Vibration Attenuation and Dynamic Study of a Two-Layer Beam with an Internal Beam-Type Coupling Nonlinear Energy Sink

Coupling beam systems have appeared widely in various engineering fields, where several additional beams are generally set near coupling beam systems, which may be designed as a vibration control mechanism by introducing some unique connecting relations. This study introduces nonlinear connecting relations to connect an additional beam and a two-layer beam system, where the additional beam equipped with connecting nonlinear stiffness is defined as an internal beam-type CNES. The Lagrange method is chosen to calculate the nonlinear vibrating system’s numerical responses, which can correctly calculate the nonlinear vibrating system’s numerical responses. Introducing the internal beam-type CNES is beneficial for broadband attenuation of the vibration of the vibrating system’s main structures. The internal beam-type CNES’s representative working states are divided into linear and nonlinear broadband vibration attenuating states. The appearance of representative nonlinear responses can be judged as a sign of the internal beam-type CNES working in the nonlinear broadband vibration attenuating state. Increasing the nonlinear stiffness of the internal beam-type CNES can motivate representative nonlinear responses of the vibrating system, while increasing its viscous damping can eliminate representative nonlinear responses. A delicate parameter selection of the nonlinear stiffness of the beam-type CNES helps enhance the vibration attenuation of the two-layer beam. Importantly, the internal beam-type CNES reveals the attractive vibration-attenuation potential in controlling the vibration of coupling beam systems. The proposed internal beam-type CNES provides a feasible way to use unimportant additional beams near main beam structures to control their vibration. It is beneficial for effectively utilizing existing engineering structures to carry out the vibration-attenuation design.