Abstract:

ESDU 81018 provides graphical data and a computer program for the estimation of the lower natural frequencies of thick-walled isotropic, circular cylinders based on the three-dimensional theory of elasticity for hollow cylinders. The data on both flexural and torsional vibrations are applicable to initially unstressed, isotropic shells having shear diaphragm end conditions. The geometric parameters and mode numbers for which the differences between natural frequency given by the three-dimensional elastic theory and thin-shell theory are more than 1 per cent and 5 per cent are indicated. General information is given on the flexural and torsional modes of free vibration of thick-walled shells. The thickness modes, which are not included in the model when shells are modelled as thin-walled, are discussed. The variations of displacements and stresses through the wall thickness, obtained using the computer program provided, are discussed and the effects of Poisson's ratio on the natural frequencies are considered. To give guidance on the desirability of modelling shells as either thin-walled or thick-walled, the range of applicability of thin-shell theories is discussed and specific information is given for a wide range of shell geometries. A worked example, which illustrates the application of these data, is given as well as the computer output for this example. The program is available as ESDUpac A8118.