Errors in shell finite element models for the vibration of circular cylinders

Four commonly used shell theories, membrane, thin, thick and proportional theories, are compared with an accurate triangular torus cubic finite element method in their ability to predict the natural frequencies and mode shapes of infinite and free-free finite length solid and hollow circular cylinders. In the computation each shell theory is replaced by a finite element approximation which satisfies the same basic assumptions as the shell theory. Error curves are given for the first two axial-shear, torsional-shear and radial-stretch modes of infinite cylinders. Error contours are given for the first symmetric and first antisymmetric mode of cylinders for circumferential wave numbers n = 0, 1, 2.