NON-LINEAR MODAL INTERACTIONS IN SHALLOW SUSPENDED CABLES

This paper examines different regimes of non-linear modal interactions of shallow suspended cables. In a high-energy level, the equations of motion in terms of in-plane and out-of-plane co-ordinates are strongly coupled and cannot be linearized. For this type of problem, a special co-ordinate transformation is introduced to reduce the number of strongly non-linear differential equations by one. The resulting equations of motion are written in terms of stretching, transverse (geometrical bending), and swinging co-ordinates, and are suitable for analysis using standard quantitative and qualitative techniques. Both free and forced vibrations of the cable are considered for in-plane and out-of-plane motions. The cable stretching free vibrations results in parametric excitation to the cable transverse motion. Under in-plane forced excitation the stretching motion is directly excited while the transverse motion is parametrically excited.

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