基于广义有限差分法的输流直管振动响应特性研究

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振动与冲击 ›› 2019, Vol. 38 ›› Issue (24) : 165-171.

论文

张挺1，林震寰1，郭晓梅1，张恒1，范佳铭2

作者信息 +

Numerical simulation of vibration response of pipe conveying fluid based on a generalized finite difference method

ZHANG Ting1,LIN Zhenhuan1,GUO Xiaomei1,ZHANG Heng1,FAN Jiaming2

Author information +

文章历史 +

摘要

基于输流直管横向振动微分方程，采用广义有限差分法和Houbolt法分别对空间和时间上的偏微分项进行离散，建立高阶精度的无网格法数值模式。将该数值模式应用于两端支撑轴向运动梁模型和两端固支输流直管模型，所得的固有频率和振幅时程等与前人研究成果和理论解均吻合良好；并对不同总点数N、时间步长△t、子区域选点数ns的数值结果进行对比，表明提出的数值模型在求解输流直管振动响应问题上具有良好的准确性和鲁棒性；对比分析了三种不同支撑条件（两端固支、两端简支和一端固支一端简支）下输流直管的振动响应特性。结果表明：两端简支时输流直管中点处的振幅最大，振动频率最小；两端固支时输流直管中点处的振幅最小，振动频率最大；且在端部约束限制条件不对称时，其振动幅值最大值出现位置会向弱约束端偏移。

Abstract

In this study, a high-order accuracy numerical model of the meshless method, called generalized finite difference method (GFDM), was generalized to analyze the transverse vibration problem of pipe conveying fluid.Based on the differential equation of transverse vibration, the GFDM and the Houbolt methods were adopted to discretize the partial differential items in space and time, respectively.The consistent with good results of natural frequency and the amplitude time range was compared with the theoretical solution and other numerical results reported in literature.Meanwhile, the numerical model proposed in this paper has good stability and robustness in solving the vibration response of pipe conveying fluid by comparing with the vibration amplitude at the midpoint with different total number of points N, time step Δt and sub-region selection points ns, respectively.Furthermore, detailed analysis of the vibration response characteristics with several typical boundary conditions indicates that the vibration amplitude at the midpoint of the pined-pined pipe is much large than that of two other boundary conditions, and the vibration frequency of the clamped-clamped pipe is more fast than that of others.Besides, the position of the maximum amplitude of the vibration is shifted to the weak constraint when the end of restrictive condition is asymmetric.

导出引用

张挺1，林震寰1，郭晓梅1，张恒1，范佳铭2. 基于广义有限差分法的输流直管振动响应特性研究[J]. 振动与冲击, 2019, 38(24): 165-171

ZHANG Ting1,LIN Zhenhuan1,GUO Xiaomei1,ZHANG Heng1,FAN Jiaming2. Numerical simulation of vibration response of pipe conveying fluid based on a generalized finite difference method[J]. Journal of Vibration and Shock, 2019, 38(24): 165-171

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