Vibration around non-trivial equilibrium of a supercritical Timoshenko pipe conveying fluid

Vibration characteristics of pipes conveying fluid in the super-critical range are investigated by using Timoshenko beam theory for the first time. Generalized Hamiltonian principle is applied to derive the nonlinear transverse vibration governing equation. The non-trivial static equilibrium configuration and critical flow velocity of the pipe are analytically deduced. These analytical results are verified by using the finite difference method. Compared with Euler-Bernoulli flow pipeline, it is found that the equilibrium configuration of Timoshenko pipe is larger. In the supercritical regime, natural frequencies of the Timoshenko flow pipe are produced by the Galerkin truncation method. Numerical examples illustrate that vibration characteristics of the pipe are highly sensitive to length, thickness, shear modulus and velocity. The relative difference between the two pipe models is influenced by the velocity of the flow and is likely to exceed 100%. In general, this work found that the flow velocity makes the Timoshenko beam theory even more needed for researching vibration properties of pipes conveying fluid, especially at a high velocity.