受迫振动的超临界输液管Galerkin数值模拟

黄慧春; 张艳雷; 陈立群

doi:10.3879/j.issn.1000-0887.2014.10.004

受迫振动的超临界输液管Galerkin数值模拟

doi: 10.3879/j.issn.1000-0887.2014.10.004

¹上海第二工业大学工学部, 上海 201209;²上海大学力学系, 上海 200072

基金项目: 国家自然科学基金(11302122);上海高校青年教师培养资助计划(ZZEGD13011)

详细信息

作者简介:
黄慧春（1961—），女，江苏人，副教授(Tel: +86-21-50215021-8216;E-mail: hchuang@sspu.edu.cn);张艳雷（1980—），男，山西人，博士(通讯作者. Tel: +86-21-50215021-8216;E-mail: ylzhang@sspu.edu.cn).

中图分类号: O322
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出版历程
- 收稿日期: 2014-04-22
- 修回日期: 2014-09-10
- 刊出日期: 2014-10-15

A Galerkin Numerical Method for the Pipe Conveying Supercritical Fluid Under Forced Vibration

¹College of Engineering, Shanghai Second Polytechnic University, Shanghai 201209, P.R.China;²Department of Mechanics, Shanghai University, Shanghai 200072, P.R.China

Funds: The National Natural Science Foundation of China(11302122)

摘要

摘要: 当流速超过临界值，输液管的直线平衡位形会发生失稳，但是系统会重新稳定在新的曲线平衡位置.通过引入坐标变换的方法，动力学模型转变为含有变系数的偏微分控制方程.采用4阶Galerkin截断的方法，使控制方程转变为常微分方程.给出具体的数值算例，发现4阶截断的固有频率要比2阶截断的固有频率更精确.同时，计算出前两阶固有频率出现可公度的情况，从而激发2∶1内共振现象.利用Runge-Kutta数值模拟的方法，在发生内共振流速范围的特定区域进行大量数值运算，结果表明高维系统的条件下，管道的不同径向坐标点的横向位置处，均出现软硬特性，而在内外共振完全调谐时，出现双跳跃现象.
- 超临界 /
- Galerkin方法 /
- 内共振 /
- 软硬特性 /
- 双跳跃
Abstract: For the pipe conveying fluid, as the flow rate increased over a critical value, the equilibrium configuration was found to get unstable and bifurcate into curved equilibrium patterns. The nonlinear dynamic model for the simply-supported pipe was built and converted to variable-coefficient partial differential control equations through coordinate transformation. The 4-term Galerkin truncation procedure was then applied and the control equations of motion were transformed to 2nd-order ordinary differential equations to be solved with numerical techniques. The natural frequencies of the simply-supported pipe conveying fluid were calculated, and the result comparison was made between the 2-term and 4-term Galerkin truncation methods to give that the latter had higher accuracy. For specific system parameters, the 2nd-order natural frequency was approximately two times of the 1st-order one within a certain range of flow velocity, and the 2-to-1 internal resonance occurred. Massive computation of the amplitude-frequency responses of the pipe conveying fluid before and after internal resonance was conducted with the Runge-Kutta numerical technique. The results show that, as the flow rate and tuning parameter vary, the softening, hardening and double jumping phenomena will be respectively identified by the amplitude-frequency responses of the pipe.
- supercritical fluid /
- Galerkin procedure /
- internal resonance /
- softening and hardening /
- double jumping

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参考文献(20)

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受迫振动的超临界输液管Galerkin数值模拟

doi: 10.3879/j.issn.1000-0887.2014.10.004

作者简介:
黄慧春（1961—），女，江苏人，副教授(Tel: +86-21-50215021-8216;E-mail: hchuang@sspu.edu.cn);张艳雷（1980—），男，山西人，博士(通讯作者. Tel: +86-21-50215021-8216;E-mail: ylzhang@sspu.edu.cn).

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A Galerkin Numerical Method for the Pipe Conveying Supercritical Fluid Under Forced Vibration

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留言板

受迫振动的超临界输液管Galerkin数值模拟

doi: 10.3879/j.issn.1000-0887.2014.10.004

作者简介: 黄慧春（1961—），女，江苏人，副教授(Tel: +86-21-50215021-8216;E-mail: hchuang@sspu.edu.cn);张艳雷（1980—），男，山西人，博士(通讯作者. Tel: +86-21-50215021-8216;E-mail: ylzhang@sspu.edu.cn).

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出版历程

A Galerkin Numerical Method for the Pipe Conveying Supercritical Fluid Under Forced Vibration

计量

出版历程

目录

作者简介:
黄慧春（1961—），女，江苏人，副教授(Tel: +86-21-50215021-8216;E-mail: hchuang@sspu.edu.cn);张艳雷（1980—），男，山西人，博士(通讯作者. Tel: +86-21-50215021-8216;E-mail: ylzhang@sspu.edu.cn).