Free resonance vibrations in strongly nonlinear hamiltonian systems

摘要

The Hamilton equations for the vibrations of a material point around the equilibrium position are derived. The dimensionless coordinates along vertical and along horizontal axis are introduced. A good qualitative agreement is achieved between the analytical and numerical solutions. The amplitudes of oscillators should be small in comparison with the spring length, and no more restrictions should be imposed on them. The Duffing-oscillator amplitude begins to decrease and its energy transfers into the linear-oscillator energy. There is the detuning of the resonance condition and the blocking of the energy-transfer effect. If the initial amplitude increases, a decrease in the Duffing-oscillator amplitude leads first to a decrease in detuning, to achieving its exact value, then to a decrease up to the complete transfer-effect blocking.