Abstract
The free vibrations of an infinitely long cylindrical shell under axisymmetrical hydrodynamic pressures due to external and internal fluids are studied theoretically. The basic equations of motion for axisymmetric vibrations of such a shell are given, based on the bending theory. These equations are solved analytically by means of Fourier cosine transformation, and the general frequency equation for the coupled systems is obtained by consideration of the dynamic interaction between the shell surface and fluids. Furthermore, seven special cases are derived from the general coupled frequency equation. The general frequency equation is calculated for some kinds of mass density of the internal fluid. Hence, it is shown that the effect of the motion of the external and internal fluids on the free vibrations of a shell is notable.
