PERIODIC SOLUTIONS OF STRONGLY NON-LINEAR OSCILLATORS BY THE MULTIPLE SCALES METHOD

The multiple scales method, developed for the systems with small non-linearities, is extended to the case of strongly non-linear self-excited systems. Two types of non-linearities are considered: quadratic and cubic. The solutions are expressed in terms of Jacobian elliptic functions. Higher order approximations, of solution as well as modulations of amplitude and phase, are derived. Comparisons to numerical simulations are provided and discussed.