Interactions of Oscillation Modes for a Weakly Nonlinear Elastic Beam with an External Force.

摘要

In this paper an initial-boundary value problem for the vertical displacement of a weakly nonlinear elastic beam with a harmonic excitation in horizontal direction at the ends of the beam will be studied. The initial-boundary value problem can be regarded as a simple model describing oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-timescales perturbation method an approximation of the solution of the initial-boundary problem will be constructed. Interactions between different oscillation modes of the beam will be studied. It will be shown that for certain external excitations the oscillation of specific modes changes.