摘要:
提出了一种具有负模量特性的新型声学超结构,并揭示了其低频带隙的形成及拓宽机理.通过理论推导给出了该新型结构的归一化有效模量表达式,由于有效模量的零值点与系统参数密切相关,可以调节合适的参数使得零值点降低或带隙下界降低,进一步实现低频带隙.理论结果表明,在一定的频率范围内,系统的弹性模量为负且负模量区域进一步拓宽,从而通过负模量区域的放大而拓宽带隙.这种新的实现低频带隙的方法克服了传统局域共振附加质量过大及惯性放大结构带隙较窄的缺点.同时,通过有限元法得到的周期结构的传输率随着结构参数的变化趋势与理论分析的变化趋势基本一致,并得到了约40—180 Hz的低频宽带.这种实现低频带隙的新思路对低频声波的控制具有很重要的理论指导意义.
Abstract:
In this paper, a new type of acoustic metamaterial with negative modulus is proposed, and the formation and broadening mechanism of the low frequency bandgap are revealed. The expression of the normalized effective modulus of the structure is derived theoretically. Since the zero value of the effective modulus is closely related to the system parameters, the appropriate parameters can be adjusted to reduce the zero point, and the lower bound of the bandgap is reduced, thus the low-frequency bandgap is realized. The theoretical results show that the elastic modulus of the system is negative and the region of the negative modulus is widened in a certain frequency range, therefore, the widening of the bandgap can be realized through the enlargement of the negative modulus region. This new mechanism for achieving low-frequency bandgap overcomes the shortcomings both in the traditional local resonance with too large additional mass, and in the inertial amplification structures with narrow bandgaps. At the same time, the transmission of this periodic structure obtained by the finite element method is highly consistent with that by the theoretical analysis, with a low-frequency band of 40–180 Hz, from which the new mechanism presented here is verified. This new idea of achieving low-frequency bandgap is of great theoretical significance for controlling low-frequency sound waves.
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