For citation:
Kovriguine D. A., Potapov A. I. Nonlinear wave dynamics of one-dimensional elastic systems. Part III. Systems with discrete spectrum. Izvestiya VUZ. Applied Nonlinear Dynamics, 1996, vol. 4, iss. 2, pp. 92-102.
Nonlinear wave dynamics of one-dimensional elastic systems. Part III. Systems with discrete spectrum
It is shown that in a ring-like systems with own frequency discrete spectrum, the isolated three-wave resonant ensembles, triads, play the role of simplest nonlinear dynamic structures. It is found that the interaction between the axisymmetric radial oscillations and two mid-frequency bending waves, travelling each towards other, is a particular case of degenerated triads. The periodic energy exchange takes place between the interacting triad modes. Break-up of the axisymmetric radial oscillations is accompanizsd by the resonant excitation of two conjugated dominant shapes of oscillations. A possibility of the self-modulation of bending waves travelling around the ring is remarked as well as their further transformation into stationary envelope soliton-like wavetrains. Stress increase constants are estimated for several illustrative examples. An agreement between obtained results and known experimental data as well as theoretical achievements, having used other investigation tools is reached.
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