展, 对碰撞振动系统的分岔与混沌研究及存在的主要问题进行了讨论, 并展望了其发展趋势.      

参-强激励联合作用下输流管的分岔和混沌行为研究

研究输送脉动流的两端固定输流管道在其基础简谐运动激励下的分岔和混沌行为,考虑管道变形的几何非线性和管道材料的非线性因素,推导了系统的非线性运动方程,并应用Galerkin方法对其进行了离散化处理。通过采用数值模拟方法,对系统的运动响应进行仿真,重点探讨了流体平均流速、流速脉动振幅以及基础简谐运动激励振幅对系统动态特性的影响。结果表明,系统在不同的参数下会发生围绕不同平衡点的周期和混沌等运动,并在系统中发现了两条通向混沌运动的途径:倍周期分岔和阵发混沌运动。     

Nonlinear dynamics of cantilevered pipes conveying fluid: Towards a further understanding of the effect of loose constraints

The nonlinear dynamics of a fluid-conveying cantilevered pipe with loose constraints placed somewhere along its length is investigated. The main objective of this study is to determine the effects of several geometrical and physical parameters of the loose constraints on the characteristics and behavior of pipes conveying fluid. Based on the full nonlinear equation of motion, the dynamical behavior of the pipe system is investigated. Phase portraits and bifurcation diagrams are constructed for a selected set of system parameters. Typical results are firstly compared to numerical ones reported previously and excellent agreement is obtained. Then, the threshold flow velocities for several key bifurcations including pitchfork, period doubling, chaos, and sticking behaviors are predicted, showing that in many cases, the gap size, stiffness, and asymmetry of the loose constraints have remarkable effects on the nonlinear responses of the cantilevered pipe conveying fluid. For a pipe system with small/large constraint gap sizes, small constraint stiffness, or large constraint offset, some of the complex dynamical behaviors including chaos and period-doubling bifurcations would disappear, at least in the flow velocity range of interest.     

FLOW-INDUCED INTERNAL RESONANCES AND MODE EXCHANGE IN HORIZONTAL CANTILEVERED PIPE CONVEYING FLUID （Ⅱ）

Based on the nonlinear mathematical model of motion of a horizontally can-tilevered rigid pipe conveying fluid, the 3:1 internal resonance induced by the minimum critical velocity is studied in details. With the detuning parameters of internal and primary resonances and the amplitude of the external disturbing excitation varying, the flow in the neighborhood of the critical flow velocity yields that some nonlinearly dynamical behaviors occur in the system such as mode exchange, saddle-node, Hopf and co-dimension 2 bifurcations. Correspondingly, the periodic motion losses its stability by jumping or flutter, and more complicated motions occur in the pipe under consideration. The good agreement between the analytical analysis and the numerical simulation for several parameters ensures the validity and accuracy of the present analysis.     

FLOW-INDUCED INTERNAL RESONANCES AND MODE EXCHANGE IN HORIZONTAL CANTILEVERED PIPE CONVEYING FLUID (Ⅱ)

Based on the nonlinear mathematical model of motion of a horizontally cantilevered rigid pipe conveying fluid, the 3:1 internal resonance induced by the minimum critical velocity is studied in details. With the detuning parameters of internal and primary resonances and the amplitude of the external disturbing excitation varying, the flow in the neighborhood of the critical flow velocity yields that some nonlinearly dynamical behaviors occur in the system such as mode exchange, saddle-node, Hopf and co-dimension 2 bifurcations. Correspondingly, the periodic motion losses its stability by jumping or flutter, and more complicated motions occur in the pipe under consideration.The good agreement between the analytical analysis and the numerical simulation for several parameters ensures the validity and accuracy of the present analysis.     

NONLINEAR DYNAMICS AND SYNCHRONIZATION OF TWO COUPLED PIPES CONVEYING PULSATING FLUID

In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration, the equations of motion of the coupled two-pipe system are obtained. The two coupled nonlinear partial differential equations, discretized using the fourth- order Galerkin method, are solved by a fourth-order Runge-Kutta integration algorithm. Results show that the connection stiffness has a significant effect on the dynamical behavior of the coupled system. It is found that for some parameter values the motion types of the two pipes might be synchronous.     

Nonlinear vibration of slightly curved pipe with conveying pulsating fluid

The nonlinear governing motion equation of slightly curved pipe with conveying pulsating fluid is set up by Hamilton’s principle. The motion equation is discretized into a set of low dimensional system of nonlinear ordinary differential equations by the Galerkin method. Linear analysis of system is performed upon this set of equations. The effect of amplitude of initial deflection and flow velocity on linear dynamic of system is analyzed. Curves of the resonance responses about \(\varOmega \approx {\omega _\mathrm{{1}}}\) and \(\varOmega \approx \mathrm{{2}}{\omega _\mathrm{{1}}}\) are performed by means of the pseudo-arclength continuation technique. The global nonlinear dynamic of system is analyzed by establishing the bifurcation diagrams. The dynamical behaviors are identified by the phase diagram and Poincare maps. The periodic motion, chaotic motion and quasi-periodic motion are found in this system.     

Vortex-induced vibrations of pipes conveying fluid in the subcritical and supercritical regimes

In this paper, the vortex-induced vibrations of a hinged–hinged pipe conveying fluid are examined, by considering the internal fluid velocities ranging from the subcritical to the supercritical regions. The nonlinear coupled equations of motion are discretized by employing a four-mode Galerkin method. Based on numerical simulations, diagrams of the displacement amplitude versus the external fluid reduced velocity are constructed for pipes transporting subcritical and supercritical fluid flows. It is shown that when the internal fluid velocity is in the subcritical region, the pipe is always vibrating periodically around the pre-buckling configuration and that with increasing external fluid reduced velocity the peak amplitude of the pipe increases first and then decreases, with jumping phenomenon between the upper and lower response branches. When the internal fluid velocity is in the supercritical region, however, the pipe displays various dynamical behaviors around the post-buckling configuration such as inverse period-doubling bifurcations, periodic and chaotic motions. Moreover, the bifurcation diagrams for vibration amplitude of the pipe with varying internal fluid velocities are constructed for each of the lowest four modes of the pipe in the lock-in conditions. The results show that there is a significant difference between the vibrations of the pipe around the pre-buckling configuration and those around the post-buckling configuration.