Comments on nonlinear dynamics of a non-ideal Duffing-Rayleigh oscillator: Numerical and analytical approaches

An analytical and numerical investigation into the dynamic interaction between a cantilever beam with nonlinear damping and stiffness behavior, modeled by the Duffing-Rayleigh equation, and a non-ideal motor that is connected to the end of the beam, is presented. Non-stationary and steady-state responses in the resonance region as well as the passage through resonance behavior when the frequency of the excitation is varied are analyzed. The influences of nonlinear stiffness, nonlinear damping and the extent of the unbalance in the motor are examined. It is found that in this situation so-called Sommerfeld effects may be observed; the increase required by a source operating near the resonance results in a small change in the frequency, but there is a large increase in the amplitude of the resultant vibration and the jump phenomenon occurs.