Band gaps appear in the frequency spectra of an elastic beam having periodic spring-mass attachment, acronymed as metabeam. Two widely used beam theories, i.e. Euler–Bernoulli and Timoshenko, are non-dimensionalized in order to obtain the dimensionless periodicity parameters. In this paper, the location and width of band-gaps are investigated due to the variation of these periodicity parameters of a metabeam. Implementing transfer matrix method in conjunction with Bloch–Floquet theorem, a unified methodology has been adopted to estimate the propagation and attenuation bands in a metabeam. This paper provides a guideline towards the designing of wide-band metabeam by tunning the non-dimensional parameters.

中文翻译：

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具有周期性线性弹簧质量谐振器的弹性梁的无量纲分析

带隙出现在具有周期性弹簧质量附着的弹性梁的频谱中，缩写为元梁。两种广泛使用的梁理论，即 Euler-Bernoulli 和 Timoshenko，是无量纲化的，以获得无量纲的周期性参数。在本文中，由于超光束的这些周期性参数的变化，研究了带隙的位置和宽度。结合Bloch-Floquet定理实施传输矩阵方法，采用统一的方法来估计元波束中的传播和衰减频带。本文通过调整无量纲参数为设计宽带超光束提供了指导。