新型声学超材料梁带隙特性分析

Band-gap property of novel acoustic metamaterial beam

为了突破局域共振带隙带宽窄的瓶颈,并获得宽频低频带隙,本文将基于磁流变弹性体的局域共振单元应用于新型超材料梁的设计.本文采用谱元法对所设计的超材料梁进行建模计算,基于离散傅里叶变换理论和变分法构建了谱梁单元,基于力-位移关系法构建了磁流变弹性体局域共振谱单元.利用有限元法计算结果的收敛趋势检验了本文结果的正确性.通过频响曲线讨论分析了外加磁场强度、局域共振单元附加质量和单胞梁段的材料组成等因素对所设计超材料梁带隙特性的影响.研究发现,采用基于磁流变弹性体的局域共振单元设计超材料梁,可以使局域共振带隙宽度达到与Bragg带隙相当的水平,有效拓展局域共振带隙的宽度,提高该超材料梁的减隔振能力;增大磁流变弹性体局域共振单元附加质量,将减小超材料梁Bragg带隙的下界频率并拓展其带隙宽度;增加磁流变弹性体超材料梁单胞数是提高其Bragg带隙和局域共振带隙衰减能力的有效手段;单胞梁段材料构成差异越大,低频带隙越多,总带宽越大,衰减能力越强.

In order to break through the bottleneck of narrowness of the local resonance band-gap(LRBG)and obtain wide band-gaps in low frequencies,we apply the local resonator based on magnetorheological elastomer(MRE)to the design of the new metamaterial beam.In this paper,the spectral element method is used for modeling and calculation.Based on the discrete Fourier transform theory and the variational method,the spectral beam element is constructed.According to the force-displacement relationship method,the spectral element of the local resonator is established.The correctness of the results in this paper is validated by the convergence of the finite element method results.The influences of the applied magnetic field,the mass of the local resonator and the material combination of the beam in a cell on the band-gap property are discussed and analyzed.It is found that the metamaterial beam designed by the local resonator based on MRE can effectively increase the bandwidth of LRBG,which is comparable to that of the Bragg band-gap(BBG),and can improve the vibration isolation performance.With the increase of the local resonator mass,the lower bound frequency of the BBG decreases while the bandwidth increases.Increasing the unit-cell number of the MRE metamaterial beam is an effective means to improve the attenuation properties of the BBG and LRBG.The larger the difference of the material combination is,the more the band-gaps in low frequency are,the larger the total bandwidth of band-gaps and the stronger the attenuation capability become.