Self-excited oscillators with asymmetric nonlinearities and one-to-two internal resonance

An analysis is presented on the dynamics of asymmetric self-excited oscilla tors with one-to-two internal resonance. The essential behavior of these os cillators is described by a two degree of freedom system, with equations of motion involving quadratic nonlinearities. In addition, the oscillators ar e under the action of constant external loads. When the nonlinearities are weak, the application of an appropriate perturbation approach leads to a se t of slow-flow equations, governing the amplitudes and phases of approximat e motions of the system. These equations are shown to possess two different solution types, generically, corresponding to static or periodic steady-st ate responses of the class of oscillators examined. After complementing the analytical part of the work with a method of determining the stability pro perties of these responses, numerical results are presented for an example mechanical system. Firstly, a series of characteristic response diagrams is obtained, illustrating the effect of the technical parameters on the stead y-state response. Then results determined by the application of direct nume rical integration techniques are presented. These results demonstrate the e xistence of other types of self-excited responses, including periodically-m odulated, chaotic, and unbounded motions.