Abstract
The (2M:1)-librational and (M:1)-rotational resonances are discovered in the stochastic layer of a parametrically excited pendulum. The analytical conditions for the onset of a resonance in the stochastic layer are derived. Numerical predictions of the appearance of resonance in thestochastic layer are also completed. Illustrations of the stochasticlayer in the parametrically excited pendulums are given through thePoincare mapping sections. This methodology can be used for resonantlayers in nonlinear Hamiltonian systems. However, the analyticalapproaches need to be improved for the better predictions of theresonant characteristics in the stochastic layer.
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