Response of Fluid-Elastically Coupled Coaxial Cylindrical Shells to External Flow

The dynamics of a system of two fluid-elastically coupled coaxial cylindrical shells is studied theoretically. The general equations of motion for free and forced-damped vibration are derived in terms of virtual mass, coupling coefficients, and uncoupled natural frequencies of the individual cylindrical shells. For free vibration, numerical solutions to the coupled equations of motion are given as a function of these parameters. For forced-damped vibration, solution is given to the special case when the external force is a normal one acting on the surface of the outer shell, such as the dynamic pressure forces arising from an external turbulent axial flow. It is shown that the coupled system can then be reduced to an equivalent single cylindrical shell. However, the effective force acting on the equivalent single cylinder, as well as its natural frequencies and effective damping ratios, are all modified from the corresponding uncoupled values. The response of the system can then be predicted by established methods in flow-induced random vibration analysis. Curves are included. The study aims mainly at applications to the vibration analysis of hydraulically coupled internal components of a pressurized nuclear reactor but is general enough to find application in other engineering disciplines.