Resonance of non-linear systems subjected to multi-parametrically excited structures: (Comparison between two methods, response and stability)

摘要

Most mechanical systems or structures are subject to parametric or self excitations. In the present work, simultaneous principal parametric resonance of two-degree-of-freedom systems with quadratic and cubic non-linearities subject to multi-frequency parametric excitations in the presence of two-to-one internal resonance is investigated. Two approximate methods are applied to construct a set of first order. non-linear ordinary differential equations governing the modulation of the amplitudes and phases of oscillations. The applied methods are; the method of multiple time scale perturbation and the generalized synchronization methods. Steady state solutions and their stability are studied for selected values of the different parameters. The obtained results from both methods are in excellent agreement.