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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.
Free Vibrations of Circular Cylindrical Shells deals with thin-walled structures that undergo dynamic loads application, thereby resulting in some vibrations. Part I discusses the treatment of problems associated with the propagation of plane harmonic waves in a hollow circular cylinder. In such search for solutions, the text employs the framework of the three-dimensional theory of elasticity. The text explains the use of tables of natural frequencies and graphs of representative mode shapes of harmonic elastic waves bounding in an infinitely long isotropic hollow cylinder. The tables are found to be useful as they can be used to check validity and provide estimates of the range of applicability of various shell theories. The purpose of the frequency equation and that of the numerical computations likewise are considered. The book includes a computer program written in the FORTRAN language to show how it is used in the computations, except in cases when H (the thickness of shell) and L (axial half of wavelength) result in extremely small values. Part II consists of related tables and graphs. Physicists, engineers, students, and researchers in advanced sciences will find this book of interest.
The vibrational characteristics and mechanical properties of shell structures are discussed. The subjects presented are: (1) fundamental equations of thin shell theory, (2) characteristics of thin circular cylindrical shells, (3) complicating effects in circular cylindrical shells, (4) noncircular cylindrical shell properties, (5) characteristics of spherical shells, and (6) solution of three-dimensional equations of motion for cylinders.