STABILITY ANALYSIS OF MAXWELL VISCOELASTIC PIPES CONVEYING FLUID WITH BOTH ENDS SIMPLY SUPPORTED

On the basis of some studies of elastic pipe conveying fluid, the dynamic behavior and stability of Maxwell viscoelastic pipes conveying fluid with both ends simply supported, which are gyroscopic conservative system, were investigated by using the finite difference method and the corresponding recurrence formula. The effect of relaxation time of vis coelastic materials on the variation curve between dimensionless flow velocity and the real part and imaginary part of dimensionless complex frequencies in the first-three-order modes were analyzed concretely. It is found that critical flow velocities of divergence instability of Maxwell viscoelastic pipes conveying fluid with both ends simply supported decrease with the decrease of the relaxation time, while after the onset of divergence instability ( buckling) critical flow velocities of coupled-mode flutter increase with the decrease of the relaxation time. Particularly, in the case of greater mass ratio. with the decrease of relaxation time, the onset of coupled-mode flutter delays, and even does not take place. When the relaxation time is greater than 10(3), stability behavior of viscoelastic pipes conveying fluid is almost similar to the elastic pipes conveying fluid.

STABILITY ANALYSIS OF VISCOELASTIC CURVED PIPES CONVEYING FLUID

Based on the Hamilton' s principle for elastic systems of changing mass, a differential equation of motion for viscoelastic curved pipes conveying fluid was derived using variational method, and the complex characteristic equation for the viscoelastic circular pipe conveying fluid was obtained by normalized power series method. The effects of dimensionless delay time on the variation relationship between dimensionless complex frequency of the clamped-clamped viscoelastic circular pipe conveying fluid with the Kelvin-Voigt model and dimensionless flow velocity were analyzed. For greater dimensionless delay time, the behavior of the viscoelastic pipe is that the first, second and third mode does not couple, while the pipe behaves divergent instability in the first and second order mode, then single-mode flutter takes place in the first order mode.

THE DYNAMIC BEHAVIORS OF VISCOELASTIC PIPE CONVEYING FLUID WITH THE KELVIN MODEL

Based on the differential constitutive relationship of linearviscoelastic material, a solid-liquid coupling vibration equation forviscoelastic pipe conveying fluid is derived by the D'Alembert'sprinciple. The critical flow velocities and natural frequencies ofthe cantilever pipe conveying fluid with the Kelvin model (flutterinstability) are calculated with the modified finite differencemethod in the form of the recurrence for- mula. The curves betweenthe complex frequencies of the first, second and third mode and flowvelocity of the pipe are plotted. On the basis of the numericalcalculation results, the dynamic behaviors and stability of the pipeare discussed. It should be pointed out that the delay time ofviscoelastic material with the Kelvin model has a remarkable effecton the dynamic characteristics and stability behaviors of thecantilevered pipe conveying fluid, which is a gyroscopicnon-conservative system.

Nonlinear Dynamic Analysis of A Viscoelastic Pipe Conveying Fluid

Incremental harmonic balance method (IHBM) is applied to geometrically nonlinear vibration analysis of a simply supported pipe conveying fluid. the material of which is viscoelastic of the Kelvin- Voigt type. Some unstable phenomena - the appearance of the peak or jumps in the pipe's amplitude frequency curves, which are considered to be of importance to this kind of structure, are presented in the numerical results, and the influence of several parameters of the system on the dynamic characteristic of the pipe are also studied. It is believed that this is the first attempt to search for the periodic solution of the pipe and its intrinsic property with such a method.

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.