含集中质量悬臂输流管的稳定性与模态演化特性研究

本文主要研究通过调控集中质量对悬臂输流管稳定性和振动模态特性的影响规律,为输流管动力学性能的可控性提供理论指导和实验依据. 首先基于扩展的哈密顿原理,建立了含集中质量悬臂输流管的非线性动力学理论模型. 基于线性动力学特性分析,研究发现集中质量沿管道轴向位置变化对输流管发生颤振失稳的临界流速有重要影响.并通过伽辽金前四阶模态截断处理线性矩阵方程式,定性地分析了集中质量位置与质量比的变化对于输流管稳定性影响的变化.实验结果表明, 输流管的颤振失稳模态随集中质量位置的变化发生了转迁. 此外,基于动力学理论分析, 发现集中质量比值对失稳临界流速也有重要的影响,且主要取决于集中质量的安装位置. 基于非线性特性,进一步分析了集中质量对输流管振动幅值的影响. 实验和理论研究发现,集中质量位置从固定端向自由端变化时, 输流管振幅表现出先增大后减小趋势,且振动模态也从二阶转迁到三阶.本研究有望为输流管振动驱动应用提供理论支撑与指导意义. 

STABILITY AND MODE EVOLUTION CHARACTERISTICS OF A CANTILEVERED FLUID-CONVEYING PIPE ATTACHED WITH THE LUMPED MASS

This work mainly investigates evolutions for the dynamic characteristics of a cantilevered pipe conveying fluid by regulating a lumped mass along the pipe's length, for the purpose of controlling the stability and vibration behaviors of the pipe. Firstly, on the base of the extended Hamilton principle, a nonlinear dynamic model for the cantilevered fluid-conveying pipe attached with the lumped mass is established. In the following, a linear analysis is performed to explore the evolution of critical flow velocity varying with the placed position of lumped mass, which is substantiated by experimental measurements showing that transition of the flutter mode occurs. In addition, it is significant that the attached lumped mass ratio has a great impact on the critical flow velocity based on the linear dynamic analysis, which is dependent on the placed positions and mass ratio. Subsequently, a nonlinear analysis is conducted to investigate the effect of lumped mass on vibration amplitude of the pipe. It is indicated that the vibration amplitude is first increased and then decreased with the lumped mass varying from the fixed end to the free end, which is well compared to those of experimental measurements. The vibration mode of the pipe conveying fluid is transferred from the second mode to the third mode with varying the placed position of lumped mass, which is also observed in the experiments. The present study is expected to be beneficial for designing an underwater driven system based on flutter of pipes conveying fluid. In this way, the pipe's vibration mode can be adjusted through adding and adapting the lumped mass.