噪声与振动控制
譟聲與振動控製
조성여진동공제
NOISE AND VIBRATION CONTROL
2014年
2期
8-11
,共4页
黄慧春%张艳雷%陈立群
黃慧春%張豔雷%陳立群
황혜춘%장염뢰%진립군
振动与波%内共振%Galerkin%多尺度%Runge-Kutta
振動與波%內共振%Galerkin%多呎度%Runge-Kutta
진동여파%내공진%Galerkin%다척도%Runge-Kutta
vibration and wave%internal resonance%Galerkin%multi-scale%Runge-Kutta
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。
研究在超臨界下受迫輸液管2：1內共振的動力學響應特性。噹內流速超過臨界值時，繫統形成新的麯線平衡位形。通過Galerkin截斷方法使繫統變為有限低維離散的繫統，再採用多呎度近似解析方法，穫得關于超臨界條件下受迫輸液管的響應特性。通過具體的數值算例，髮現內共振附近繫統齣現Hopf分岔現象。通過Runge-Kutta數值方法，繪製瞭時間歷程和相平麵圖繫統的展示分岔前與分岔後的情況。
연구재초림계하수박수액관2：1내공진적동역학향응특성。당내류속초과림계치시，계통형성신적곡선평형위형。통과Galerkin절단방법사계통변위유한저유리산적계통，재채용다척도근사해석방법，획득관우초림계조건하수박수액관적향응특성。통과구체적수치산례，발현내공진부근계통출현Hopf분차현상。통과Runge-Kutta수치방법，회제료시간역정화상평면도계통적전시분차전여분차후적정황。
The dynamic response behavior of a fluid-conveying pipe under supercritical fluid velocity is investigated by taking 1:2 internal resonances into account. The equilibrium configuration of the system can bifurcate into multiple equilibrium positions when the fluid velocity exceeds the critical value. The partial differential equation of the system is discretized into several equations via the Galerkin’s truncation method. These equations are then numerically solved by the multi-scale method. Attention is concentrated on the possible response of the system with different governing dimensionless parameters. Finally, the cumulative effect of frequency on the internal resonance is studied and the Hopf bifurcation is briefly discussed. Dynamic response of the system in the vicinity of Hopf bifurcation is presented in the form of time histories and phase plane trajectories via the Runge-Kutta numerical method.
