Nonlinear vibration analysis of a fractional dynamic model for the viscoelastic pipe conveying fluid

Abstract

• A new non-linear, fractional dynamic model of the viscoelastic pipe is established. • Analytical solutions of the fractional model are derived using the method of multiple scales. • The amplitude predicted by the fractional model is much larger than that predicted by the previous model. • With the fractional order increase, the nonlinear frequency increases at first and then diminishes. • The fractional order can change the variation trend of the amplitude versus the fluid velocity. The nonlinear free vibration of a fractional dynamic model for the viscoelastic pipe conveying fluid is studied in this paper. The dynamic equations of coupled planar motion for the pipe are derived by employing the Euler beam theory and the generalized Hamilton principle when we consider both the fractional material model and the geometric non-linearity. Then the equations are simplified into a new nonlinear, fractional order dynamic model governing transverse vibration of the pipe in small but limited stretching issues. The method of multiple scales is directly applied for the analysis and simulation of the nonlinear vibration. Numerical results show the influence of the factional order, the mass ratio, the fluid velocity and the nonlinear coefficient on the nonlinear amplitudes and frequencies of the viscoelastic pipe. It is noticeable that the amplitudes of the fluid-conveying pipe constituted by the fractional viscoelastic material model display much higher than those predicted by the previous models.