Flexural Wave Propagation in a Double-Beam System Interconnected by Local Resonators with Two Degrees of Freedom

Abstract

The flexural band gaps in a double-beam system on elastic foundations periodically interconnected by local resonators with two degrees of freedom were investigated using the plane wave expansion method. The transmission property of the finite periodic system was examined by the finite-element method to verify the existence of the band gaps. The mechanism of band gap formation was further studied according to the eigenmodes at the edges of band gaps and the transverse deformation patterns. The technique of broadening the band gaps was also proposed. The results indicated that significant attenuation still appears outside the band gaps for the heterolateral transmission due to the counteraction of the approximate symmetric and antisymmetric flexural bands. The band gaps can be effectively broadened, and the propagating waves are even completely eliminated in the last pass band by only adding a spring. It was also observed that increasing the distance between the left and right attached points and the gravity of the resonator gradually from the asymmetric distribution to the symmetric distribution makes two band gaps coupled to form a superwide gap. The presented results emphasize the promising potential of the double-beam system in controlling the propagation of the flexural wave.