粘弹性地基上粘弹性输流管道的稳定性分析

从Winkler假设和单轴线性粘弹性本构方程出发，推导了Kelvin-Voigt粘弹性地基上三参量固体模型输流管道的运动微分方程，采用改进的有限差分法，分析了管道和地基的粘弹性参数对输流管道无量纲复频率和无量纲流速之间的变化关系的影响。

Stability analyses of viscoelastic pipes conveying fluid on viscoelastic foundation

Based on Winkler assumption and uniaxial linear viscoelastic constitutive relation,a differential equation of motion for viscoelastic pipes conveying fluid with three-parameter solid model on foundation with Kelvin-Voigt model is derived.Using the finite difference method,let the pipes conveying fluid be subdivided into several equal-length segments.The mesh points should be taken at the center of each segment.Introducing the displacement vector and transfer matrix,the difference equations can be rewritten as the recurrence formula.For the simply supported viscoelastic pipes conveying fluid with three-parameter solid model, nonlinear equation systems including dimensionless complex frequency,dimensionless flow velocity,dimensionless relaxation time of the foundation,mass ratio, dimensionless relaxation coefficient of the pipes conveying fluid and other parameters,are obtained by discomposing the complex eigen-equation into real part and imaginary part.Variations of the real part and imaginary part of the dimensionless complex frequencies of the system with dimensionless flow velocity for various different parameters are obtained from the above-mentioned nonlinear equation systems,and effects of the viscoelastic material parameters on vibration and stability of pipes conveying fluid are discussed.