受迫振动的超临界输液管Galerkin数值模拟  

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

作　　者：黄慧春[1] 张艳雷[1] 陈立群[2] 

机构地区：[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

出　　处：《应用数学和力学》2014年第10期1100-1106,共7页Applied Mathematics and Mechanics

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

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.For the pipe conveying fluid, as the flow rate increased over a critical value, the e- quilibrium configuration was found to get unstable and bifurcate into curved equilibrium pat- terns. 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 tech- niques. 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 meth- ods to give that the latter had higher accuracy. For specific system parameters, the 2nd-order natural frequency was approximately two times of the lst-order one within a certain range of flow velocity, and the 2-to-1 internal resonance occurred. Massive computation of the ampli- tude-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 re- spectively identified by the amplitude-frequency responses of the pipe.

关 键 词：超临界 GALERKIN方法 内共振 软硬特性 双跳跃 

分 类 号：O322[理学—一般力学与力学基础]