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.
出处
《噪声与振动控制》
CSCD
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)
