Modal coupling in the free nonplanar finite motion of an elastic cable
In the finite motions of a suspended elastic cable the in-plane and out- of-plane oscillations are coupled, which is in contrast with what is predicted by the theory of small oscillations. To study the phenomenon of nonlinear coupling, a simple but meaningful two degree-of-freedom model is refered to, one parameter being used to describe the in-plane motion and the other the out-of-plane motion. The solution of the dynamic equilibrium equations is accomplished by an perturbational expansion of order three, which furnishes the time solution of the two displacement parameters. The modification of the free oscillations due to the exchange of energy between the two modes in absence of internal resonance is studied for different initial conditions and the effect of modal coupling is proven.
scientific article; zbMATH DE number 4057136