Cable dynamics under non-ideal support excitations: Nonlinear dynamic interactions and asymptotic modelling

Abstract

Cable dynamics under ideal longitudinal support motions/excitations assumes that the support׳s mass, stiffness and mechanical energy are infinite. However, for many long/slender support structures, their finite mass and stiffness should be taken into account and the cable-support dynamic interactions should be modelled and evaluated. These moving supports are non-ideal support excitations, deserving a proper coupling analysis. For systems with a large support/cable mass ratio, using the multiple scale method and asymptotic approximations, a cable-support coupled reduced model, with both cable׳s geometric nonlinearity and cable-support coupling nonlinearity included, is established asymptotically and validated numerically in this paper. Based upon the reduced model, cable׳s nonlinear responses under non-ideal support excitations(and also the coupled responses) are found, with stability and bifurcation characteristics determined. By finding the modifications caused by the support/cable mass ratio, boundary damping, and internal detuning, full investigations into coupling-induced dynamic effects on the cable are conducted. Finally, the approximate analytical results based on the reduced model are verified by numerical results from the original full model.