The dynamic stability of transverse vibration for a viscoelastic pipe conveying pulsating fluid on Winkler elastic foundation was investigated under a simply-supported boundary condition.The pipe's material obeys Kelvin constitutional relation with material time derivative used.The axial fluid speed was characterized as a simple harmonic variation about a constant mean speed.When the viscoelastic damping and the periodical excitation were considered small,the method of multi-scale was applied directly to the governing equation to establish the solvability conditions of parametric resonances.The effects of pulsating fluid flow velocity,damping coefficient and mass ratios on the parametric instability were discussed.Some numerical examples were presented to demonstrate the effects of related parameters on the stability boundaries.%研究黏弹性输流管在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.
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