Winkler地基上黏弹性输流管的参数共振稳定性

本文研究了黏弹性输流管在Winkler地基上的横向振动。管道的黏弹性材料用Kelvin本构关系描述，在两端铰支边界条件下，对系统的控制方程应用直接多尺度法建立相应的可解性条件，得到了系统次谐波共振和组合共振的稳定性边界条件，考察了系统的各种参数如阻尼、脉动流速、质量比、弹性地基对稳定性边界条件的影响。

DYNAMIC STABILITY IN PARAMETRIC RESONANCE OF VISCOELASTIC PIPES CONVEYING PULSATING FLUID ON WINKLER ELASTIC FOUNDATION

The dynamic stability in transverse vibration of a viscoelastic pipe on Winkler elastic foundation for conveying pulsating fluid is investigated for the simply-supported case. The pipe’s material obeys the Kelvin model in which the material time derivative is used. The axial fluid speed is characterized as simple harmonic variation about a constant mean speed. When the viscoelastic damping and the periodical excitation are considered small, the method of multiple scales is applied directly to the governing equation to establish the solvability conditions in summation and principal parametric resonances. The effects of the pulsating fluid flow velocity, damping coefficient, mass ratios of the parametric instability are discussed. Some numerical examples are presented to demonstrate the effects of related parameters on the stability boundaries.