Flexural Vibrations of Fluid-Filled Circular Cylindrical Shells

Using exact three dimensional equations of linear elasticity, the frequency equation for the vibrations of a fluid-filled circular cylindrical shell of homogeneous, isotropic material and having a circumferential symmetry of order n has been derived. The frequency equation has been qualitatively analysed to study the flexural vibrations (n = 1) of empty and fluid-filled shells of different thicknesses. Besides propagating modes, the analysis also includes attenuating modes. It has been observed that the effect of the fluid is negligible on the vibrations of thick shells. But as the thickness of the shell decreases, the presence of fluid gives extra modes of vibrations. In the attenuating region, the frequency spectra of fluid-filled shells behave either like the spectra of an empty shell or like the spectra of a fluid column with rigid walls.