Nonlinear vibrations of a slightly curved Maxwell viscoelastic pipe conveying two phase flow under various boundary conditions.

Two phase flows are common in pipeline engineering, and most times, the assumption of single phase flow is usually assumed. In this paper, the dynamics of a slightly curved Maxwell viscoelastic pipe conveying two phase flow under four boundary conditions; cantilever, simple supported, clamped simply supported and clamped clamped supported is investigated. Eigenfunction expansion was used to discretize the PDE into four modes. The linear analysis results show that the Maxwell viscoelastic parameter has no significant effect on the first and the second modes of the vibration, but on the third and fourth modes for the three boundaries conditions considered. The void fraction has effects on the frequency and critical velocity only if the densities of the components of the two phase fluid are significantly large. The nonlinear dynamics shows that Maxwell viscoelastic parameter reduces the bifurcation position and changes the bifurcation point from being sharp to a gentle curve at the bifurcation point. Further results were presented for the Maxwell parameter and velocity of fluid and temperature loading on the pipe, which are very important to understanding the behavior of Maxwell viscoelastic pipe conveying two phase flow. • Vibrations of a slightly curved Maxwell viscoelastic pipe conveying two phase flow are investigated. • The governing equation for the pipe is derived based on Hamilton's principle. • The two-phase components densities determine whether the flow can be classified as single phase or two phase. • Maxwell parameter tends to affect the response of the nonlinear system significantly when the value ranges from zero to 50. [ABSTRACT FROM AUTHOR]