GDQR 求解弹性地基上输流管道的稳定性

摘要

Here,the generalized differential quadrature rule (GDQR)was applied to investigate the stability of a pipe conveying fluid on an elastic foundation.Based on the motion equations and boundary conditions of a pipe conveying fluid,the eigenvalue matrix equation was obtained after the pipe was discretized with GDQR.After analyzing the corresponding eigenvalue equations,the critical fluid's flowing velocities for divergence and flutter of the pipe under different support conditions were calculated,the effects of translational and rotational spring stiffnesses on the critical unstable flowing velocites and the stability regions were analyzed.Meanwhile,the influences of mass ratio,reaction force coefficient and shear modulus of the two-parameter model of the foundation on the stability regions were studied,some useful conclusions were drawn.These conclusions provided a guidance for engineering practices.%用广义微分求积法（GDQR）研究了弹性地基上输流管道的稳定性问题。基于输流管道运动微分方程及边界条件，采用 GDQR 进行离散化，获得由动力方程组及边界条件合成的特征值矩阵方程。通过对相应特征值方程的具体分析，计算了左端固定、右端弹性支承下输流管道的发散失稳流速和颤振失稳流速，研究了临界失稳流速和稳定区域随两端支撑弹簧刚度、扭转弹簧刚度的变化情况，分析了质量比、双参数模型地基反力系数和剪切模量对输流管道稳定区域图的影响，得到了一些有益的结论。研究结论对于工程实践有一定的指导意义。