超临界条件下固支边界输液管的内共振

Internal Resonance of Clamped-clamped Pipes Conveying Fluid in Supercritical Range

运用摄动方法研究固支边界条件下的弹性输液管道的横向非线性振动。随着输液管道内流体流动的速度增大至临界流速以上时,输液管道的平衡位形将会发生屈曲变形,变成零静平衡解以及一对称的非零静平衡解。对于超临界管道系统的非零静平衡解的扰动方程,通过迦辽金方法截断使系统变为标准的有限维离散陀螺系统。运用离散多尺度方法以及陀螺系统的可解性条件,获得关于内共振条件下的幅值与相角方程,因而确立在超临界速度范围内输液管道横向振动幅值频率的调谐关系。通过给出超临界条件下的输液管道的数值算例,研究超临界输液管道系统内共振的存在性以及频率对振动幅值的影响。

The nonlinear vibration of clamped-clamped pipes conveying fluid was investigated in the supercritical range.If the fluid transport speed is larger than critical value,the straight equilibrium configuration becomes unstable and bifurcates into two possible curved equilibrium positions.For the motion around each bifurcated equilibrium position,Galerkin method was applied to truncate the gyroscopic continuous systems.The analysis was done by using the method of multiple scales.Finally,the conclusions drawn through the analytical results of internal resonance were discussed with respect to the effect of steady-state response.