超临界流速下两端固定输流管道横向非线性受迫振动

Transverse nonlinear forced vibration of pipe conveying supercritical fluid with both fixed ends

研究横向谐波激励作用下两端固定输流管道在超临界流速下的非线性受迫振动,采用Euler-Bernoulli梁理论,运用广义哈密顿原理建立输流管道横向受迫振动控制方程。推导两端固定输流管道的屈曲静平衡位形和临界流速。通过有限差分法数值仿真得到输流管道在超临界流速下的全局振动稳态幅频响应。通过分析全局稳态振动响应,验证屈曲静平衡位形的正确性。此外,系统参数对超临界输流管道受迫振动稳态响应的影响表明非线性系数和刚度系数会显著影响输流管道的超临界振动平衡位置;管流质量比的减小会使共振频率增大。

Transverse nonlinear forced vibration of a pipe with both fixed ends conveying high velocity fluid are studied.Applying Euler-Bernoulli beam theory,the governing equation of motion of the pipe conveying fluid subjected to harmonic excitation is established by using generalized Hamilton’s principle.The non-trivial static equilibrium configuration and critical velocity of the pipe conveying fluid are derived.By analyzing the global steady-state vibration response,the correctness of the non-trivial static equilibrium configuration and is verified.In addition,the influence of system parameters on the steady-state vibration response in the supercritical regime are presented.The results show that the nonlinear coefficient and stiffness coefficient can significantly affect the equilibrium position of vibration in the supercritical regime.The resonance frequency increases when the mass ratio of pipe flow decreases.