Phononic dispersion in anisotropic pseudo-fractal hyper-lattices

Abstract

Fractal and pseudo-fractal microstructures have proved promising in increasing the range of detectable frequencies for devices used in the realm of electromagnetism. Due to mechanical-electrical duality it is conjectured they may provide flexible solutions capable of closing/widening bandgaps and increasing tailorability in phononic lattices. Pseudo-fractal hyper-lattices have been considered in this work and different aspects of dispersion surface morphology and frequency band structure are studied. It has been observed that higher frequencies that can be excited in the simple square lattice are almost the same as those in the pseudo-fractal structures, however; through introduction of higher levels the pseudo-fractal hyper-lattice presents new features not observable in the ordinary lattice. By increasing the order of pseudo-fractal structure the number of degrees-of-freedom increases and dispersion surfaces morphologies change thus frequency gaps are eliminated. This phenomenon can be of advantage for acoustic/phononic visibility/detectability e.g. in designing sensors. In the classical analogy to quantum level repulsion surfaces flatten which sufficiently decreases the sound group velocity in the pseudo-fractal structure, and can be used for numerous practical applications. Keywords: Fractals, Bandgap, Tailorability, Dispersion surface, Brillouin zone, Floquet-Bloch's principle