Free Vibration of Fluid-Coupled Coaxial Cylindrical Shells of Different Lengths

Abstract

This paper considers the free vibration of two coaxial cylinders with finite lengths immersed in a restricted fluid medium. The general coupled equations of motion are derived. Qualitative study of the governing differential equation shows that only modes of the cylinders with their axial mode numbers directly proportional to their lengths are coupled. For the uncoupled modes, each cylinder vibrates as if the other one is rigid, and the only effect of fluid loading is an apparent increase in its mass (virtual mass effect). The natural frequencies in the fluid can then be computed by including the virtual mass to its physical mass. Experimental results have been used to verify the analysis. Agreement between experimental and theoretical results is excellent.