Experimental study of coupled vibration in a finite periodic dual-layered structure with transverse connection

The analytical equations of the transfer matrix method are further derived for the multi-coupled vibration of flexural and longitudinal waves in a periodic dual-layered beam structure with connection branches, with full consideration given to the flexural and longitudinal motions that are tri-coupled at each connection. Measurements of mobilities at the junctions on the uni-layered beam and the cross-layered beam are made. The numerical results agree well with the experimental results at all frequencies from 10 to 2000 Hz, which verifies the theoretical methodology for the multi-coupled vibration in a finite dual-layered beam. The cross-layer energy transmission is calculated, which reveals that the transmitted longitudinal energy is enhanced not only at the longitudinal resonant modes but also at the flexural resonant modes of the connection branches due to the structural wave coupling. The flexural energy is excited by wave coupling and becomes stronger at the longitudinal resonant modes and the flexural resonant modes of the connection branches. The cross-layer vibration motions from coupled waves in the branches can be effectively controlled by the attached cantilevers with mass at the resonance modes. This method can be used to control the structure-borne sound transmission in multi-layer beam structures.