A series solution of the general three-dimensional equations of linear elasticity is developed and used to find accurate natural frequencies for the vibration of hollow elastic circular cylinders with traction free surfaces. The series solution is found to converge to accurate frequencies with the use of very few terms. Comparison of the results with previous finite element results, shows good agreement. The highly accurate series solution is used as a basis of comparison for the Timoshenko beam theory. The comparison of results clearly shows the accuracy and range of applicability of the Timoshenko beam theory as well as suggesting a reasonable choice of shear coefficient.
No takes yet. Share an insight, caveat, or question.
Hutchinson et al. (1986) studied this question.
Synapse has enriched 5 related papers. Consider them for comparative context: