Effects of Material Characteristics on Nonlinear Dynamics of Viscoelastic Axially Functionally Graded Material Pipe Conveying Pulsating Fluid

Abstract

The nonlinear dynamic behaviors of viscoelastic axially functionally graded material (AFG) pipes conveying pulsating internal flow are very complex. And the dynamic behavior will induce the failure of the pipes, and research of vibration and stability of pipes becomes a major concern. Considering that the elastic modulus, density, and coefficient of viscoelastic damping of the pipe material vary along the axial direction, the transverse vibration equation of the viscoelastic AFG pipe conveying pulsating fluid is established based on the Euler-Bernoulli beam theory. The generalized integral transform technique (GITT) is used to transform the governing fourth-order partial differential equation into a nonlinear system of fourth-order ordinary differential equations in time. The time domain diagram, phase portraits, Poincaré map and power spectra diagram at different dimensionless pulsation frequencies, are discussed in detail, showing the characteristics of chaotic, periodic, and quasi-periodic motion. The results show that the distributions of the elastic modulus, density, and coefficient of viscoelastic damping have significant effects on the nonlinear dynamic behavior of the viscoelastic AFG pipes. With the increase of the material property coefficient k, the transition between chaotic, periodic, and quasi-periodic motion occurs, especially in the high-frequency region of the flow pulsation.

Keywords

Axially functionally graded pipe / Pipe conveying pulsating flow / Integral transforms / Nonlinear dynamics / Chaotic motion / Quasi-periodic motion