超临界下受迫输液管2:1内共振的响应特性  

Resonance Analysis of a Forced Fluid-conveying Pipe with 2:1 Internal Resonances under Supercritical Fluid Velocity

作　　者：黄慧春[1] 张艳雷[1] 陈立群[2,3] 

机构地区：[1]上海第二工业大学,上海201209 [2]上海大学上海市应用数学和力学研究所,上海200072 [3]上海大学力学系,上海200444

出　　处：《噪声与振动控制》2014年第2期8-11,共4页Noise and Vibration Control

基　　金：国家杰出青年科学基金:(10725209);国家自然科学基金:(10902064);上海市优秀学科带头人计划:(09XD1401700)

摘　　要：研究在超临界下受迫输液管2:1内共振的动力学响应特性。当内流速超过临界值时,系统形成新的曲线平衡位形。通过Galerkin截断方法使系统变为有限低维离散的系统,再采用多尺度近似解析方法,获得关于超临界条件下受迫输液管的响应特性。通过具体的数值算例,发现内共振附近系统出现Hopf分岔现象。通过Runge–Kutta数值方法,绘制了时间历程和相平面图系统的展示分岔前与分岔后的情况。The dynamic response behavior of a fluid-conveying pipe under supercritical fluid velocity is investigated bytaking 1：2 internal resonances into account. The equilibrium configuration of the system can bifurcate into multipleequilibrium positions when the fluid velocity exceeds the critical value. The partial differential equation of the system isdiscretized into several equations via the Galerkin’s truncation method. These equations are then numerically solved by themulti-scale method. Attention is concentrated on the possible response of the system with different governing dimensionlessparameters. Finally, the cumulative effect of frequency on the internal resonance is studied and the Hopf bifurcation isbriefly discussed. Dynamic response of the system in the vicinity of Hopf bifurcation is presented in the form of timehistories and phase plane trajectories via the Runge-Kutta numerical method.

关 键 词：振动与波 内共振 GALERKIN 多尺度 RUNGE-KUTTA 

分 类 号：O32[理学—一般力学与力学基础]