两端弹性支承输流管道固有特性研究

输流管道广泛应用于航天航空、石油化工、海洋等重要的工程领域, 其振动特性尤其是系统固有特性一直是国内外学者研究的热点问题. 本文研究了两端弹性支承输流管道横向振动的固有特性, 尤其是在非对称弹性支承下的系统固有特性. 使用哈密顿原理得到了输流管道的控制方程及边界条件, 通过复模态法得到了静态管道的模态函数, 以其作为伽辽金法的势函数和权函数对线性派生系统控制方程进行截断处理. 分析了两端对称支承刚度、两端非对称支承刚度、管道长度以及流体质量比对系统固有频率的影响规律, 重点讨论了管道两端可能形成的非对称支承条件下固有频率的变化规律. 结果表明, 较大的对称支承刚度下管道的第一阶固有频率下降较快; 当管道两端支承刚度变化时, 管道的各阶固有频率在两端支承刚度相等时取得最值; 对于两端非对称支承的管道而言, 两端支承刚度越接近, 第一阶固有频率下降的越快, 而且相应的临界流速越小; 流体的流速越大, 其对两端非对称弹簧支承的管道固有频率的影响更为明显. 

STUDY ON NATURAL CHARACTERISTICS OF FLUID-CONVEYING PIPES WITH ELASTIC SUPPORTS AT BOTH ENDS

Fluid-conveying pipes have been widely used in aerospace, petrochemical, offshore and other important engineering fields. The vibration characteristics of the fluid-conveying pipes, especially the natural characteristics of the system, have been an important issue in the research of scholars around the world. This study investigates the natural characteristics of transverse vibration of a fluid-conveying pipe with elastic supports at both ends. In particular, the natural characteristics of the fluid-conveying pipe with asymmetric elastic supports at both ends are discussed. The governing equation and boundary conditions of the fluid-conveying pipe system are derived by the Hamilton’s principle. The modal functions of the static pipe are obtained by the complex modal method, and then they are used as the potential function and weight function for the Galerkin method to truncate the control equation of the linear derived system. The effects of symmetrical support stiffness at both ends, asymmetric support stiffness at both ends, pipe length and fluid mass ratio on the natural frequencies of the system are discussed. The discussion focuses on the variation of natural frequencies under the condition of asymmetric supports that may happen at both ends of the pipe. Results show that a fast decrease in the first natural frequency for large symmetrical support stiffness. When the support stiffness at both ends of the pipe changes, the natural frequencies of each order of the pipe obtain the maximum or minimum value when the support stiffness at both ends is equal. For the pipe with asymmetric supports at both ends, the closer the support stiffness at both ends, the faster the first natural frequency decreases, and the smaller the corresponding critical flow velocity. The greater the flow velocity of the fluid, the more significant is the effect on the natural frequency of the pipe supported by asymmetric supports at both ends.