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Traditional structural damage detection methods in aerospace applications face challenges in accuracy and sensitivity, often necessitating multiple sensors to evaluate various measurement paths between the reference and defective states. However, the recently developed topological acoustic (TA) sensing technique can capture shifts in the geometric phase of an acoustic field, enabling the detection of even minor perturbations in the supporting medium. In this study, a diagnostic imaging method for damage detection in plate structures based on the TA sensing technique is presented. The method extracts the geometric phase shift index (GPS-I) from the Lamb wave response signals to indicate the location of the damage. Using Abaqus/CAE, a finite element model of the plate was established to simulate the Lamb wave response signals, which were then used to validate the feasibility of the proposed method. The results indicate that this technique enables rapid and precise identification of damage and its location within the plate structure, requiring response signals from only a few points on the damaged plate, and it is reference-free. 

Defect localization in homogeneous structures using ultrasonic waves is relatively easy to implement. However, locating defects in heterogeneous structures made of different materials can be challenging. This is because complicated reflections, refractions and scatterings occur when ultrasonic waves pass through the interfaces between two dissimilar materials of the heterogeneous structures. To address this issue, a localization methodology based on geometric phase change – index (GPC-I), derived from topological acoustic (TA) sensing, is proposed to adapt to the complicated scenarios when defects are present in heterogeneous plate structures. The GPC-I is adopted as the damage index (DI) to present the possibility of defects appearing on different acoustic sensing paths. A maximum peak value-dependent threshold in GPC-I plots (GPC-I vs. sensor sites) is defined to filter out unreliable sensing paths resulting from the heterogeneity. Different sensing modes (I and II) are combined to comprehensively provide a more reliable and accurate localization framework. Numerical modeling carried out by Abaqus/CAE software verifies the proposed GPC-I based localization technique. Comparison results among GPC-I and other two commonly used acoustic parameters—wave velocity differences (VD) and amplitude ratio (AR) (or wave attenuation) show that the GPC-I has superiority with higher sensitivity and stability for defect localization. This work can provide promising guidance for localizing defects in complex heterogeneous plate structures used in real-world engineering applications. 

Defect localization in homogeneous plate structures is relatively easy with various well-established acoustics-based techniques. However, localizing defects in heterogeneous structures can be challenging due to complicated reflection, refraction and scattering patterns arising from heterogeneous boundaries during wave propagations. This work introduces a topological acoustic (TA) sensing technique for localizing defects in heterogeneous plate structures. The geometric phase change – index (GPC-I) derived from TA sensing is used to detect perturbations caused by defects along the sensing paths between transmitters and receivers. The proposed method identifies the largest GPC-I values for various sensing paths. A higher GPC-I value on a sensing path implies a higher probability of having a defect on that path. A maximum peak value dependent threshold in GPC-I plots (GPC-I vs. sensor sites) is defined to identify and filter out those unreliable sensing paths in the proposed localization method. Finite element based numerical analysis in Abaqus/CAE software verifies the effectiveness of the proposed method. The commonly used methods using velocity differences (VD) and amplitude ratios (AR) are also tried out for defect localization for comparison. The performance comparison of the localization results using GPC-I, VD, and AR reveal that the GPC-I based technique is the most effective technique for defect localization. 

This study introduces a framework using acoustic phase bits (phibits) as classical analogs to quantum bits for realizing quantum-like gates. These phibits are realized on a metastructure composed of aluminum rods glued with epoxy. First, we realize a single phibit gate in a general form for a Bloch sphere representation, providing a foundation for implementing arbitrary gate operations on a single phibit. Second, within a single mathematical representation, we achieve either the Hadamard or NOT gate by applying the corresponding distinct physical actions for each. Third, we demonstrate the implementation of a sequence of two quantum-like gates, Hadamard followed by CNOT, using a single physical action. This illustrates the effectiveness of the phibit framework, which has the potential to simplify the implementation of a whole series of sequential gates into a single unified physical operation. Finally, we realize a universal set of gates, including the Hadamard, CNOT, and T gates, within a single mathematical representation with three distinctive actions. This approach addresses prior limitations of phibit-based gates, such as Hadamard and CNOT, which were implemented in separate mathematical representations, by introducing a unified framework that eliminates the need for distinct formulations maintaining computational efficiency. 

We demonstrate an integrated non-destructive inspection methodology that employs the nonlinear ultrasonics-based sideband peak counting (SPC) technique in conjunction with topological acoustics (TA) sensing to comprehensively characterize the acoustic response of steel plates that contain differing levels of damage. By combining the SPC technique and TA, increased sensitivity to defect/damage detection as well as the ability to spatially resolve the presence of defects was successfully established. Towards this end, using a Rockwell hardness indenter, steel plates were subject to one, three and five centrally located indentations respectively. The acoustic response of the plate as a function of number of indentations was examined at a frequency range between 50 kHz and 800 kHz, from which the change in a global geometric phase was valuated. Here, geometric phase is a measure of the topological acoustic field response to the spatial locations of the indentations within the steel plates. The global geometric phase unambiguously showed an increase with increasing number of indentations. In addition, spatial variations in a ‘local’ geometric phase as well as spatial variations in the PC index (SPC-I) were also determined. Spatial variations in both the local geometric phase as well as the SPC-I were particularly significant across the indentations for frequencies below 300 kHz, and by combining the respective spatial variations in the SPC-I and geometric phase, the locations of the indentations were accurately identified. The developed SPC-TA nondestructive method represents a promising technique for detecting and evaluating defects in structural materials. 

We present both the theoretical framework and experimental implementation of permutation gates using logical phi-bits, classical acoustic analogs of qubits. Logical phi-bits are nonlinear acoustic modes supported by externally driven acoustic metamaterials. Using a tensor product of modified Bloch sphere representations, we realize all possible two logical phi-bit permutations including SWAP and C-NOT. We also illustrate the scalability of a permutation for any number of logical phi-bits. Experimental demonstrations of these permutations require a single physical action on the driving conditions of the acoustic metamaterial. All logical phi-bits exist in the same physical system. We compare the phi-bit system with its quantum counterpart using Qiskit simulations, which illustrate the complexity of realizing these permutations in a quantum context. 

Commonly used methods for defect localization in structures are based on velocity differences (VD) or amplitude ratio (AR) (or attenuation due to scattering) measured along different sensing paths between a reference system and a defective system. A high value on a sensing path indicates a higher probability of the presence of defect on that path. We introduce an alternative approach based on the newly developed topological acoustic (TA) sensing technique for localizing defects in plate structures using Lamb waves. TA sensing exploits changes in geometric phase of acoustic waves to detect perturbations in the supporting medium. This approach uses a geometric phase change – index (GPC-I), a measure of the geometry of the acoustic field averaged over a spectral domain, as detection metric in lieu of VD or AR. Calculations based on the finite element method (FEM) in Abaqus/CAE software verifies the effectiveness of the proposed GPC-I-based defect localization method. Randomly located defects on the surface of a plate are localized with higher sensitivity and accuracy, by the GPC-I method in comparison to VD or AR-based methods. 

This work presents numerical modeling-based investigations for detecting and monitoring damage growth and material nonlinearity in plate structures using topological acoustic (TA) and sideband peak count (SPC)-based sensing techniques. The nonlinear ultrasonic SPC-based technique (SPC-index or SPC-I) has shown its effectiveness in monitoring damage growth affecting various engineering materials. However, the new acoustic parameter, “geometric phase change (GPC)” and GPC-index (or GPC-I), derived from the TA sensing technique adopted for monitoring damage growth or material nonlinearity has not been reported yet. The damage growth modeling is carried out by the peri-ultrasound technique to simulate nonlinear interactions between elastic waves and damages (cracks). For damage growth with a purely linear response and for the nonlinearity arising from only the nonlinear stress–strain relationship of the material, the numerical analysis is conducted by the finite element method (FEM) in the Abaqus/CAE 2021 software. In both numerical modeling scenarios, the SPC- and GPC-based techniques are adopted to capture and compare those responses. The computed results show that, from a purely linear scattering response in FEM modeling, the GPC-I can effectively detect the existence of damage but cannot monitor damage growth since the linear scattering differences are small when crack thickness increases. The SPC-I does not show any change when a nonlinear response is not generated. However, the nonlinear response from the damage growth can be efficiently modeled by the nonlocal peri-ultrasound technique. Both the GPC-I and SPC-I techniques can clearly show the damage evolution process if the frequencies are properly chosen. This investigation also shows that the GPC-I indicator has the capability to distinguish nonlinear materials from linear materials while the SPC-I is found to be more effective in distinguishing between different types of nonlinear materials. This work can reveal the mechanism of GPC-I for capturing linear and nonlinear responses, and thus can provide guidance in structural health monitoring (SHM). 

Abstract A newly developed nonlinear ultrasonic (NLU) technique called sideband band peak count-index (or SPC-I) measures the degree of nonlinearity associated with the inspected specimen – larger SPC-I values indicate higher nonlinearity. In various published papers, the SPC-I technique has shown its effectiveness and superiority in comparison to other techniques for nondestructive testing (NDT) and structural health monitoring (SHM) applications. In this work, the performance of SPC-I in non-homogeneous specimens having different topographies is investigated using peridynamics based periultrasound modeling. Three types of topographies – “X” topography, “Y” topography and “XY” topography are introduced by adding thin strips made up of a second material and thus converting the homogeneous plate into a heterogeneous structure. It is observed that “X” and “XY” topographies can help to hide the crack growth, thus making cracks undetectable to the nonlinear SPC-I based monitoring technique. In addition to the SPC-I technique, we investigate the applicability of the emerging method of topological acoustic sensing. This method monitors the changes in the geometric phase; a measure of the changes in linear or nonlinear wave’s spatial behavior during its propagation in plate structures having various topographies. The computed results show that the magnitudes of jumps in geometric phase change plots can be good indicators to distinguish cracks with different thicknesses although these cracks can remain hidden in some topographies during the single point inspection based on the nonlinear SPC-I based monitoring technique. 

Abstract Cryptography is crucial in protecting sensitive information and ensuring secure transactions in a time when data security and privacy are major concerns. Traditional cryptography techniques, which depend on mathematical algorithms and secret keys, have historically protected against data breaches and illegal access. With the advent of quantum computers, traditional cryptography techniques are at risk. In this work, we present a cryptography idea using logical phi-bits, which are classical analogues of quantum bits (qubits) and are supported by driven acoustic metamaterials. The state of phi-bits displays superpositions similar to quantum bits, with complex amplitudes and phases. We present a representation of the state vector of single and multi-phi-bit systems. The state vector of multiple phi-bits system lies in a complex exponentially scaling Hilbert space and is used to encode information or messages. By changing the driving conditions of the metamaterial, the information can be encrypted with exceptional security and efficiency. We illustrate experimentally the practicality and effectiveness of encoding and encryption of a message using a 5 phi-bits system and emphasize the scalability of this approach to anNphi-bits system with the same processing time.