Date of Award

Fall 2018

Document Type

Open Access Thesis


Mechanical Engineering

First Advisor

Sourav Banerjee


The unique phenomena in acoustic metamaterial at the Dirac-like cone, and at the exceptional spawning ring could transform the field of engineering with multiple new applications that were never possible before. Localized conical dispersion called Dirac cone at the Brillouin Zone boundaries are the well-known phenomena demonstrated by photonics and phononic metamaterials. However, Dirac cone-like dispersion at the center of the Brillouin zone (where wave number, k = 0) [1] is rare and only happens due to accidental degeneracy at finite frequencies in two-dimensional periodic crystals (PCs), with or without microarchitectures. Accidental degeneracies are generally the ‘sweet spots’ where the time-reversal symmetry of the material breaks down and might have tremendous applications in engineering, which are not fully realized yet. Additionally, unlike Topological insulators, which is one of the most currently discussed topics in condensed matter physics, we have developed an acoustic topological conductor which helps to conduct acoustic pressure energy along the crystals, keeping the topology protected. Exploiting these behaviors of Dirac cones and spawning rings at the origin and boundaries of the Brillouin zone, a directional and bifurcation lens were designed which will propagate sound wave in specific directions at multiple frequencies.

In this study, it is shown that even simplest geometrical microarchitecture of the Phononic Crystals (PnCs) in a periodic structure can be modulated to obtain the accidental degeneracies at different frequencies, while the frequency of a nondispersive ‘deaf’ band’ obtained from any arbitrary periodic structure made of similar PnCs remains unaltered. Exploiting this behavior of the Dirac cones at the origin of the Brillouin zone, a ‘deaf band’ based predictive modulations of the PnCs are realized and multiple occurrences of the Dirac like points are demonstrated.

Moreover, a formation of dual Dirac cones at the center of the Brillouin zone, at different frequencies has also never been reported in the literature. Generation of multiple Dirac like cones at the center and the edge of a Brillouin zone, which is rare and, usually, non-manipulative is also demonstrated in this article. By deploying variable angular position of the square PVC resonator as a unit cell in a phononic crystals (PC) system, the locations of the degenerated double Dirac cones have been manipulated at various frequency points. A baseline periodic structure having a square array of cylindrical polyvinylchloride (PVC) inclusions in air media is studied numerically in this study, which was previously studied for band gaps and wave bifurcation. Detailed numerical study of the PnCs showed that by predictively adjusting the PnCs parameters, even an accidental triple degeneracy of dispersion at Γ point (k = 0) can be achieved. The claims were further validated using numerical experiments on a metamaterial slab composed of designed PnCs which demonstrates the unique Dirac cone phenomena e.g. orthogonal wave transport, negative refractive index material, and wave vortex.