Vibration of cables under determministic and randon excitations.

Abstract

Conclusions i) A new method of linear analysis has been developed to handle the non planar free vibration behaviour of cables in the presence of a spatially non uniform lateral load. ii) If the lateral load, even though uniform, contains a time varying periodic component, the resulting cable oscillations are affected by parametric instability. iii) For long span cables, excessive change in cable tension is possible due to the seismic propagation velocity, which induces a time lag in the support displacements during an earthquake. iv) Consideration of nonlinear behaviour in the presence of periodic external forcing leads to the interesting phenomenon of internal resonance. v) For low amplitudes of oscillation, the quadratic nonlinear term controls the dynamics, leading to a softening type response. As the amplitude grows, the cubic term takes over and tends to bend the frequency response curve to the right, indicating a hardening type behaviour. vi) The equivalent linearization technique, in conjunction with a sample stability analysis, is a useful method to obtain approximate solutions to the random response of a cable under narrow band or periodic plus white noise excitation.