Frequency Shifting in Nonlinear Resonant Systems With Damping

Abstract

The dynamical behavior of a three degree-of-freedom system is considered in the presences of a resonance between two modes with nonlinear coupling. One resonant frequency describes a translational oscillation and is a flxed quantity while the second characterizes an unbalanced rotational component and is allowed to slowly vary in time. When a system is attracted to a state of sustained resonance, the steady-state frequency of the sustained resonance shifts, depending on the parameter values of the system. As the applied torque increases, the resonant frequency shifts upward, approaching the natural frequency of the translational mode. If the applied torque is too large, the sustained resonance no longer exists and the system cannot be attracted to a long-term resonance motion. Likewise, increasing damping in the translational mode reduces the resonant frequency and the amplitude of the translational oscillations, as well as the critical torque for which sustained resonances exist. This frequency shifting, seen in both the simulations of the original system and verifled in a experimental system, is characterized through the analysis of a reduced-order model developed through the method of averaging.