Internal-External Resonance and Saturation Phenomenon in a Two Coupled Nonlinear Oscillators

摘要

A class of two degree of freedom nonlinear oscillators, with parametric excitation forces is considered and investigated. The case of one-to-one internal resonance and subharmonic external resonance of both modes of vibrations are considered simultaneously. Using the analytical method of multiple scales, a set of slow-flow equations governing the amplitudes and the phases of the motion is derived. Effects of system parameters on the existence and stability properties of periodic motion are studied. The frequency response curves are presented and investigation is focused on understanding the interaction of the branches of these curves as the nonlinear parameters and external forcing are varied. Finally the equations of motion are integrated numerically to verify analytical predictions. It is also found that the system exhibits different kinds of responses.