HARMONICALLY FORCED WAVE-PROPAGATION IN ELASTIC GABLES WITH SMALL CURVATURE

This study presents an investigation of coupled longitudinal-transvers e waves that propagate along an elastic cable. The coupling considered derives from the equilibrium curvature (sag) of the cable. A mathemat ical model is presented that describes the three-dimensional nonlinear response of an extended elastic cable. An asymptotic form of this mod el is derived for the linear response of cables having small equilibri um curvature. Linear, in-plane response is described by coupled longit udinal-transverse partial differential equations of motion, which are comprehensively evaluated herein. The spectral relation governing prop agating waves is derived using transform methods. In the spectral rela tion, three qualitatively distinct regimes exist that are separated by two cut-off frequencies which are strongly influenced by cable curvat ure. This relation is employed in deriving a Green's function which is then used to construct solutions for in-plane response under arbitrar ily distributed harmonic excitation. Analysis of forced response revea ls the existence of two types of periodic waves which propagate throug h the cable, one characterizing extension-compressive deformations (ro d-type) and the other characterizing transverse deformations (string-t ype). These waves may propagate or attenuate depending on wave frequen cy. The propagation and attenuation of both wave types are highlighted through solutions for an infinite cable subjected to a concentrated h armonic excitation source.