Abstract

A new kind of elastic metamaterial plate is designed to control the vibration and elastic wave propagation based on the band-gap mechanism. For the proposed elastic metamaterial plate, local resonant rods are periodically distributed between the two cover plates of the metamaterial plate structure. The dynamic stiffness matrix and the frequency response function of the structure under the time-harmonic excitation are obtained by the finite element and spectral element hybrid method (FE-SEHM). The experiment and simulation validations have been carried out. The effects of the material and structural parameters on the band-gap characteristics are analyzed. It is shown that the band-gaps can be computed more accurately and efficiently based on the FE-SEHM to avoid confusion between the pass-bands and band-gaps. Three band-gaps of the elastic metamaterial plate appear near the odd-order natural frequencies of the local resonant rods. Increasing the damping and mass of the local resonant rods results in the enlargement of the band-gap width, this enhances the capacity of the vibration reduction and sound isolation more effectively.

摘要

设计了一种基于带隙机制的弹性超材料板来控制振动和弹性波的传播。对于所提出的弹性超材料板，局部共振棒周期性地分布在超材料板结构的两个盖板之间。通过有限元和谱元混合法(FE-SEHM)得到结构在时谐激励下的动刚度矩阵和频率响应函数。已经进行了实验和仿真验证。分析了材料和结构参数对带隙特性的影响。结果表明，基于 FE-SEHM 可以更准确、更有效地计算带隙，以避免通带和带隙之间的混淆。弹性超材料板的三个带隙出现在局部共振棒的奇数阶固有频率附近。增加局部谐振杆的阻尼和质量会导致带隙宽度的扩大，从而更有效地提高减振和隔声能力。