Flexural vibration band gaps for a phononic crystal beam with X-shaped local resonance metadamping structure

Abstract

Structural vibration is commonly seen in engineering, which can cause resonance and fatigue damage in structure. Therefore, it is very desirable in vibration control techniques to achieve structure with low-frequency and broadband damping feature. In this paper, we design a phononic crystal (PC) beam with X-shaped locally resonant metadamping (X-LRMD) structures. Based on the PC theory, the flexural wave propagation in X-LRMD beam is studied. The equivalent dynamic properties of the X LRMD structure are analyzed by Lagrange equation. It is shown that due to its geometric nonlinearity, the X LRMD can effectively increase the damping of the system, which is validated by the transfer matrix method. The influence of structural parameters of X LRMD on band gap characteristics of the PC beam is then discussed in detail by using the finite element method with COMSOL multiphysics software in conjunction with Matlab, where the PC beam with X LRMD is modeled with the multi-body dynamic module within COMSOL and the band gap characteristics are calculated. The damping properties of the system are studied also using the finite element method. It is shown that compared with the equivalent structures, the PC beam with X LRMD can magnify the damping of the structure system, demonstrating a meta-damping phenomenon. The X LRMD in the PC beam can not only generate lower frequency and wider range band gaps but also suppress the vibration in passband ranges. This can bring a new design for reducing the vibration of structural systems.