Longitudinal-radial vibrations of a elastic cylindrical shell filled with a viscous compressible liquid

In this paper, the longitudinal-radial vibrations of the elastic cylindrical shell filled with a viscous compressible fluid are studied using the mathematical model proposed. The general equations for the longitudinal-radial vibrations of the shell made of the homogeneous and isotropic material are derived. These equations can be used to obtain refined equations of vibrations. The proposed algorithm allows one to uniquely determine the stress-strain state of points in any section of the considered hydroelastic system using the field of the required functions in coordinates and time. The benchmark problem of harmonic oscillations in a cylindrical shell with a viscous fluid is solved. The dependences of the frequency on the wave number are obtained for various shell- fluid interaction cases.