Analysis of the interaction between torsion wave and phononic crystal in pipes

This article presents an analysis of torsional wave propagation in phononic crystal-based metamaterials. Such structures hold great promise as tools for wave manipulation. The unit cell of the presented structure was meticulously examined to obtain dispersion curves, revealing the presence of bandgaps and negative group velocities. The calculations of effective material parameters, based on eigenfrequencies, are presented to substantiate the existence of the bandgap and the negative value of group velocity. Time-domain simulations were conducted at various frequencies to analyze the wave behavior. In the case of negative group velocity, the wave inside the metamaterial propagates in the same direction as the incident wave. To verify the existence of negative velocity, a 2D Fast Fourier Transform (FFT) was performed, and the results from the 2D FFT data analysis align perfectly with the eigenfrequency analysis.