多振子梁弯曲振动中的局域共振带隙

从梁的弯曲振动方程出发,利用传递矩阵法,给出了无限周期结构的一维多振子声子晶体梁的弯曲振动能带结构,并利用有限元方法计算了有限周期结构梁的弯曲振动频率响应.建立了多振子声子晶体梁的简化模型,推导出带隙起始截止频率公式.结果表明:一维多振子声子晶体梁具有比单振子声子晶体梁更宽更丰富的振动带隙,可应用于呈倍频关系的减振降噪中;振动在带隙频率范围内频率响应具有明显的衰减;所建立的简化模型与理论模型结果符合较好.研究工作为梁类结构的减振提供一种新的思路.

Locally resonant elastic wave band gaps in flexural vibration of multi-oscillators beam

The flexural vibration behavior of elastic wave across a slender beam with locally resonant multi-oscillators structure is studied by using the transfer-matrix method and the finite element method. A simplified model is proposed, and the formulas of start and end frequencies of band gap are deduced. The more abundant and wider flexural elastic wave band gaps are found in this locally resonant multi-oscillator beam than in one oscillator beam, which can be used in the reduction of multiple-frequency vibration and noise. The frequency response of vibration in the band gap frequency range has obvious attenuation. The results of simplified model are in good agreement with results from the theory model. The research project will provide a new way for vibration reduction of beam structure.