To achieve the target band-gap in finite locally resonant phononic crystal beams, a method for determining the minimum period number is proposed. The vibration transmissibility method is extended to deal with the finite locally resonant phononic crystal beam. Comparing the vibration attenuation region obtained from the transmissibility method with the band-gap from the conventional transfer matrix method, the minimum period number can be calculated. Based on two forming patterns of locally resonant phononic crystal beams, the effects of the lattice constant and structural parameters of resonators on the band-gap as well as the influence of the period number on the vibration transmission characteristic are investigated. The minimum period number method can improve the applicability of the transmissibility method in the design of band-gaps and overcome the drawback that the transfer matrix method lacks the actual vibration attenuation. Finally, a comprehensive index is introduced to evaluate the effect of vibration reduction.

中文翻译：

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确定有限局部共振声子晶体束中最小周期数的方法

为了在有限的局部共振声子晶体束中实现目标带隙，提出了一种确定最小周期数的方法。扩展了振动传递方法，以处理有限的局部共振声子晶体束。将通过透射率方法获得的振动衰减区域与通过常规传递矩阵方法获得的带隙进行比较，可以计算出最小周期数。基于局部共振声子晶体束的两种形成方式，研究了共振器的晶格常数和结构参数对带隙的影响以及周期数对振动传递特性的影响。最小周期数法可以提高可传输性方法在带隙设计中的适用性，克服了传递矩阵法缺乏实际振动衰减的缺点。最后，引入了综合指标来评估减振效果。