Response of an infinitely long cylindrical shell with a convected internal fluid

Abstract

The response of an infinitely long cylindrical shell excited by a point force, with an internal heavy medium (water) moving with a constant flow speed is examined. The solution is obtained by linearizing the differential equations describing the behavior of the fluid and the structure by using a spatial Fourier transform in the axial direction and a modal decomposition in the circumferential direction. The inverse Fourier transform of the solution of the linear set of equations gives the coupled solution for the shell/fluid system. Using this solution, input and transfer mobility functions are determined for a copper pipe of radius 0.025 m and wall thickness 1.5 min. For the input mobility functions, the nearfield effects combine with the coriolis effects of the moving fluid to produce instabilities of the circumferential modes at velocities that depend upon the mode number. For the transfer mobility functions, broadband peaks appear caused by the phase lag between waves of different circumferential mode numbers. These peaks are shifted and modified as the flow speed changes.