Flexural Vibrations of a Thick-Walled Circular Cylinder According to the Exact Theory of Elasticity

Abstract

This paper gives results of the exact theory for flexural or nonaxially symmetric vibrations of a thick-walled cylindrical shell having freely supported ends. The results also apply to flexural wave propagation in infinitely long cylindrical shells. Curves of phase velocity and frequency as a function of wavelength ratio and wall thickness ratio are given. Included are some comparisons between the exact theory, the Timoshenko beam theory, and shell theory. ki = shear constant (such that Q = ki'AGy) Q = shear force A = cross-sectional area y = angle of shear at neutral axis