On the Role of Extension in the Flexural Vibrations of Rings

Abstract

Abstract In a generalization of the classical analysis of A. E. H. Love, equations describing the flexural vibrations of thin rings are derived without making use of the usual assumption of no extension of the central line. Direct comparison with the nonextensional formulas of Love leads to a criterion for the validity of the assumption. In the process, the forced-vibration problem is shown to require the possibility of extension in certain cases in which its neglecting in a free-vibration analysis is valid.