Analysis of dispersion characteristics of an infinite cylindrical shell submerged in viscous fluids considering hydrostatic pressure

In previous investigations of the vibro-acoustic characteristics of a submerged cylindrical shell in a flow field, the fluid viscosity was usually ignored. In this paper, the effect of fluid viscosity on the vibrational dispersion characteristics of an infinite circular cylindrical shell immersed in a viscous acoustic medium and subject to hydrostatic pressure is studied. The Flügge's thin shell theory for an isotropic, elastic, and thin cylindrical shell is employed to obtain the equations of motion of the structure. Together with the wave equations for the viscous flow field as well as continuity conditions at the interface, the dispersion equation of the coupled system is derived. Numerical analysis based on a winding-number integral method is conducted to solve the dispersion equation for the shell loaded with viscous fluids with varying levels of viscosity. Then the variations of the dispersion characteristic, the amplitude ratio of complex waves and the relative difference parameter against the nondimensional axial wave number in the coupled system with different circumferential mode numbers are discussed in detail. It is found that the influence of fluid viscosity on dispersion characteristics of the propagating waves is more significant in the low-frequency range than at high frequencies. As for the complex waves, the amount of the waves in the coupled system and the cut-off frequency is dependant on the fluid viscosity coefficients.