A Dirac-cone-like dispersion at the center of the Brillouin zone where the wave number $\vec{k}=0$ [L. Brillouin, Wave Propagation in Periodic Structures (Dover, New York, 1953)], is rare and only happens due to accidental degeneracy. At certain frequencies, the Dirac cone breaks the time-reversal symmetry of acoustic waves, which has not yet been fully explored. In this paper, even the simplest geometric microarchitecture of phononic crystals (PnCs) in a periodic structure can be modulated to obtain the accidental triple degeneracies that make a Dirac-like cone at the Γ point ($\vec{k}=0$). While doing so, it was observed that the frequency of a nondispersive "deaf" band obtained from any arbitrary periodic structure made of similar PnCs remains unaltered. Then, a deaf band based predictive modulation of the PnCs is realized, and multiple occurrences of the Dirac-like points are demonstrated. The claims are validated using a numerical and experimental study of a baseline periodic structure having a square array of cylindrical polyvinylchloride inclusions in an air matrix. Phenomena such as orthogonal wave transport, negative refraction, and wave vortex are verified to exist at the deaf band based engineered Dirac cone.

Exotic acoustical features, like acoustic transparency, ultrasonic beam focusing, acoustic band gap and super lensing capability using a single metamaterial architecture is unconventional and unprecedented in the literature, demonstrated herein. Conventional metamaterials can focus an ultrasonic beam at specific frequency which results into unwanted distortion of the output wave fields at neighboring sonic frequencies in the host medium. However, ultrasonic wave focusing by virtue of negative refraction and simultaneous transparency of the metamaterial at sonic frequencies are uncommon due to their frequency disparity. To circumvent this problem and to avoid the unwanted distortion of wave at sonic frequencies, metamaterial with an array of butterfly-shaped thin ring resonators are proposed to achieve the beam focusing at ultrasonic frequency (37.3 kHz) and keep the structure transparent to the sonic frequencies (<20 kHz). The butterfly metamaterial with local ring resonators or butterfly crystals (BC) were previously proposed to create wide band gaps (∼7 kHz) at ultrasonic frequencies above 20 kHz. However, in this study a unique sub-wavelength scale wave focusing capability of the butterfly metamaterial utilizing the negative refraction phenomenon is demonstrated, while keeping the metamaterial block transparent to the propagating wave at lower sonic frequencies below the previously reported bandgaps.

Through an alternative paradigm, a predictive design of a Dirac-like point is introduced in a linear periodic metamaterial for the spatial guidance of acoustic waves. Dirac conelike dispersion at the Г point (for $\overrightarrow{\mathrm{k}}=0$ ) in a Brillouin zone is called a “Dirac-like cone,” which seldom occurs due to accidental degeneracy. However, a deaf band-based predictive model shows incredible potential to achieve an engineered Dirac cone at a predictive pivoted frequency. A targeted Dirac cone at a higher frequency is carried out in this article validating the orthogonal energy transport in a spiral pattern. The dominance of asymmetric deaf band modes triggers total internal reflection and guiding of acoustic waves inside phononic crystals. To elucidate the versatility of this methodology, experimental validation of orthogonal wave transport is presented.

Hermitian Dirac-like cones are proposed for creating acoustic logic gates herein. The predictive phenomenon of creating Dirac-like cones near a bipolar antisymmetric deaf band was found to be useful for acoustic computing of Boolean algebra. Unlike previous approaches, Dirac-like cone creates exclusive opportunity to perform all possible Boolean algebra computation with valid inputs. The phenomenon is demonstrated in two-dimensional phononic crystals (PnCs), consisting of tunable square columns in air media. By predictive tuning of the deaf bands, a triply to doubly degenerated Dirac-like cone is reported to form and is particularly useful for acoustic computing. It is only possible when a bottom band has a negative curvature that is lifted from a nearby doubly degenerated band with positive curvature, which is again degenerated with a deaf band. On the contrary, similar computing possibilities are difficult when the bottom band degenerates with the deaf band and the top band is lifted. Using these phenomena, acoustic logic gates are designed to perform Boolean algebra through AND, NAND, OR, and NOR gate operations. A simple one degree of freedom system and a complex six degrees of freedom system are proposed and demonstrated in which simple rotation of the PnCs activates a specific gate.

Simultaneous occurrence of Dirac-like cones at the center of the Brillouin zone (Γ) at two different energy states is termed Dual-Dirac-like cones (DDC) in this article. The occurrence of DDC is a rare phenomenon. Thus, the generation of multiple Dirac-like cones at the center of the Brillouin zone is usually non-manipulative and poses a challenge to achieve through traditional accidental degeneracy. However, if predictively created, DDC will have multiple engineering applications with acoustics and vibration. Thus, the possibilities of creating DDC have been identified herein using a simple square periodic array of tunable square phononic crystals (PnCs) in air media. It was found that antisymmetric deaf bands may play critical roles in tracking the DDC. Hence, pivoting on the deaf bands at two different energy states, an optimized tuning parameter was found to achieve Dirac-like cones at two distinct frequency states, simultaneously. Orthogonal wave transport identified as key Dirac phenomena was achieved at two frequencies, herein. It was identified that beyond the Dirac-like cone, the Dirac phenomena remain dominant when a doubly degenerated state created by a top band with positive curvature and a near-flat deaf band are lifted from a bottom band with negative curvature. Utilizing a mechanism of rotating the PnCs near a fixed deaf band, frequencies are tracked to form the DDC, and orthogonal wave transport is demonstrated. Exploiting the dispersion behavior, unique acoustic phenomena, such as ballistic wave transmission, pseudo diffusion and acoustic cloaking are also demonstrated at the Dirac frequencies using numerical simulation. The proposed tunable acoustic PnCs will have important applications in acoustic and ultrasonic imaging, waveguiding and even acoustic computing.

This article presents a concept, materials, and methods to devise a Bond Quality Index (BQI) for assessing composite bond quality, approximately correlating to the respective bond strength. Interface bonding is the common mechanism to join two composite structural components. Ensuring the health and quality of the bond line between two load-bearing composite structures is crucial. The article presents the classification and data-driven distinction between two types of bond lines between similar structural components. The interface bonds in composite plates were prepared using polyester peel ply and TX-1040 nylon peel ply. For all the plates, ultrasonic inspection through scanning acoustic microscopy (SAM) (>10 MHz) was performed before and after localized failure of the plate by impinging energy. Energy was impinged 0–10 J/cm² of in the 16-ply plates, and 0–25 J/cm² were impinged in 40-ply plates. Followed by bond failure and SAM, a new parameter called the Bond Quality Index (BQI) was formulated using ultrasonic scan data and energy data. The BQI was found to be 0.55 and 0.45, respectively, in plates with polyester peel ply and TX-1040 nylon peel ply bonds. Further, in 40-ply plates with polyester peel ply resulted in a BQI equivalent to 3.49 compared to 0.75 in plates with a TX-1040 nylon peel ply bond. Currently, the BQI is not normalized; however, this study could be used for AI-driven normalized BQIs for all types of bonds in the future.