Wave motion of spinning periodically multi-stepped pipes — Dynamics of a novel motional 2D phononic crystal structure

Abstract

With the rapid development of processing technology, phononic crystals (PCs) have been gradually applied from conceptual model to practical engineering structure. In this paper, a novel motional two-dimensional (2D) PC structure — spinning periodically multi-stepped pipes is proposed. Due to the spinning motion, there will be two flexural waves respectively in the orthogonally transverse directions, forming such a planar PC structure. Considering a constant internal flow, the wave propagation and self-attenuation characteristics of the system are explored. Improved spectral element method and transfer matrix method are applied to treat such spatial wave motion. Based on the attained band structure in conjunction with the frequency response and wave shape, a significant mechanism is revealed that for a spinning periodically multi-stepped pipe conveying fluid, there are two sets of pseudo band gaps (BGs) generated owing to the gyroscopic effect, which do not exist in a static PC structure. However, the effective BG regions, where both the flexural waves truly attenuate, are actually located in their coincident frequency areas. Furthermore, the effects of number and geometry of sub-segments and motional parameters on the BG are discussed in detail. The present research will develop the PC dynamics in motional structures, and provide an in-depth theoretical basis for vibration suppression of engineering pipe system.