Some results on the dynamics of the linear parametric oscillator with general time-varying frequency

The dynamics of single-degree-of-freedom linear oscillators under parametric excitation of general type (periodic or non-periodic) is considered. An analytical approach based on complexification and amplitude-phase decomposition of the response is developed leading to an (exact) set of first-order ordinary differential equations governing the amplitude and phase of the motion. Perturbation schemes for solving this set are developed and the solutions of the derived modulation equation are outlined. In addition, some results and comments on the stability of the derived solutions are provided.