Vibration analysis of pipes conveying fluid resting on a fractional Kelvin-Voigt viscoelastic foundation with general boundary conditions

Abstract

In this paper, the stability of pipes conveying fluid with viscoelastic fractional foundation is investigated. The pipe is fixed at the beginning while the pipe end is constrained with two lateral and rotational springs. The fluid flow effect is modeled as a lateral distributed force, containing the fluid inertia, Coriolis and centrifugal forces. The pipe is modeled using the Euler-Bernoulli beam theory and a fractional Kelvin-Voigt model is employed to describe the viscoelastic foundation. The equation of motion is derived using the extended Hamilton’s principle. Presenting the derived equation in Laplace domain and applying the Galerkin method, a set of algebraic equations is extracted. Calculating the determinant of the coefficients of the extracted algebraic equations results in the stability margin of the pipe. Some run is done and effects of some physical parameters such as stiffness and damping of fractional viscoelastic foundation, fractional order parameter and the end lateral and rotational stiffness of end springs on the stability boundary of the pipe are considered and some conclusions are drawn.