TRANSIENT DYNAMICS OF A DISPERSIVE ELASTIC WAVEGUIDE WITH AN ESSENTIALLY NONLINEAR ATTACHMENT

We consider the dynamics of a dispersive semiinfinite linear rod weakly connected to an essentially nonlinear end attachment. We examine resonant interactions of the attachment with incident traveling waves propagating in the pass band of the rod, as well as resonance capture phenomena where the attachment engages in transient 1:1 internal resonance with the in-phase mode of the rod, at the bounding frequency of its pass and stop bands. The studied resonant interactions of the nonlinear attachment with traveling waves are similar to resonance capture cascades occurring in finite chain–nonlinear attachment configurations; these are the transient dynamics of the attachment as it engages in a series of instantaneous resonances with a
continuous spectrum of frequencies in the pass band of the medium. As the energy of the attachment decreases due to damping and energy radiation back to the rod, the attachment engages in 1:1 resonance capture with the in-phase mode of the rod; this resonance capture occurs due to the dispersion property in the linear medium.