Free and Forced Vibrations of an Infinitely Long Cylindrical Shell in an Infinite Acoustic Medium

Abstract

Abstract The paper presents a general method for the treatment of free and forced-vibration problems of infinitely long thin cylindrical shells. Surprisingly simple results are obtained by utilizing the known and tabulated modes of the shell in vacuo as generalized co-ordinates describing the response of the shell. The frequencies of free vibrations of submerged shells are obtained, and the response of the shell and medium to sinusoidally distributed, periodic, radial forces is determined. The results indicate that there is a low-frequency range where no radiation occurs and a high-frequency range where energy is radiated. Free vibration, or resonance in the case of forced vibrations, occurs only in the low-frequency range. The results of the paper may be applied to obtain the response to arbitrarily distributed, periodic, or nonperiodic forces by expanding such forces in Fourier series and/or integrals. The results for free and forced vibrations are discussed in general and for the specific case of steel shells in water. Tables are provided to facilitate numerical computations. With limitations the method is also applicable to ring-stiffened shells, and to the case of a static pressure in the surrounding medium.