DYNAMIC PROPERTIES OF A TOROIDAL SHELL WITH FLOWING INTERNAL FLUID
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Abstract
This paper investigates the dynamics of curved segments of large-diameter thin-walled pipelines modeled as a portion of a toroidal shell conveying an ideal incompressible fluid. Based on the Kirchhoff-Love hypothesis and the relations of the semi-membrane (semi-momentless) shell theory, the equations of motion are derived in toroidal curvilinear coordinates taking into account inertia forces and internal pressure. The pressure acting on the pipe wall is represented as the sum of a constant hydrostatic component and a hydrodynamic component of the flow, expressed via Legendre functions. The solution is obtained by expanding the displacement field in beam-type (fundamental) functions that satisfy the boundary conditions and the cyclicity requirement, reducing the problem to an eigenvalue problem for a matrix whose eigenvalues correspond to the squares of the natural frequencies. The influence of flow velocity, segment curvature, and the shell’s relative thickness on the natural frequencies of bending vibrations is analyzed. It is shown that within the range of practical flow velocities the effect of velocity on the natural frequencies is small, whereas increasing curvature and relative thickness leads to higher natural frequencies; for certain velocity values, frequency minima may occur, associated with increased forces and deformations.
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