Band structure and effective properties of one-dimensional thermoacoustic Bloch waves

We investigate the dispersion characteristics and effective properties of acoustic waves propagating in a one-dimensional duct equipped with periodic thermoacoustic coupling elements. Each element consists classical regenerator subject to spatial temperature gradient. When pass through regenerator, thermal-to-acoustic energy conversion takes place can either amplify or attenuate wave, depending on direction propagation wave. The presence gradient naturally induces loss reciprocity. This study provides comprehensive theoretical model as well an in-depth numerical analysis band structure this thermoacoustically-coupled, tunable, metamaterial. Among most significant findings, it is shown that metamaterial capable supporting non-reciprocal Bloch are associated particular form unidirectional transport. Remarkably, also allows achieving zero compressibility refractive index ultimately lead phase invariance sound waves. single property have very interesting implications attainment cloaking.