This paper investigates theoretically for the first time the dynamical behavior and stability of a simply supported shell located coaxially in a rigid cylindrical conduit. The fluid flow is incompressible and the fluid forces consist of two parts: (i) steady viscous forces which represent the effects of upstream pressurization of the flow; (ii) unsteady forces which could be inviscid or viscous. The inviscid forces were derived by linearized potential flow theory, while the viscous ones were derived by means of the Navier-Stokes equations. Shell motion is described by the modified Flu¨gge’s shell equations. The Fourier transform technique is employed to formulate the problem. First, the system is subjected only to the unsteady inviscid forces. It is found that increasing either the internal or the annular flow velocity induces buckling, followed by coupled mode flutter. When both steady viscous and unsteady inviscid forces are applied, for internal flow, the system becomes stabilized; while for annular flow, the system loses stability at much lower velocities. Second, the system is only subjected to the unsteady viscous forces. Calculations are only performed for the internal flow case. The results are compared to those of inviscid theory. It is found that the effects of unsteady viscous forces on the stability of the system are very close to those of unsteady inviscid forces.
On the Dynamics and Stability of Cylindrical Shells Conveying Inviscid or Viscous Fluid in Internal or Annular Flow
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Chebair, A. E., and Misra, A. K. (August 1, 1991). "On the Dynamics and Stability of Cylindrical Shells Conveying Inviscid or Viscous Fluid in Internal or Annular Flow." ASME. J. Pressure Vessel Technol. August 1991; 113(3): 409–417. https://doi.org/10.1115/1.2928775
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