On the symmetric modal interaction of the suspended cable: Three-to-one internal resonance

The two-mode nonlinear response of a suspended cable subjected to the primary resonance is investigated, and the three-to-one internal resonance is analyzed. Because the treatment of Galerkin discrete models of spatially continuous systems with initial curvature may lead to erroneous quantitative or even qualitative results, the method of multiple scales is applied to directly attack the nonlinear partial differential equation and the boundary conditions, which leads to the modulation equations for the primary resonance of either the first or third symmetric mode. The Newton–Raphson method and the pseudo-arclength scheme are used to obtain the frequency-response curves and force-response curves, and the dynamic solutions of the modulation equations are also investigated.