On the resonance wave interaction phenomenon

Abstract

Resonant wave interaction is a nonlinear process in which energy is transferred between different natural modes of a system by resonance. For a nonlinear system, the motion is not a summation of the linear modes, but consists of the linear harmonics plus their nonlinear coupling. This paper is studying the dynamic interaction between an attachment of cubic stiffness nonlinearity and the beam. The resonant interactions of the attachment with incident traveling wave propagating in the beam are studied by using the cnoidal method.