Internal resonance of a two-degree-of-freedom tuned bistable electromagnetic actuator

Abstract

Internal resonance is a unique nonlinear phenomenon which could exchange energy between the first two commensurate linear natural frequency modes. This paper explores a 2:1 internal in a two-degree-of-freedom (DOF) tuned bistable electromagnetic actuator (T-BEMA). The T-BEMA combines with an inclined-spring-based bistable oscillator, an auxiliary oscillator, and an adjustable bolt. The T-BEMA is a 2DOF nonlinear system, and it could exhibit the 2:1 internal resonance for bandwidth actuation when controlled by an appropriate harmonic input excitation. Multi-scale method is adopted to obtain the analytical results of the amplitude-frequency responses under small input excitation amplitude. Results reveal the characteristics of both the first and second primary resonances. Owing to the 2:1 internal resonance, the double-jumping phenomenon of the first primary resonance is discovered, which significantly expands the actuation bandwidth. In the second primary resonance response, the mode displacement amplitude is presented, and the saturation phenomenon is observed with the increase of the excitation amplitude. In addition, the numerical analyses are presented to show the mode interaction and energy exchange as well. The response spectrum illustrates that when the excitation frequency is equal to either of the first two linear natural frequencies, the energy is easy to transfer to the other one, which significantly improves the actuation displacement. Afterward, this study conducts the bifurcation analysis and the basin-of-attraction studies to further demonstrate the advantage of the 2:1 internal resonance for highly efficient actuation performance under large excitation amplitude. Finally, the comparison of actuation performance for the T-BEMA and an actuator without internal resonance is conducted, and the internal resonance is proved to be an effective method to improve the actuation performance.