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The Quarterly Journal of Mechanics and Applied Mathematics 1961 14(2):155-172; doi:10.1093/qjmam/14.2.155
© 1961 by Oxford University Press
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ELASTIC WAVES IN A NATURALLY CURVED ROD{dagger}

L. S. D. MORLEY

( R.A.E., Farnborough )

The propagation is considered of free elastic waves of small amplitude in a naturally curved rod where the neutral axis forms a plane curve of constant radius. The effects of rotatory inertia and radial shear are included, in the same way as in Timoshenko's theory for straight rods, as well as the effect of the extension of the neutral axis.

When the curvature is slight there are considerable simplifications and a Timo-shenko-type equation is obtained which governs the nexural motion. A simple relationship is then found with the phase velocity of nexural waves in the straight rod. This means that data already available for straight rods are now readily applicable to slightly curved rods of the same material and cross-section.


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