Stability analysis of oil-conveying pipes on two-parameter foundations with generalized boundary condition by means of Green's functions

This paper mainly concentrates on obtaining the explicit solutions of the forced vibrations of oil-conveying pipes on two-parameter foundations and studying the stabilities of these pipes. With the assistance of the Euler-Bernoulli assumption, the dynamic equations of the pipes are modelled by means of Hamilton's principle. The generalized boundary condition (BC), which can be reduced to many different simple BCs, is considered in the vibration problems. Green's function and the superposition property of linear vibrations are employed to derive the analytical solutions, and the Laplace transforms are applied with intention of gaining the Green's functions under various BCs. In the numerical section, the present solutions are validated by comparing with the results in the other literature. In addition, the effects of some important physical parameters, for instance boundary stiffness, foundation parameters, geometric parameters, etc., on the natural frequencies and the critical flow velocities are discussed as well.