Dynamic Behavior Study of a Two-Layer-Beam with an Internal Two-Freedom-of-Degrees Nonlinear Model

In practical engineering scenarios, intricate structural configurations can be effectively idealized as coupled beam systems, and excessive vibration of coupled beams can lead to significant issues. In this study, an internal two-degree-of-freedom nonlinear model (TNM) is introduced into a two-layer beam (TLB), and its efficacy in reducing vibration is investigated. A mathematical model of the TLB equipped with the TNM is developed, and the vibration response of the TLB under harmonic excitation is analyzed by the Lagrange method. The vibration attenuation characteristics and vibration characteristics of the TLB equipped with the TNM are comprehensively investigated. The effects of different combinations of kn N and kn C nonlinear parameters in the TNM on the vibration attenuating ratio of TLB are also discussed. Numerical simulations show that the TNM can simultaneously attenuate the vibration magnitude of sub-beams without altering their original characteristics and eliminate the non-monocyclic responses of the TLB. The optimal vibration attenuation ratio of the TLB at the global level can be achieved by selecting a suitable combination of nonlinear stiffnesses. Overall, the rational use of the TNM can significantly attenuate the global vibration magnitude of the TLB within the target frequency band without altering its original characteristics. This research presents an innovative approach to nonlinear vibration control in engineering applications involving elastically coupled structures.