Influence of conicity on the free wave propagation in symmetric tapered periodic beam

Abstract

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.