Stability analysis of fluid conveying Timoshenko pipes resting on fractional viscoelastic foundations

This study examines the dynamic stability of short cantilevered pipes carrying flow mounted on fractional viscoelastic foundations. The Timoshenko beam theory and a fractional Zener model are employed to model the tubular structure of the pipe as well as the viscoelastic foundation. Assuming the plug-flow assumptions, the effect of fluid flow is taken into account as a laterally distributed load, being a function of the pipe's deformation states and their respective derivatives. The extended Hamilton's principle is then used to obtain the motion equations. In order to solve the given equations of motion, a combination of the extended Galerkin and Laplace methods are employed to map the differential equations of motion to a set of equivalent algebraic equations. Therefore, to obtain the non-trivial solution of the problem and the pipe's stability margins, the determinant of the coefficients of the retrieved algebraic equations is set to zero. Both real and imaginary components of the characteristic solutions are determined fora variety of parameter variations to check for stability thresholds. Several different parameters such as mass parameter, slenderness ratio, Poisson's ratio, inner-to-outer radius ratio, fractional order parameter, foundation stiffness, and damping parameters are examined and some conclusions are drawn.