摘要
研究了3:1内共振下输流管道在超临界领域的参激稳态响应.基于输流管道的非平凡静平衡位形,通过坐标代换得到超临界输流管道非线性振动的偏微分-积分控制方程.运用直接多尺度法,分析得到3:1内共振下输流管道参激振动响应的近似解析解,并用Galerkin截断法数值验证近似解析结果的可靠性.数值算例表明,内共振条件下输流管道系统不同模态间存在能量转移.通过近似解析结果预测了参激幅值对内共振条件下幅频响应曲线的影响.
The parametric vibration responses were studied in the supercritical fluid-conveying pipes in the 3 ： 1 internal resonance condition. In the control equation, the non-normal static configuration of the pipe at the supercritical velocity was introduced, and the partial differenti- al-integral control equation was obtained. The approximate analytic solution was deduced with the direct multiscale method, and the reliability of the approximate analytic results was verified with the Galerkin truncation method. Numerical examples show that, there exists energy transfer between different modes of the pipeline system in internal resonance. The influence of the parameter amplitude on the amplitude-frequency response was predicted based on approximate analytical results.
作者
张凯凯
谭霞
丁虎
陈立群
ZHANG Kaikai;TAN Xia;DING Hu;CHEN Liqun(Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University,Shanghai 200072,P.R.China;Department of Mechanics,Shanghai University,Shanghai 200444,P.R.China）（Contributed by CHEN Liqun,M.AMM Editorial Board)
出处
《应用数学和力学》
CSCD
北大核心
2018年第11期1227-1235,共9页
Applied Mathematics and Mechanics
基金
国家自然科学基金(11772181)
上海市教育委员会"曙光"计划(17SG38)
上海市教育委员会创新计划(2017-01-07-00-09-e00019)~~
关键词
输流管道
内共振
多尺度法
参激振动
超临界
fluid-conveying pipe
internal resonance
multiscale method
parametric vibra-tion
supercritical
