Band Gaps and Vibration Attenuation Characteristics Analysis in Homogeneous Beam Coupled With Periodic Oscillators Based on the Method of Reverberation-Ray Matrix

Abstract

A periodic beam-oscillators coupling system is proposed as a physical model in this paper for analyzing the dynamic characteristics of periodic support beams and low-frequency flexural wave vibration of slender stiffened plate structures. The dispersion relation of flexural wave in the infinite long homogeneous beam coupled with periodic oscillators is calculated using the method of reverberation-ray matrix combined with the Bloch theorem. The accuracy and effectiveness of the method of reverberation-ray matrix in analyzing the band gaps and vibration characteristics of the homogeneous beam coupled with periodic oscillators are verified by the numerical results of the finite long homogeneous beam coupled with periodic oscillators. Both the analytical and numerical results show the existences of flexural wave band gaps in the homogeneous beam coupled with periodic oscillators, in which the propagation of the flexural waves is prohibited and flexural wave vibration is significantly suppressed. Furthermore, the effects of structural and material parameters on the flexural wave band gaps characteristics are respectively investigated. The flexural wave band gaps can be adjusted and optimized manually by adjusting structural and material parameters, which can be applied to vibration and noise control design of periodic support beams and slender stiffened plate structures.