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 引用本文: 王乙坤, 王琳. 分布式运动约束下悬臂输液管的参数共振研究[J]. 力学学报, 2019, 51(2): 558-568.
Yikun Wang, Lin Wang. PARAMETRIC RESONANCE OF A CANTILEVERED PIPE CONVEYING FLUID SUBJECTED TO DISTRIBUTED MOTION CONSTRAINTS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(2): 558-568.
 Citation: Yikun Wang, Lin Wang. PARAMETRIC RESONANCE OF A CANTILEVERED PIPE CONVEYING FLUID SUBJECTED TO DISTRIBUTED MOTION CONSTRAINTS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(2): 558-568.

## PARAMETRIC RESONANCE OF A CANTILEVERED PIPE CONVEYING FLUID SUBJECTED TO DISTRIBUTED MOTION CONSTRAINTS

• 摘要: 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.

Abstract: Pipes conveying fluid have been widely used in the fields of aerospace, mechanics, marine, hydraulic and nuclear engineering. The stability analysis, dynamic response and safety assessment of fluid-conveying pipes subjected to nonlinear constraints are particularly important for both engineering applications and scientific researches. Although the dynamical behaviors of fluid-conveying pipes subjected to single-point loose constraints have been discussed for four decades, the literature on the dynamics of fluid-conveying pipes subjected to distributed motion constraints is very limited. To obtain a better understanding of the dynamics of a cantilevered pipe conveying fluid subjected to distributed motion constraints, both cubic and modified trilinear spring models are employed in this study to describe the restraining force between the pipe and the motion constraints. This study is also concerned with the parametric resonance when the pipe is excited by an internal pulsating fluid. Firstly, the modified nonlinear equation of the pipe system was discretized via Galerkin's approach and solved using a fourth-order Runge-Kutta method. Via the Floquet theory, the nonlinear equation of motion was simplified to a linear one to calculate the parametric resonance regions versus the pulsating amplitude and frequency. Two representative values of mean flow velocity were employed to calculate the parametric resonance regions. Both the two values of mean flow velocity are assumed to be lower than the critical velocity for the cantilevered pipe system. Then, considering the geometric nonlinearity, the nonlinear dynamic responses focusing on the effect of external nonlinear restraining forces generated by the distributed motion constraints are discussed in detail. Results show that the stability regions of the nonlinear system agree well with that predicted by analyzing the linearized system. It is found that the distributed motion constraints would mainly affect the displacement amplitudes. Various oscillation types may arise when the pulsating frequency of the flow velocity is varied. Several bifurcation diagrams show that, however, a significant difference can be observed between the routes to chaos for the two constraint models, i.e., the pipe with a trilinear spring model can exhibit chaotic oscillations more easily than that with a cubic spring model.

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