Non-linear modal interactions in shallow suspended cables

This paper examines different regimes of non-linear modal interactions of s hallow 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 c annot be linearized. For this type of problem, a special co-ordinate transf ormation is introduced to reduce the number of strongly non-linear differen tial equations by one. The resulting equations of motion are written in ter ms of stretching, transverse (geometrical bending), and swinging co-ordinat es, and are suitable for analysis using standard quantitative and qualitati ve 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. (C) 1999 Academic Press.