输流弯管的面内强迫振动分析

In-plane Forced Vibration Analysis of Curved Pipe Conveying Fluid

针对承受外载荷和内部流体共同作用下两端支承式输流弯管的强迫振动问题,基于修正的不可伸长理论,根据牛顿第二运动定律建立了它的面内强迫振动微分方程,利用拉普拉斯变换法推导得到了相应的格林函数,进而结合叠加原理获得了稳态响应的解析解.主要研究了外部载荷与弯管正切方向的夹角、激振频率以及激振位置对两端支承式输流弯管切向位移稳态响应的影响.发现基于共振原理求解得到的固有频率具有较高的精度;夹角和激振位置的变化引起响应幅值的变化较为复杂;利用本方法可计算响应幅值的局部最大值产生的位置以及该值的大小.研究对设计管路的布局以及后续的可靠性设计均有良好的指导意义和较高的应用价值.

To solve the forced vibration problem the ends-supported fluid conveying curved pipe suffering both external load and internal fluid force,the linear non-homogeneous in-plane forced vibration differential equation was founded according to Newton’s second law of motion on the basis of modified inextensible theory.Laplace transform method was introduced to deduce the corresponding Green’s functions,and then combined with superposition principle,the analytical steady-state responses were obtained.Influences of drift angle between excitation and tangential direction,excitation frequency and position on steady-state responses along tangential direction were primarily investigated.The calculated natural frequency based on resonance principle is found to be accurate enough;change of drift angle and exciting position will lead to complex variation of the response amplitudes;the locations and values of local maximum response amplitudes can be worked out by the proposed method.The investigation has both good directive significance and high reference value in designing layout of the pipe and subsequent reliability design.