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 (XLRMD) structures. Based on the PC theory, the flexural wave propagation in XLRMD beam is studied. The equivalent dynamic properties of the XLRMD structure are analyzed by Lagrange equation. It is shown that due to its geometric nonlinearity, the XLRMD can effectively increase the damping of the system, which is validated by the transfer matrix method. The influence of structural parameters of XLRMD 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 XLRMD 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 XLRMD can magnify the damping of the structure system, demonstrating a meta-damping phenomenon. The XLRMD 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.%以声子晶体理论为基础,设计了一种具有超阻尼特性的X形局域共振结构,分析了周期性附加X形局域共振的梁弯曲振动传播特性.利用拉格朗日方程分析了X形局域共振结构动力学等效特性,揭示了该结构的阻尼放大的机理,分析了几何结构参数对于带隙特性的影响,并利用有限元法验证了X形局域共振结构的超阻尼特性.研究结果表明,周期性附加X形局域结构能够有效地抑制低频弯曲振动在梁中的传播,产生超阻尼特性,实现低频、宽带的减振效果,为结构的低频减振提供了一个新的设计方案.
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