The subject of this paper is the study of dynamics and stability of a pipe flexibly supported at its ends and conveying fluid. First, the equation of motion of the system is derived via the extended form of Hamilton’s principle for open systems. In the derivation, the effect of flexible supports, modelled as linear translational and rotational springs, is appropriately considered in the equation of motion rather than in the boundary conditions. The resulting equation of motion is then discretized via the Galerkin method in which the eigenfunctions of a free-free Euler-Bernoulli beam are utilized. Thus, a general set of second-order ordinary differential equations emerge, in which, by setting the stiffness of the end-springs suitably, one can readily investigate the dynamics of various systems with either classical or non-classical boundary conditions.

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