Influence of fluid viscosity and pressure on shell vibrations in a fluid (Q1117748)

It is shown that for a broad class of problems in shell theory the fluid viscosity can be taken into account by separating the system of viscous fluid equations into two subsystems, one of which is integrated in quadratures by taking account of the viscosity, while the other agrees with the Helmholtz equation. Consequently, the related problem for a shell making contact with a fluid is reduced to integration of the equations of shell theory with certain additional terms in combination with the Helmholtz equation. It is clarified that the hydrostatic fluid pressure only affects the resonance frequencies and the amplitudes of those vibrations that satisfy the definite conditions formulated.