Non-dimensional analysis of the bandgap formation in a locally resonant metamaterial pipe conveying fluid

The objective of this paper is to investigate the effects of fluid flow velocity on the edge frequencies of the bandgap in an acoustic metamaterial pipe in a non-dimensional framework. Two methodologies are presented to predict the formation of the bandgap. In the first methodology, the pipe is considered to be infinitely long and the dispersion of an elastic wave in a single representative periodic unit cell of the structure is used to estimate the bandgap edge frequencies. In the second method, the pipe is modeled as a finite structure with defined boundary conditions and a modal analysis-based method is used to estimate the edge frequencies. A parametric study is performed wherein parameters identified from the non-dimensional analysis are varied, namely, the dimensionless flow velocity, the ratio of the resonator's mass to that of the pipe and the fluid and the ratio of the fluid's mass to that of the pipe and the fluid. It is shown that a close agreement in the bandgap edge frequencies is achieved using both methodologies. Furthermore, it is observed that an increase in the fluid velocity induces a decrease in the bandgap width, an increase of the mass ratio of the fluid to that of the pipe and the fluid results in a small decrease in the bandgap width and finally an increase in the mass of the resonators relative to that of the pipe leads to an increase in the bandgap width.