Galerkin模态截断对计算悬臂输液管道固有频率的影响  

Effect of Galerkin modal truncation on natural frequency analysis of a cantilevered pipe conveying fluid

作　　者：齐欢欢 徐鉴[2] 

机构地区：[1]核反应堆系统设计技术重点实验室,成都610041 [2]同济大学航空航天与力学学院,上海200092

出　　处：《振动与冲击》2011年第1期148-151,共4页Journal of Vibration and Shock

基　　金：国家杰出青年基金项目(10625211);国家自然科学基金重点项目(10532050);上海市优秀学科带头人计划资助项目(08XD14044)

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,通过割线法求解复模态的超越方程,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脱。Two methods, Galerkin method and the complex mode method, were developed to analyze natural frequency character of a cantilevered pipe conveying fluid system at different flow rate. The influence of Galerkin modal truncation to natural frequency results was analyzed. Firstly, the complex mode one was used in a simplified cantilevered system, then the complex transcendental equations were solved with the secant method, and the natural frequencies were obtained as the flow rate was varying. Secondly, the first N-order natural frequencies could be obtained approximately with Galerkin method discretizing partial differential equations into ordinal7 differential ones. Finally, comparing the results obtained with the two methods, it was found that a sufficiently accurate and appropriate model can be built with Galerkin method truncating appropriate modes, it is convenient for control system designing and engineering realization.

关 键 词：悬臂输液管道 固有频率 GALERKIN法 复模态分析 

分 类 号：O326[理学—一般力学与力学基础] TB123[理学—力学]