Galerkin模态截断对计算悬臂输液管道固有频率的影响

齐欢欢;徐鉴

振动与冲击 ›› 2011, Vol. 30 ›› Issue (1) : 148-151.

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PDF(1156 KB)
振动与冲击 ›› 2011, Vol. 30 ›› Issue (1) : 148-151.
论文

Galerkin模态截断对计算悬臂输液管道固有频率的影响

  • 齐欢欢1; 徐鉴2
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Effect of Galerkin Modal Truncation on Natural Frequency Analysis of Cantilevered Pipe Conveying Fluid

  • QI Huan-huan1;XU Jian2
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摘要

通过Galerkin方法和复模态方法研究悬臂输液管道在不同流速下固有频率的变化情况,通过比较说明Galerkin模态截断对输液管道固有频率计算结果的影响。首先利用复模态方法(精确的方法)分析简化的输液管控制模型,通过割线法求解复的超越方程,求得简化系统在不同流速下的固有频率;然后利用Galerkin方法将无简化的系统偏微分控制方程离散化为常微分方程组,可以得到系统的前N阶固有频率;最后通过对两种方法求解结果的比较发现:通过Galerkin法截取适当的模态,可建立一个能比较精确地反映真实系统动力学特性的低阶模型,便于进行控制系统的设计和工程实现。

Abstract

: Two methods, Galerkin method and complex mode method, are developed to analyze natural frequency character of cantilevered pipe conveying fluid system at different flow rate. The influence of Galerkin modal truncation to natural frequency results is analyzed. Firstly, complex mode is used in a simplified cantilevered system, then the complex transcendental equations are solves by secant method, and the natural frequencies are obtained as flow rate varying. Secondly, the first N-order natural frequencies can be obtained approximately by Galerkin method which discretizes partial differential equations into ordinary differential. Finally, comparing the results that obtained by two methods, we can found that a sufficient exact appropriate model can be build by Galerkin method truncating appropriate mode, what facilitates control system designing and engineering practice.

关键词

悬臂输液管道 / 固有频率 / Galerkin / 复模态分析

Key words

  1. cantilevered pipe conveying fluid
/ natural frequency / Galerkin method / complex mode method

引用本文

导出引用
齐欢欢;徐鉴. Galerkin模态截断对计算悬臂输液管道固有频率的影响[J]. 振动与冲击, 2011, 30(1): 148-151
QI Huan-huan;XU Jian. Effect of Galerkin Modal Truncation on Natural Frequency Analysis of Cantilevered Pipe Conveying Fluid[J]. Journal of Vibration and Shock, 2011, 30(1): 148-151

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