Analysis of dispersion characteristics and control of multiple passbands in a metamaterial pipe

Understanding and controlling pipe vibrations are of key concern as they affect the serviceability and performance of pipeline systems. A novel metamaterial concept can be exploited to control these vibrations. In this article, propagation characteristics of flexural waves in a pipe coupled with rack are investigated. The dispersion relation, which corelates the propagation constant with frequency is obtained using the transfer matrix method in conjunction with Bloch's theorem. The results reveal the existence of multiple wide passbands in the low frequency range. These propagation characteristics are verified using a finite element model. The emergence of these multiple passbands is attributed to various bending modes of the pipe, and it is necessary to efficiently control them. In order to achieve both independent and simultaneous control of multiple passbands, the feasibility of deploying either a single or a two degree of freedom resonator at each span of the pipe is evaluated. As the positioning of resonators within a span governs their performance, to gain a deeper understanding of this, an iterative procedure is adopted wherein resonators are placed at each possible location in the span. A genetic algorithm-based optimization is then performed to arrive at the corresponding optimal parameters. The ideal location for placing a resonator to control each passband is the one that yields the best performance. Finally, the efficacy of the proposed control scheme is verified using Gaussian white noise as input. The dispersion relation and control schemes proposed herein not only provide insights into understanding the propagation behavior of flexural wave and their control in pipes, but also can be equally applied to other analogous periodic structures.