AMPLITUDE-MODULATED CHAOS IN 2 DEGREE-OF-FREEDOM SYSTEMS WITH QUADRATIC NONLINEARITIES

Two degree-of-freedom systems with weak quadratic nonlinearities are s tudied under weak external and parametric excitations respectively. AI I six possible cases, that arise in the presence of 1:2 internal reson ance, are investigated. The method of averaging is used to obtain a se t of four first-order amplitude equations that govern the dynamics of the first-order asymptotic approximation to the response. An analytica l technique, based on Melnikov's method is used to predict the paramet er range for which chaotic dynamics exists in the undamped averaged sy stem. Numerical studies show that such chaotic responses are quite com mon in these quadratic systems, and they seem to persist even in the p resence of damping.