Wave propagation in elastic cables with and without fluid interaction.

摘要

The objective of this research is to develop linear and nonlinear theories of wave propagation in extended elastic cables with and without fluid interaction. The motivation for doing so is the need to understand the dynamic response of long cable suspensions, the high frequency/short wavelength response of shorter suspensions, and transient response phenomena. This objective is achieved through both analytical and numerical investigations for cables in air and in water.;To this end, a mathematical model is derived for the three-dimensional nonlinear response of extended cables submerged in a surrounding quiescent fluid medium. An asymptotic form of this model is derived for the linear response of a cable in air having small equilibrium curvature. The linear model predicts decoupled in-plane and out-of-plane waves. The out-of-plane waves are non-dispersive and obey a classical theory. By contrast, the in-plane waves are dispersive and generate coupled longitudinal and transverse motions. Analysis of in-plane response reveals the existence of two distinct wave types: (1) transverse-dominant waves, (2) longitudinal-dominant waves whose characteristics are determined by two cut-off frequencies. Closed-form solutions demonstrate significant tension waves following disturbances or excitation in the normal direction.;The nonlinear theory of submerged cables is also decomposed into waves lying in and orthogonal to the equilibrium plane. For the out-of-plane theory, attention focuses on two nonlinear mechanisms governing wave response; namely, (1) hydrodynamic drag, and (2) finite centerline stretching (geometric stiffening). The major effect of hydrodynamic drag is to attenuate cable response away from the excitation source and to do so sharply as the excitation frequency increases. The major effect of geometric stiffening is to increase the wave propagation speed. Like the analysis of out-of-plane waves, the analysis of nonlinear in-plane waves reveals that hydro-dynamic drag preferentially attenuates the transverse-dominant wave type. For submerged cables of finite extent, an interesting low frequency tensioning phenomenon is resolved. The maximum dynamic tension occurs at the first cut-off frequency and beyond the second cut-off frequency there is a very sharp reduction in the dynamic tension.