Amplitude modulated chaos in two-degree-of-freedom systems with quadratic nonlinearities
The authors investigate two-degree-of-freedom systems with weak quadratic nonlinearities in the presence of 1:2 internal resonance. All six possible cases of external or parametric/combination resonance are considered. A set of four first-order equations is obtained by the method of averaging. For the averaged system without damping, using Melnikov's method, the authors present the parameter range which chaotic dynamics exists. In the presence of damping this analytical approach does not work, but numerical studies show the persistence of chaotic responses.
scientific article; zbMATH DE number 1143324
scientific article