Modeling and Vibration Analysis of a Nonlinear Connecting Two-Plate Model

In actual applications, multi-plate systems are broadly applied in various engineering fields. In marine engineering, some floating raft systems are simplified as multi-plate systems with linear connecting layers. If nonlinear connecting layers were used to connect multi-plate systems, nonlinear vibration transmission pathways between the sub-plate would be established. It is hoped that introducing the above nonlinear connecting layers could provide an attractive vibration control effect for the multi-plate systems. However, a few studies implement nonlinearities as a connecting layer between plates, which hinders a comprehensive understanding of the vibration behavior of plates coupled by nonlinear connecting layers and limits their engineering application in vibration reduction for multi-plate systems. Comprehensively considering the limitation of existing research and the potential application value of nonlinear connecting layers in multi-plate systems, this research develops a vibration analysis model for a nonlinear two-plate system in which the nonlinear vibration behavior is predicted using numerical methods. The representative nonlinear behaviors of the system are investigated, with a focus on the influence of the key control parameter of the nonlinear connecting layer on the vibration dynamics of the two-plate model. It is demonstrated that the vibration behavior of the nonlinear two-plate system can be accurately analyzed using GTM. The introduction of the nonlinear connecting layer induces various nonlinear phenomena, including complex behaviors, quasi-periodic vibrations, and the monotonic transfer of vibrational energy. The nonlinear connecting layer establishes an efficient energy transfer pathway, where an optimal parameter value of the nonlinear connecting layer aids in reducing the vibration of Plate 1. Additionally, under appropriate parameters for the nonlinear connecting layer, vibrational energy is effectively transferred from Plate 1 to Plate 2. Notably, to maximize the vibration reduction effectiveness of the two-plate system and leverage the complex behaviors, the nonlinear connecting layer should operate at low values of viscous damping.