In this study, the attenuation characteristics of the unit cell of an infinitely long double symmetric tapered beam (DSTB) is examined. The exact flexural shape functions of the DSTB is derived using the Bessel functions. The band-structures for rectangular and circular solid section with varying conicity is evaluated implementing the transfer matrix method. It is found that the tapered beam produces wider band gaps for an ideal selection of conicity for both rectangular and circular cross-section. It is also evidenced in this paper that the circular cross-section produces wider band gaps with higher level of attenuation in comparison to the rectangular section. Specifically, the first normalized attenuation bandwidth of $165\%$ can be achieved in case of circular section and 97$\%$ in case of rectangular section. A representative cantilever finite beam structure comprised of the periodic DSTB also elucidates the reduction in flexural vibration for the same frequency ranges obtained from the dispersion curve of the infinite structure’s unit cell.

在这项研究中，研究了无限长双对称锥形光束（DSTB）的晶胞衰减特性。DSTB的确切弯曲形状函数是使用Bessel函数得出的。采用传递矩阵法评估了锥度变化的矩形和圆形实心截面的能带结构。已经发现，对于矩形和圆形横截面，锥形束产生更宽的带隙以理想地选择锥度。本文还证明，与矩形截面相比，圆形截面产生的带隙更宽，衰减水平更高。具体来说，第一归一化衰减带宽为$165％$ 在圆形截面和97的情况下可以实现$％$如果是矩形截面。由周期性DSTB组成的代表性悬臂有限梁结构还阐明了从无限结构的晶胞的色散曲线获得的相同频率范围内挠曲振动的减小。