The equations of motion of initially stressed Timoshenko tubular beams conveying fluid

Abstract In this paper the equations of motion of an initially stressed Timoshenko tubular beam subjected to a tensile follower load and conveying fluid are derived by using the appropriate statement of Hamilton's principle. This latter is obtained first for “open” systems, the instantaneous total mass of which does not necessarily remain constant in the course of deformation—“open” denoting that there is momentum transport in and out of the system. The equations of motion are derived separately for a cantilevered system and for one with both extremities of the tube clamped. Yet another derivation for the cantilevered tube is presented with the system considered to be quasi-closed, where all flow-induced effects are incorporated through the virtual work, as if they were “external” forces. All three sets of equations are found to be identical. These equations are then compared with those obtained, more simply, by the Newtonian force-balance approach. Some differences between them are found to exist, the principal of which are associated with the follower or other tensile forces; these are discussed at some length, and the equations of motion obtained here are compared to those obtained by other researchers for Timoshenko beams subjected to follower or tensile forces.

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