Date of Award

Spring 2023

Document Type

Open Access Dissertation


Mechanical Engineering

First Advisor

Sourav Banerjee


A unique bulk-boundary distinction and acoustic topological phenomena is discovered and explained in this dissertation. The overall objective was to discover the hidden physics, dynamic and mechanics of acoustic wave behavior that causes the formation of extremely rare ‘Topologically protected Black Hole’ (TBH) in acoustic microarchitecture metamaterials. This behavior is immensely valuable for numerous mechanical and civil engineering applications where acoustic insulators are required to create sound-free or vibration-free exterior surfaces. On the other hand, to contain the energy within the structure, for impact mitigation and energy absorption in vehicles, space crafts, aircrafts, and civil infrastructures such materials will be immensely valuable. Unlike other unit cell acoustic black holes, TBH has unique bulk-boundary distinction creating an acoustic energy sink during wave propagation inside the bulk metamaterial, while keeping the boundaries insulated. This is exactly opposite to the behavior of a topological acoustic insulator (TAI).

Traditionally, mechanical vibration, acoustic waves and elastic waves are widely studied using Newtonian mechanics. Surprisingly since the beginning of the twenty first century for some cases of acoustic and elastic waves in periodic media were observed to demonstrate properties that are analogous to the quantum behavior prevalent in solid state physics. Suddenly the quantum mechanical understanding of acoustic and elastic waves become imperative. Thus, in this dissertation many such quantum mechanical terms are used to explain the phenomena discovered. Primary understanding starts from the physics of Dirac cones and Dirac-like cones at the boundary and at the center of the Brillouin zone in a periodic metastructure. The study of this periodic acoustic or mechanical metastructures consists of Phononic Crystals (PnCs), has now matured into an exciting research field. Over the past two decades, complementary to the photonics, phononics in periodic architecture with PnCs and periodic metamaterials have dominated the acoustic and elastic wave research field.

This dissertation first presents the understanding of accidental degeneracies in periodic media at the center of the Brillouin zone. It is shown that simplest geometric microarchitecture of PnCs in a periodic structure can be modulated to obtain the accidental triple degeneracies that make a Dirac-like cone at the Γ point (𝑘⃗ = 0) by breaking the time reversal symmetry. A non-trivial nondispersive "deaf" band is demonstrated and obtained from any arbitrary periodic structure made of similar PnCs which remains unaltered. Further this deaf band-based tuning is demonstrated to achieve orthogonal wave guiding at selected frequencies and the phenomena is exploited to demonstrate the possibility of acoustic computing for engineering applications. While doing so, at a specific doubly degenerated frequency near Dirac-like cone the TBH phenomena emerged. It was found that TBH is microarchitecture independent phenomenon and does not require any breaking of the time reversal symmetry or the space inversion symmetry if the ‘Deaf band’ dominates the local dispersion.

This phenomenon is not like the previously reported topological trio phenomena namely Quantum Halle Effect (QHE), Quantum Spin Hall Effect (QSHE) and Quantum Valley Hall Effect (QVHE), where the media boundary is conductive i.e., the acoustic wave energy is confined to the boundary while keeping the bulk media insulated. It was found that TBH will only happen when the polarization of two doubly degenerate mode for all possible wave direction is orthogonal to each other. This scenario results continuously changing up spin and down spin of the wave energy in the media and remain trapped without specific preferential direction of wave transport. The spin here as it is described in this dissertation was found to generate the positive orbital angular momentum and cause the change in geometric phase from 0 − 2𝜋 for the up spin, and then generate the negative orbital angular momentum and cause the change in geometric phase from 2𝜋 − 0, leaving no resultant geometric phase, while the energy is trapped in the media. This trapped wave was found to be topologically protected, means irrespective of media configuration, wave is always trapped within the entire bulk. Owing to the clockwise and anti-clockwise spin that eventually causing the topologically contained wave, the term blackhole is used herein.