Interaction Of Ultrasonic Waves Research Articles

Novel cell-based smoothed extended finite element method for simulating the interactions of ultrasonic waves with randomly distributed cracks in solid structures

The conventional extended finite element method (XFEM) is a powerful tool for simulating crack-related problems in materials; however, several limitations exist, such as numerical instabilities and convergence issues. These problems arise because enriched elements have higher stiffness than standard elements, and this difference can cause computational difficulties. To overcome these limitations, we developed the cell-based smoothed extended finite element method (CS-XFEM), an advanced computational technique designed to simulate the intricate interactions between ultrasonic waves and randomly distributed cracks within solid materials. This innovative approach integrates a cell-based smoothing technique into the XFEM, effectively softening the stiffness of the enriched elements around crack tips. Therefore, the CS-XFEM eliminates numerical instability, providing a more stable and reliable computational framework. In this study, numerical experiments were conducted in which plasticity properties were assigned to both the crack bodies and tips to reflect crack yielding. Further, frictional contact in the crack body elements was formulated using the Heaviside function, and deformation around the crack tips was approximated using a singular function. Through comprehensive numerical investigations, we demonstrated that the conventional XFEM fails to converge and, instead, diverges when ultrasonic waves interact with randomly distributed cracks. By contrast, our proposed CS-XFEM method demonstrates strong convergence capabilities, rendering it well-suited for exploring the interactions between ultrasonic waves and randomly distributed cracks under varying crack quantities, lengths, and friction coefficients. Overall, the proposed CS-XFEM is an efficient, accurate, and robust method for investigating the acoustic nonlinearity induced by randomly distributed cracks with frictional contact in solid structures.

Studying the nonlinearity effects in ultrasound-assisted water purification and treatment systems

In light of industrial sectors' rapid and exponential growth, the deleterious specter of water pollution looms ominously over our environment. One of the significant challenges is obtaining a sustainable and energy-efficient water purification/treatment system. Since the 1990s, several research studies have been proposed to demonstrate the usefulness of ultrasound as a water purification tool. As a result, newly designed devices such as ultrasound-assisted electrochemical treatment and ultrasound-assisted heat exchanging devices are becoming more common. However, such devices' high voltage ultrasonic emission is a significant problem because the nonlinear acoustic effects are not well understood and are, therefore, not adequately integrated into the design of the devices. Furthermore, the presence of biofilms in these devices creates more complexity due to the interaction of high-amplitude ultrasonic waves with the biofilm network. To better overcome the inefficient functioning of such devices and adverse operational issues, the current study aims to investigate and explain the nonlinear ultrasonic effects in ultrasonic-assisted purification devices, with and without biofilm deposits. The obtained insight will help develop an effective design strategy for high efficiency.

Block-matching and 3D filtering-based denoising of acoustic images obtained through point contact excitation and detection method

A novel experimental method based on the Coulomb coupling technique is used for visualizing the interaction of ultrasonic waves in PZT (Lead Zirconate Titanate - (Pb[ZrxTi1-x]O3 (0 ≤ x ≤ 1)) ceramic materials. The method of excitation and detection through a point contact produces representations of propagating wave vectors in the time domain as a series of images. In the acoustic image, several types of noises from different types of sources corrupt the signal as well as the image. As a result, the resolution and quality of the images are reduced. Block matching and 3D filtering (BM3D) algorithm is implemented for the reduction of noises from ultrasonic signals that are in the form of 2D images. Here, we also implemented a custom-designed hybrid filter and conventional total variation (TV-L1) filter on the noisy images to compare the final denoised outputs from the BM3D filter. Comparison metrics like PSNR (peak signal-to-noise ratio) and SSIM (structural similarity index measure) are used for quantitative analysis of those denoised ultrasonic images with respect to their ground truth or almost noise-free counterparts. Based upon those parameter values, the BM3D filter demonstrated the best results for the denoising of the acoustic images acquired from the sample PZT material. This paper discusses and explains the results and proves the successful application of the BM3D algorithm on acoustic image data.

Modeling ultrasound modulation of neural function in a single cell

BackgroundLow intensity ultrasound stimulation has been shown to non-invasively modulate neural function in the central nervous system (CNS) and peripheral nervous system (PNS) with high precision. Ultrasound sonication is capable of either excitation or inhibition, depending on the ultrasound parameters used. On the other hand, the mode of interaction of ultrasonic waves with the neural tissue for effective neuromodulation remains ambiguous. New methodHere within we propose a numerical model that incorporates the mechanical effects of ultrasound stimulation on the Hodgkin-Huxley (HH) neuron by incorporating the relation between increased external pressure and the membrane induced tension, with a stress on the flexoelectric effect on the neural membrane. The external pressure causes an increase in the total tension of the membrane thus affecting the probability of the ion channels being open after the conformational changes that those channels undergo. ResultsThe interplay between varying the acoustic intensities and frequencies depicts different action potential suppression rates, whereby a combination of low intensity and low frequency ultrasound sonication proved to be the most effective in modulating neural function.Comparison with Existing Methods: Our method solely depends on the HH model of a single neuron and the linear flexoelectric effect of the dielectric neural membrane, when under an ultrasound-induced mechanical strain, while varying the ion-channels conductances based on different sonication frequencies and intensities. We study the effect of ultrasound parameters on the firing rate, latency, and action potential amplitude of a HH neuron for a better understanding of the neuromodulation modality of ultrasound stimulation (in the continuous and pulsed modes). ConclusionsThis simulation work confirms the published experimental data that low intensity and low frequency ultrasound sonication has a higher success rate of modulating neural firing.

The complexity of harmonically scattered nonlinear waves from triangular, circular, and rectangular corners of the 2-D domain

Considering recent advancements in the nonlinear pulse-echo technique, understanding reflected nonlinear waves from inaccessible edges and surfaces becomes important. A unique geometrical model solved numerically using the finite element method is proposed and studied via extensive numerical experiments to gain insight into harmonically scattered waves from different shapes of the 2-D spaced corners considering the challenges of theoretical solutions that can capture the interplay between multiple phenomena. Tang et al. (2012), Kube (2017-18), and Achenbach and Wang (2017-18) studied the harmonic scattering of waves from nonlinear inclusions using analytical techniques. Linear longitudinal waves scattered from the triangular, circular, and rectangular-shaped free and fixed edges of the 2-D spaced corner show mode conversion and energy transfer between bulk wave modes at fundamental frequencies. The interaction of nonlinear ultrasonic waves with the edges makes things complex due to an interplay between harmonic generation, linear scattering, harmonic scattering, bulk wave mode conversion, and harmonic energy redistribution between all harmonics of the scattered longitudinal and transverse waves. This results in non-intuitive interesting responses. These studies are extended to explore one-way and two-way two-wave mixing of longitudinal waves and their interesting nonlinear effects. Phase difference introduced during harmonic scattering distinguishes the sensitivity of fundamental harmonics.

Multiple Damage Detection in PZT Sensor Using Dual Point Contact Method

Lead Zirconate Titanate (PZT) is used to make ultrasound transducers, sensors, and actuators due to its large piezoelectric coefficient. Several micro-defects develop in the PZT sensor due to delamination, corrosion, huge temperature fluctuation, etc., causing a decline in its performance. It is thus necessary to identify, locate, and quantify the defects. Non-Destructive Structural Health Monitoring (SHM) is the most optimal and economical evaluation method. Traditional ultrasound SHM techniques have a huge impedance mismatch between air and solid material, and most of the popular signal processing methods define time series signals in only one domain, which provides sub-optimal results for non-stationary signals. Thus, to improve the accuracy of detection, the point contact excitation and detection method is implemented to determine the interaction of ultrasonic waves with micro-scale defects in the PZT. The signal generated from this method being non-stationary in nature, it requires signal processing with changeable resolutions at different times and frequencies. The Haar Discrete Wavelet Transformation (DWT) is applied to the time series data obtained from the coulomb coupling setup. Using the above process, defects up to 100 μm in diameter could be successfully distinguished.

FEM-based simulation tools for ultrasonic concrete inspection

The simulation of nondestructive evaluation is a useful tool in the design of inspection procedure or the interpretation of results. In the case of the ultrasonic inspection of concrete, modeling the complex interaction of ultrasonic waves with the heterogeneous material is challenging. A finite element code for the simulation of ultrasonic inspections is developed in the CIVA software platform. It is the kernel of a new simulation module dedicated to concrete in a custom version of CIVA. This module relies on automated meshing managed through a user-friendly interface and offers comparatively fast numerical computations. Its aims at modeling practical concrete inspection configurations, involving for example distributions of aggregates, voids and metallic objects. In this communication, we present these modelling efforts and focus on configurations of interests and evaluation of the modelling performances performed in a recent collaboration between CEA and EDF.

Ultrasonic inspection for ice accretion assessment: effects on direct wave propagation in composite media

From aeroplane wings to overhead power lines, through giant blades of wind turbines, a build up of ice can cause problems ranging from impaired performance all the way to catastrophic failure. Therefore, it is of the utmost importance to control or prevent ice formation, especially on the critical areas of a structure. However, de-icing and anti-icing countermeasures can result energetically expensive and hazardous to the environment. In addition, excessive use of such of them will reduce the life of the ice protection system and introduce fatigue to the controlled structures. Thus, in order to manage properly the available resources, it is desirable to have an ice detection system that can both detect ice formation and monitor the thickness of ice on critical surfaces. This would allow acting when it is necessary. Ultrasonic guided-wave-based technique has been proved reliable for ice detection, but approaches to establish ice accretion over time have not been provided yet. The paper investigates the interaction of ultrasonic direct waves in composite plate with ice layers and the effects of ice thickening on the ultrasound propagation. Moreover, the use of metrics is discussed as indicators of ice growth.

Advances in nonlinear ultrasonic detection of microcracks

<p indent="0mm">A large number of key components are widely operated under extreme conditions of high temperature and high pressure in power, nuclear energy, aerospace and other important industrial fields. Microdefects are inevitably generated in these key components during the process of manufacturing. Due to the periodic loading and thermal stress, microcracks are generally initiated from these microdefects at the location with stress concentration. It has been found that the initiation and propagation of fatigue microcracks usually occur prior to 70%–90% of fatigue life. It is difficult to observe the evidence before the formation of macrocracks, which may result in catastrophic accidents. Thus, the risk of sudden failure of key components increases greatly. Therefore, the accurate detection of microcracks is crucial for guaranteeing the safe operation of key components. Based on the diffraction, reflection and transmission, traditional ultrasonic testing method is merely validated to effectively detect macroscopic defects within half a wavelength. The nonlinear ultrasonic testing method is found to be sensitive to microcracks, as high order harmonics, sub-harmonics, DC components and frequency mixing waves can be generated due to the strong nonlinear interaction microcracks and ultrasonic waves. With the outstanding effectiveness to detect microcracks, the nonlinear ultrasonic testing method has attracted much attention in recent years. In this work, the research on detection of microcracks using nonlinear ultrasonic testing method is systematically reviewed in terms of theoretical models, numerical simulations and experimental measurements. Firstly, according to the breathing effect and sliding mechanism of microcrack surfaces, we present several theoretical models of nonlinear interaction between ultrasonic waves and microcracks, namely contact acoustic nonlinearity (CAN), bi-linear stiffness model, nonlinear spring model, Hertz contact theory, and rough contact surface model. The advantages and disadvantages of these theoretical models are discussed comparatively. Two mechanisms are mainly considered for the nonlinear interaction of microcracks and ultrasonic waves, namely the macroscopic opening and closing of crack surfaces and the microscopic contact of rough microcracks surfaces. Secondly, we introduce numerical simulation studies on the nonlinear ultrasonic generation induced by microcracks. The applicability is analyzed for several simulation methods, such as finite element method, spectral finite element method, finite difference method, boundary element method and local interaction simulation approach, and the generation and propagation of nonlinear ultrasonic waves are analyzed as well. The effect of microcrack geometries on the nonlinear ultrasonic waves is then summarized. The microcrack geometries are considered mainly clouding the microcrack length, width, depth, density and direction. Furthermore, we present the experimental measurements on the generation of nonlinear ultrasonic waves induced by microcracks and on the localization and imaging of microcracks based on the nonlinear ultrasonic waves. The generation of high order harmonics, sub-harmonics, DC components and frequency mixing waves was observed in the specimens with microcracks. The nonlinear ultrasonic detection is presented to evaluate fatigue microcracks with various microcrack length, width, depth, density and direction. Based on this phenomenon, nonlinear ultrasonic mixing method, transducer array imaging method and nonlinear ultrasonic phased array method are introduced to localize the microcracks. Finally, further studies on evaluation of microcracks using nonlinear ultrasonic waves are proposed, including the comprehensive physical model for actual microcracks in engineering components, robust detection method, and quantitative evaluation of microcracks and service life.

Automatic Quantification of Subsurface Defects by Analyzing Laser Ultrasonic Signals Using Convolutional Neural Networks and Wavelet Transform.

The conventional machine learning algorithm for analyzing ultrasonic signals to detect structural defects necessarily identifies and extracts either time- or frequency-domain features manually, which has problems in reliability and effectiveness. This work proposes a novel approach by combining convolutional neural networks (CNNs) and wavelet transform to analyze the laser-generated ultrasonic signals for detecting the width of subsurface defects accurately. The novelty of this work is to convert the laser ultrasonic signals into the scalograms (images) via wavelet transform, which are subsequently utilized as the image input for the pretrained CNN to extract the defect features automatically to quantify the width of defects, avoiding the necessity and inaccuracy induced by artificial feature selection. The experimentally validated numerical model that simulates the interaction of laser-generated ultrasonic waves with subsurface defects is first established, which is further utilized to generate adequate laser ultrasonic signals for training the CNN model. A total number of 3104 data are obtained from simulation and experiments, with 2480 simulated signals for training the CNN model and the remaining 620 simulated data together with 4 experimental signals for verifying the performance of the proposed algorithm. This approach achieves the prediction accuracy of 98.5% on validation set, particularly with the prediction accuracy of 100% for the four experimental data. This work proves the feasibility and reliability of the proposed method for quantifying the width of subsurface defects and can be further expanded as a universal approach to various other defects detection, such as defect locations and shapes.

Inversion methodology for ultrasonic characterization of polycrystals with clusters of preferentially oriented grains

Titanium alloys are widely used in the aerospace industry. However, due to presence of microtexture, which is characterized by preferred crystallographic orientation clustering of thousands of alpha crystallites, cold dwell fatigue may significantly reduce the part life. To satisfy the practical need for nondestructive microtexture characterization, an inverse ultrasonic methodology is proposed to quantify mean parameters of microtexture regions (MTRs) having ellipsoidal shapes. One limitation of previous model-based ultrasonic inversion methods is required knowledge of elastic constants of the crystallites, which are rarely available for engineering alloys. This study overcomes this constraint by adopting the far field attenuation model, JASA, 137 (5), 2655–2669 (2015), and the backscattering model for ultrasonic wave interaction with microtexture. In the methodology developed, all necessary averaged MTR characteristics are obtained solely from directional ultrasonic measurements (backscattering, attenuation, and velocity) without a prior knowledge of material microstructures or elastic properties of different material phases. The inversion method is illustrated by simulations. To support the inversion methodology, the mean MTR sizes, morphology, and elastic scattering factors are determined from the ultrasonic experiment on a Ti-6242 alloy sample. The inversion results are compared with destructive electron backscatter diffraction (EBSD) analysis from which the MTRs are segmented using a non-contiguous grouping criteria. Good agreement is found.

Modeling of physical processes of interaction of ultrasonic wave with metal structures for detection of defects

In the article the features of the physical processes modeling of the ultrasonic wave interaction to the metal structures are considered. The mathematical model for calculating the acoustic field of a single element of a 32-element electromagnetic acoustic phased array of SV-waves is developed. The computer simulation of the process of reflection of the ultrasonic beam from a defect is carried out. The developed model allows to study the influence of the shape, size, location of defects in the plate, as well as the geometric parameters of the plate, on the formation of the reflected signal.

ДОСЛІДЖЕННЯ ЗГАСАННЯ УЛЬТРАЗВУКОВИХ ХВИЛЬ ПРИ ЇХ ПРОХОДЖЕННІ ТА ВІДБИТТІ ВІД ОДНОШАРОВИХ МАТЕРІАЛІВ З ПОРАМИ РІЗНОГО РОЗМІРУ

Research of attenuation of ultrasonic waves in various single-layer materials with available pores of different sizes changes in this work. The above is necessary for the possibility of creating non-contact means of ultrasonic testing of such materials. In the work to analyze the processes of interaction of ultrasonic waves with single-layer materials and various changes depending on the thickness or basis weight of the material. Expressions are given for the modules of the complex coefficient of transmission and reflection of ultrasonic waves from single-layer materials with small pores, as well as from textile single-layer materials with through pores, through which most of the vibrations pass. The dependences of relative changes in the amplitude attenuation of waves on the oscillation frequency, thickness and basis weight of the material are given. It is shown that the attenuation of the amplitude of ultrasonic waves that interact with single-layer materials with small pores, and the damping of vibrations for single-layer textile fabrics can be very different from each other. This difference is caused by the bending of part of the sound waves of the fibers of textile fabrics with through pores during the interaction of vibrations. The dependences of the relative changes in the difference of the modules with and without attenuation are obtained for the complex reflection and transmission coefficients of ultrasonic waves. These vibrations interacting with single-layer materials with different pores are considered taking into account the frequency of ultrasonic waves, pore sizes, thickness or basis weight of the material itself. The obtained dependences for determining the attenuation of the amplitude of the probe ultrasonic waves on the structure, porosity of the material, its thickness or surface density. This will allow to create non-contact control tools for materials with complex internal structures and automatically configure them to change pore sizes, which can significantly affect the errors of such devices. The accuracy of the devices that will be tuned to the complex structure of the monolayer material being controlled will be affected precisely by the attenuation parameter of the probe oscillations. In the future, this line of research will make it possible to create non-contact methods and means of monitoring the technological parameters of various single-layer materials and integrate such devices and systems directly into the production process.

Multiresolution Dynamic Mode Decomposition (mrDMD) of Elastic Waves for Damage Localisation in Piezoelectric Ceramic

The performance of piezoelectric sensors deteriorated due to the presence of defect, delamination, and corrosion that needed to be diagnosed for the effective implementation of the structural health monitoring (SHM) framework. A novel experimental approach based on Coulomb coupling is devised to visualise the interaction of ultrasonic waves with microscale defects in the Lead Zirconate Titanate (PZT). Multiresolution dynamic mode decomposition (mrDMD) technique in conjunction with image registration, and Kullback Leibler (KL) divergence is utilised to diagnose and localise the surface defect in the PZT. The mrDMD technique extracts the spatiotemporal coherent mode and provides an equation-free architecture to reconstruct underlying system dynamics. Additionally, due to the strong connection between mrDMD and Koopman operator theory, the proposed technique is well suited to resolve the nonlinear and dispersive interaction of elastic waves with boundaries and defects. The mrDMD sequentially decomposes the three-dimensional spatiotemporal data into low and high frequency modes. The spectral modes are sensitive to defects based on the scaling of wavelength with the size of the defect. The error due to offset and distortion was minimised with ad hoc image registration technique. Further, localisation and quantification of defect are performed by evaluating the distance metric of the probability distribution of coherent data of mrDMD acquired from healthy and defected samples. In the arena of big-data that is ubiquitous in SHM, the paper demonstrates an efficient damage localisation algorithm that explores the nonlinear system dynamics using spectral multi-mode resolution techniques by sensitising the damage features.

Evaluation of subsurface defects in metallic structures using laser ultrasonic technique and genetic algorithm-back propagation neural network

An effective nondestructive evaluation technique that enables the detection and quantification of subsurface defects is highly demanded for assuring safety and reliability of safety-critical structures. In this work, an improved genetic algorithm-back propagation neural network (GA-BPNN) model and non-contact laser ultrasonic technique are combined to quantify the width of subsurface defects. An experimentally validated numerical model that simulates the interaction of laser-generated Rayleigh ultrasonic waves with subsurface defects is firstly established, which is further utilized to generate a large number of labeled laser ultrasonic signals for training the GA-BPNN model. A total number of 189 data are obtained from simulation and experiments, with 173 simulated signals for training the GA-BPNN model and the remaining 13 simulated signals together with 3 experimental signals for verifying the performance of the trained GA-BPNN model. Five features including three time-domain features (maximum, minimum and peak-to-peak value of the Rayleigh ultrasonic waves) and two frequency-domain features (Fc, BW-6dB), which are identified sensitive to the width of subsurface defects by both experiments and simulation, are extracted as inputs to train the machine learning algorithm. The result demonstrates that the GA-BPNN model trained with the combination of time and frequency features has the average error of 2.15%, which is substantially smaller than the errors obtained from the model trained with only time-domain features and frequency-domain features, with the average errors of 4.43% and 21.81%, respectively. This work proves the feasibility and reliability to quantify the width of subsurface defects in metallic structures using laser ultrasonic technique and the improved GA-BPNN algorithm.

Application of laser ultrasonic technique for detecting weld defect based on FDST method

The propagation image of laser-generated ultrasonic wave interaction with the weld defect are investigated by the finite element method (FEM) and experimental system. We analyses the changes of ultrasonic wave at the different positions from weld defect in detail. Then analyses the frequency changes of ultrasonic wave at different source-receiver distance based on FDST (fast discrete sine transform). In order to quantitative detect weld defect, we compare the different spectrum images of laser-generated ultrasonic wave based on FFT (fast frequency transform) with the different spectrum images of laser-generated ultrasonic wave based on FDST, which demonstrates the FDST analysis of the spectrum images method can be intuitive, efficient detection of weld defect.

Acoustic radiation torque exerted on a subwavelength spheroidal particle by a traveling and standing plane wave.

The nonlinear interaction of ultrasonic waves with a nonspherical particle may give rise to the acoustic radiation torque on the particle. This phenomenon is investigated here considering a rigid prolate spheroidal particle of subwavelength dimensions that is much smaller than the wavelength. Using the partial wave expansion in spheroidal coordinates, the radiation torque of a traveling and standing plane wave with arbitrary orientation is exactly derived in the dipole approximation. In this paper, asymptotic expressions of the torque as the particle geometry approaches a sphere and a straight line are obtained. As the particle is trapped in a pressure node of a standing plane wave, its radiation torque equals that of a traveling plane wave. This paper also finds how the torque changes with the particle aspect ratio. The findings in this paper are in excellent agreement with previous numerical computations. Also, by analyzing the torque potential energy, the stable and unstable spatial configurations available for the particle are determined.

Enhanced boiling heat transfer on micro-structured surfaces via ultrasonic actuation

Abstract Emerging issues in boiling heat transfer include enhancing heat transfer uniformity/stability, and critical heat flux (CHF). Microcavity structures improve heat transfer uniformity/stability by departing bubbles with arranged formation due to pinning effects and regular pitch. Ultrasonic actuation induces an acoustic field on departed bubbles, and this enhances contact line instability between the bubble and microcavity structures, resulting in an increased dissipation rate of smaller bubbles. In this study, we demonstrate that synergetic effects from microcavity structures and ultrasonic actuation can enhance CHF and thermal stability while also improving temporal/spatial temperature uniformity. Applying microcavity structures with ultrasonic actuation, we observe smaller and faster bubbles' departure with the proposed formation. These bubble departure characteristics on the microcavity surface with ultrasonic actuation enhance CHF and thermal stability by delaying bubble coalescence and ensuring liquid paths between smaller and faster-departed bubbles. Thus, when ultrasonic actuation is applied to the microcavity structure, CHF increased by 20%, and temporal/spatial temperature variations near CHF were reduced to less than 1/2 and 1/3, respectively, compared to no actuation case. This research will help to understand the interaction of ultrasonic wave and bubbles, and to show the way to overcome CHF limitations of passive methods using microsized structures.

Nonlinear Behavior of High-Intensity Ultrasound Propagation in an Ideal Fluid

In this paper, nonlinearity associated with intense ultrasound is studied by using the one-dimensional motion of nonlinear shock wave in an ideal fluid. In nonlinear acoustics, the wave speed of different segments of a waveform is different, which causes distortion in the waveform and can result in the formation of a shock (discontinuity). Acoustic pressure of high-intensity waves causes particles in the ideal fluid to vibrate forward and backward, and this disturbance is of relatively large magnitude due to high-intensities, which leads to nonlinearity in the waveform. In this research, this vibration of fluid due to the intense ultrasonic wave is modeled as a fluid pushed by one complete cycle of piston. In a piston cycle, as it moves forward, it causes fluid particles to compress, which may lead to the formation of a shock (discontinuity). Then as the piston retracts, a forward-moving rarefaction, a smooth fan zone of continuously changing pressure, density, and velocity is generated. When the piston stops at the end of the cycle, another shock is sent forward into the medium. The variation in wave speed over the entire waveform is calculated by solving a Riemann problem. This study examined the interaction of shocks with a rarefaction. The flow field resulting from these interactions shows that the shock waves are attenuated to a Mach wave, and the pressure distribution within the flow field shows the initial wave is dissipated. The developed theory is applied to waves generated by 20 KHz, 500 KHz, and 2 MHz transducers with 50, 150, 500, and 1500 W power levels to explore the effect of frequency and power on the generation and decay of shock waves. This work enhances the understanding of the interactions of high-intensity ultrasonic waves with fluids.

Speed of sound ultrasound transmission tomography image reconstruction based on Bézier curves

Speed of Sound (SoS) maps from ultrasound tomography (UST) provide valuable quantitative information for soft tissue characterization and identification of lesions, making this technique interesting for breast cancer detection. However, due to the complexity of the processes that characterize the interaction of ultrasonic waves with matter, classic and fast tomographic algorithms such as back-projection are not suitable. Consequently, the image reconstruction process in UST is generally slow compared to other more conventional medical tomography modalities. With the aim of facilitating the translation of this technique into real clinical practice, several reconstruction algorithms are being proposed to make image reconstruction in UST to be a fast and accurate process. The geometrical acoustic approximation is often used to reconstruct SoS with less computational burden in comparison with full-wave inversion methods. In this work, we propose a simple formulation to perform on-the-flight reconstruction for UST using geometrical acoustics with refraction correction based on quadratic Bézier polynomials. Here we demonstrate that the trajectories created with these polynomials are an accurate approximation to reproduce the refracted acoustic paths connecting the emitter and receiver transducers. The method is faster than typical acquisition times in UST. Thus, it can be considered a step towards real-time reconstructions, which may contribute to its future clinical translation.