Vibrations Of Infinitely Long Cylindrical Shells Under Initial Stress PDF Download

A method is presented which permits the determination of the frequencies of vibrations of infinitely long thin cylindrical shells in an acoustic medium. Expressions are obtained for the displacements of the shell and for the pressures in the medium in the case of forced vibrations due to sinusoidally distributed radial forces. The results indicate that there is a low-frequency range, where no radiation takes place, and a high-frequency range where the external force provides energy which is radiated. Resonance occurs in the low-frequency range only; in the high-frequency range it is prevented by the damping due to radiation. Free and forced vibrations of steel shells submerged in water are discussed; with limitations, the theory may be applied approximately to stiffened shells. The method requires only a minor modification to account for the effect of static pressure in the surrounding medium. The treatment of transient problems is also considered. If high-frequency terms occur in the force, or shock effects are wanted within a short time after the application of the force, a treatment using solely modes of vibration of the submerged structure would be incomplete, as additional terms occur in the solution. As an alternative approach, the modes of free vibration of the structure may be used as generalized coordinates which fully describe the response of the structure but leave the medium to be treated, by means of the differential equations for the potential or in any other way desired.