Introduction

Most of this book is concerned with the performance of shells under static loading. In contrast, the present chapter is concerned with an aspect of the response of shells to dynamic loading. The response of structures to dynamic loads is an important part of design in many branches of engineering: examples are the impact loading of vehicles, the aeroelastic flutter of aircraft, and wave-loading on large marine structures.

In this chapter we shall be concerned with the vibration of cylindrical shells, and in particular with the calculation of undamped natural frequencies. Calculations of this kind sometimes give the designer a clear indication that trouble lies ahead for a proposed structure; but if the design can be altered so that the natural frequencies of vibration of the structure are sufficiently different from the frequencies of the exciting agency, the occurrence of vibration can often be avoided.

For reasons of brevity, this chapter is restricted to cylindrical shells. The methods of the chapter may be adapted to the study of other sorts of shell, e.g. hyperboloidal shells used for large natural-draught water-cooling towers: see Calladine (1982).

Two very early papers on the subject of shell structures, by Rayleigh and Love, respectively, were on the subject of vibration, and the present chapters represent in fact only a relatively small advance on their work. Rayleigh (1881) was concerned with the estimation of the natural frequencies and modes of vibration of bells.