Nonlinear Fractional-Order Dynamic Stability of Fluid-Conveying Pipes Constituted by the Viscoelastic Materials with Time-Dependent Velocity

Considering that the fluid-conveying pipes made of fractional-order viscoelastic material such as polymeric materials with pulsatile flow are widely applied in engineering, we focus on the stability and bifurcation behaviors in parametric resonance of a viscoelastic pipe resting on an elastic foundation. The Riemann–Liouville fractional-order constitutive equation is used to accurately describe the viscoelastic property. Based on this, the nonlinear governing equations are established according to the Euler–Bernoulli beam theory and von Karman’s nonlinearity, with using the generalized Hamilton’s principle. The stability boundaries and steady-state responses undergoing parametric excitations are determined with the aid of the direct multiple-scale method. Some numerical examples are carried out to show the effects of fractional order and viscoelastic coefficient on the stability region and nonlinear bifurcation behaviors. It is noticeable that the fractional-order viscoelastic property can effectively reconstruct the dynamic behaviors, indicating that the stability of the pipes can be conspicuously enhanced by designing and tuning the fractional order of viscoelastic materials.