On the behavior of parametrically excited purely nonlinear oscillators

In this study, parametrically excited purely nonlinear oscillators are considered. Instabilities associated with 2:1, 3:1, and 4:1 subharmonics resonances are analyzed by assuming the solution for motion in the form of a Jacobi elliptic function, the elliptic parameter, and the frequency of which are calculated based on the energy conservation law of the corresponding conservative system. Chirikov??s overlap criterion is used to obtain the approximate critical value of the amplitude of the parametric excitation that causes the transition from local irregular behavior (seen as chaotic) to global chaos. The analytical results derived are compared with numerically results.