WALSH, S.J. and WHITE, R.G., 2002. Authors' reply. Journal of Sound and Vibration, 253(3), pp. 734.
Thank you for the complementary comments on the experimental work reported in
reference . As you note, when considering the vibration of curved beams, it is important
to acknowledge the work of L. S. D. Morley in the early 1960s. In reference , Morley
developed a unified theory for the vibration of curved rods where the neutral axis forms
a curve of constant radius of curvature. Morley's theory included the effects of rotary inertia
and radial shear in a manner analogous to that of Timoshenko's theory for straight rods.
Morley's theory also included the effect of extension of the neutral axis. It was shown in
reference  that when the curvature is slight, the equations can be simplified and
a Timoshenko-type equation can be obtained for the flexural motion. For this case, it was
shown that the extension of the neutral axis has no effect upon the flexural motion. When
the rod has pronounced curvature these simplifications are no longer valid and the more
general equations must be considered.