Abstract
Suspended cable’s non-planar resonant coupled dynamics under out-of-plane support motion is investigated by the multiple- scale method, with a boundary modulation formulation established and nonlinear dynamic responses analyzed. Explicitly, to cope with the difficulty due to moving boundary, the small resonant support motion is properly rescaled and incorporated into cable’s modulation equations as a boundary resonant modulation term, through constructing solvability conditions of the multi-scale expansions. And the boundary resonance dynamic coefficient, characterizing the boundary modulation effect, is derived analytically for cable’s two-to-one resonant coupled dynamics. Numerical results for cable’s non-planar coupled dynamic responses, including stability and bifurcation analysis for the equilibrium solutions of modulation equations, are obtained and presented in the end, with both saddle-node bifurcations and Hopf bifurcations detected.
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