Nonlinear dynamics of cable stays. Part 1: sinusoidal cable support excitation

An extensive behavioural study of cable vibrations, induced by sinusoidal cable-plane structural vibrations, is presented. Nonlinear equations of motion are formulated for a hanging cable with a small sag-to-span ratio. The effects of sinusoidal cable support displacements, with abrupt and gradual transients, are studied. Cable in-plane and out-of-plane displacements are generated through multiple shape-function analyses. Previously observed regions of large amplitude cable vibrations, in the excitation amplitude/frequency parameter plane and for sinusoidal cable end displacements, are verified and new regions of response instability are found. In addition, regions wit e parameter plane are characterised as periodic, quasi-periodic or chaotic. The effects of changes in initial cable conditions are examined and differences in maximum displacement amplitudes are found and compared to those found from a zero-initial-condition sinusoidal support excitation. For specific excitation amplitude/frequency parameter pairs, ‘cable stiffening’ is observed. Throughout the analysis, maximum cable stresses are calculated and found to be less than those required for material yielding. The significance of a cable-support interaction is briefly discussed.