ULTRASONICS

Investigation of electrochemical micromachining on magnesium alloy using hollow tool electrode
Sivashankar N, Thanigaivelan R, Selvarajan L and Venkataramanan K
This study investigates the application of Electrochemical Micromachining (ECMM) on magnesium alloy AZ31 using a hollow tool electrode. Magnesium alloys, particularly AZ31, are valued for their lightweight properties and strength-to-weight ratio but pose challenges in precision machining due to their high reactivity and susceptibility to corrosion. Utilizing a hollow tool electrode in ECMM offers potential advantages in precision and control, crucial for micro-scale manufacturing applications. This research focuses on studying the effect of process parameters such as electrolyte composition, voltage, and duty cycle to achieve high-quality micro holes. Experimental results demonstrate the effects of these parameters on machining speed and overcut. Findings indicate that the use of a hollow tool electrode significantly improves the hole geometry and surface integrity of the machined features, making ECMM a viable technique for the micromachining of magnesium alloys. The experimental outcome shows that the maximum MS of 0.439 μm/s was noted with 156 OC. The machining was enhanced by 12 % when compared to traditional submerged machining with a solid tool.
Subsurface damage identification and localization in PZT ceramics using point contact excitation and detection: An image processing framework
Pal R, Ghosh N, Kalimullah NMM, Ahmad A, Melandsø F and Habib A
Piezoelectric sensors hold immense potential in structural health monitoring (SHM) applications. However, their performance can be deteriorated by defects and extreme weathering. Therefore, diagnosing the sensor before implementation is very crucial. Unreliable experimental methods and inaccurate damage detection algorithms are major concerns that need addressing to develop a robust damage detection framework. In this work, we propose a subsurface anomaly detection framework that uses the evolution of ultrasonic waves in spatial and temporal domains. This framework comprises three key components: a novel Coulomb coupling-based experimental approach to visualize ultrasonic wave interactions with microscale Lead Zirconate Titanate (PZT) subsurface defects, an advanced denoising algorithm using block matching 3D (BM3D) filtering to reduce noise, and a multiresolution dynamic mode decomposition (mrDMD) algorithm to identify subsurface defects in PZT. The results conclude that the proposed framework is robust, efficient, and can provide reliable detection and localization of damage even with significant measurement noise and without any reference damage-free counterpart of the PZT material.
Focused ultrasonic transducer for aircraft icing detection
Wang Y, Wang Y, Chen S, Zhu C, Wu D, Zhu C and Lu X
Ultrasonic detection technique (UDT) serves as a pivotal method for monitoring aircraft icing conditions. However, the inherently porous and irregular shape of atmospheric ice leads to a pronounced attenuation of ultrasonic wave energy during propagation. Current ultrasonic transducers (UTs) fall short of meeting the requisite sensitivity and depth parameters for effective detection. This study proposes an innovative focused ultrasonic transducer (FUT) designed to extend the range of ice detection capabilities. Constructed using a 1-3 piezoelectric composite configuration, this FUT is characterized by its flexibility and slender profile. The focusing effect was accomplished through a deliberate bending mechanism. The FUT demonstrates its efficacy in detecting ice on aluminium skin surfaces. Furthermore, we validated the focusing effect and conducted a thorough optimization process. A comparative analysis between the FUT and traditional planar UTs revealed that the FUT enhances detection energy by approximately 30%, while also nearly doubling the detection range for glaze ice. These findings underscore the FUT's promising potential for applications in the detection of substantial ice.
Acoustic emission detection and modal decomposition using a relaxor ferroelectric single crystal linear array
Vien BS, Gray J, Baddiley E, Hills Z, Lalbakhsh P, Lee SXM, Szydzik C, Moss SD, Rosalie C, Rajic N, Mitchell A and Chiu WK
This paper reports on an acoustic emission (AE) sensor based on relaxor ferroelectric single crystal (RFSC) transduction. The sensor crystal is arranged into a Linear Array for Modal Decomposition and Analysis (LAMDA), with the sensor interrogated by a bespoke high-bandwidth instrument. The efficacy of RFSC LAMDA sensors is showcased through a series of comparative experiments, which include the simultaneous acquisition of pencil lead break (PLB) AEs in a 1.6 mm thick aluminium plate using RFSC LAMDA, a wideband commercial sensor, and laser vibrometry. Subsequent modal decomposition and analysis of the PLB AE signals, as detected by RFSC LAMDA, identified the guided wave modes below 1.4 MHz. Furthermore, it was found that RFSC LAMDA exhibits, on average, 26.6 times greater improvement in sensitivity compared with polyvinylidene fluoride LAMDA variant with near-identical geometry.
Improving the signal-to-noise ratio of the laser ultrasonic synthetic aperture focusing technique to detect submillimeter internal defects using echo array similarity
He H, He J, Xia Z, Sun K, Wang C and Liu Q
Laser ultrasonic imaging is a promising technique for structural health monitoring because it is noncontact and nondestructive. However, this technique will only find more industrial applications if it has a high signal-to-noise ratio (SNR) and short data acquisition time. In existing delay-and-sum algorithms, such as the synthetic aperture focusing technique (SAFT) and the total focusing method, a higher SNR requires more A-scan signals, which mean a longer data acquisition time. It is difficult for these algorithms to consider these two aspects simultaneously. Thus, in this study, we propose a post-processing algorithm that extracts neglected information from laser ultrasonic B-scan data to improve the SNR of the SAFT without increasing the data acquisition time. The SNR was increased by multiplying the SAFT image intensity with the echo array similarity defined using the directivity and echo shape information of laser ultrasound. In experiments, SNR was increased from 4.1 dB to 31.3 dB for two submillimeter defects having a diameter of 0.5 mm and depth of 15 mm. Deeper defects can be detected because of the improved SNR. In this study, two submillimeter defects with a depth of 30 mm were detected. Compared with existing delay-and-sum algorithms, the proposed algorithm performs well in terms of both SNR and data acquisition time, which can promote its use in more industrial applications.
Temperature-compensated acoustoelastic measurements of the stress in bolts
Han Y, Huang H, Cai W, Li M, Mao Y and Li C
Temperature is an important factor influencing the results of non-destructive acoustoelastic measurements of the internal stress in objects like bolts owing to its impact on the elastic modulus of the material. However, conventional methods that seek to obtain the temperature field of the measurement object independently suffer from high complexity and low accuracy. The present work addresses this issue by developing a method that eliminates the influence of temperature on the acoustoelastic measurements of stress in bolts based on the time interval between the head and coda waves of ultrasonic signals. The origin of coda waves in rod-shaped objects is investigated theoretically, and this understanding is applied for analyzing the relationship between the temperature and internal stress of the object and the time interval between the head and coda waves of ultrasonic signals. The analysis demonstrates that the observed time interval is related to temperature and stress in accordance with a linear relationship with the velocity of the longitudinal wave and the rod diameter. Finally, the obtained relationship is applied within an acoustoelastic measurement model to eliminate the influence of temperature from the measurement results.
In-situ monitoring of µm-sized electrochemically generated corrosion pits using Lamb waves managed by a sparse array of piezoelectric transducers
Nicard C, Rébillat M, Devos O, El May M, Letellier F, Dubent S, Thomachot M, Fournier M, Masse P and Mechbal N
Corrosion is a major threat in the aeronautic industry, both in terms of safety and cost. Efficient, versatile, and cost affordable solutions for corrosion monitoring are thus needed. Ultrasonic Lamb Waves (LW) appear to be very efficient for corrosion monitoring and can be made cost effective and versatile if emitted and received by a sparse array of piezoelectric elements (PZT). A LW solution relying on a sparse PZT array and allowing to monitor µm-sized corrosion pit growth on stainless 316L grade steel plate is here evaluated. Experimentally, the corrosion pit size is electrochemically controlled by both the imposed electrical potential and the injection of a corrosive NaCl solution through a capillary located at the desired pit location. In parallel, the corrosion pit growth is monitored in-situ every 10 s by sending and measuring LW using a sparse array of 4 PZTs bonded to the back of the steel plate enduring corrosion. As a ground truth information, the corrosion pit volume is estimated as the dissolved volume balancing the electronic charges exchanged during corrosion. The corrosion pit radius is additionally checked post-experiment precisely with an optical measurement. Measured LW signals are then post-processed in order to compute a collection of synthetic damage indexes (DIs). After dimension reduction steps, obtained DI values correlates extremely well with the corrosion pit radius. Using a linear model relating those DI values to corrosion pit radius, it is demonstrated that corrosion pit from 30 µm to 150 µm can be reliably detected, located, and their upcoming size extrapolated. Two independent experiments were achieved in order to ensure the repeatability of the proposed approach. LW managed by a sparse PZT array thus appears to be reliable and efficient to monitor growth of µm-sized corrosion pits on 316L steel plates. If embedded in aeronautical structure, such an approach could be a versatile and cost-effective alternative to actual non-destructive maintenance procedures that are time and manpower consuming.
3D complex dispersion curves and attenuation characteristics based on Drude-Lorentz oscillators for Lamb wave in various metal-piezoelectric composites
Zhu F, Li P, Qian Z and Kuznetsova I
Given that many micro-nano piezoelectric acoustic devices operate at very high frequencies, the dissipation caused by metal electrodes significantly affects their performance (e.g., quality factor), but these dissipation characteristics cannot be explained by conductivity at high frequencies. This study uses the Drude-Lorentz oscillator model, incorporating the frequency-dependent dielectric properties of metals, which in physics refer to electron oscillations at high frequencies, to investigate the three-dimensional (3D) complex dispersion curves and attenuation characteristics of Lamb waves in metal-piezoelectric composites. Five commonly used electrode metals (Pt, Al, Ag, Au, Cu) are analyzed to reveal the widespread attenuation characteristics. The Multidimensional Moduli Ratio Convergence Method (MMRCM) is employed, which utilizes the convergence and divergence of the moduli ratio to accurately locate zeros of complex dispersion equations. Meanwhile, multidimensional scanning is adopted to ensure comprehensive identification of minima moduli points. Two primary attenuation characteristics are identified: (1) attenuation trends related to the real part of the wavenumber for different branches, and (2) significant jumps in attenuation due to mode shape conversions in metals with veering regions. Furthermore, a size-dependent attenuation characteristic is observed, showing a quadratic increase in attenuation as the composite structure's total thickness decreases. These findings provide crucial insights for optimizing the design and performance of micro-nano devices where precise control over wave attenuation and dispersion is essential.
Twice reflected ultrasonic bulk wave for surface defect monitoring
Wong VK, Li X, Yousry YM, Philibert M, Jiang C, Lim DBK, Christopher Subhodayam PT, Fan Z and Yao K
This work offers an ultrasonic structural health monitoring (SHM) approach for assessing the defects located on the same surface and at one side of piezoelectric ultrasonic transducer array. It is based on the analysis of ultrasonic bulk wave travelling in the thickness direction obtained from an enhanced full-skip configuration of the time-of-flight diffraction (TOFD) technique. In contrast to existing TOFD setup only considering the direct paths between the ultrasonic transducer and defect, our ultrasound monitoring configuration involves twice reflected ultrasonic bulk wave (TRBW). The TRBW travels following the propagation route from an ultrasonic transmitter located at the same side of the defect initiated, the backwall, the defect tip, the backwall again and finally to the same or another ultrasonic transducer. Both theoretical analyses and experimental validations have been conducted in our study. A simplified algorithm for efficient detection and mapping the growth of a surface defect in an aluminum alloy block has been demonstrated with an incremental surface defect growth starting from 2.80 mm in depth, in which conformable direct-write ultrasonic transducers (DWT) made of in-situ piezoelectric coating are implemented. Our approach provides an ultrasonic method for effective monitoring the near surface defects with the ultrasonic transducers conveniently implemented on the same surface and at the same side of the defects.
Enhanced integrated acoustofluidics with printed circuit board electrodes attached to piezoelectric film coated substrate
Sun C, Mikhaylov R, Yang X, Zhang X, Feng K, Zheng T, Fu YQ and Yang X
The current key issues in applying acoustofluidics in engineering lie in the inflexibility of manufacturing processes, particularly those involving modifications to piezoelectric materials and devices. This leads to inefficient prototyping and potentially high costs. To overcome these limitations, we proposed a technique that is capable of prototyping acoustofluidic devices in a straightforward manner. This is achieved by simply clamping a printed circuit board (PCB) featuring interdigital electrodes (IDEs) onto a substrate coated with a piezoelectric thin film. By applying appropriate clamping force between the PCB and the substrate, one can effectively generate surface acoustic waves (SAWs) along the surface of the substrate. This approach simplifies the prototyping process, reducing the complexity and fabrication time. The clamping mechanism allows for easy adjustment and optimization of the SAW generation, enabling fine-tuning of the fluid and particle manipulation capabilities. Furthermore, this method allows for customizable interdigital transducers (IDTs) by 'patterning' IDEs on thin-film piezoelectric substrates (such as ZnO/Al and ZnO/Si) with various anisotropy orientations. This facilitates the on-demand generation of wave modes, including A0 and S0 Lamb waves, Rayleigh waves, and Sezawa waves. One notable advantage of this method is its capability to rapidly test acoustic wave patterns and performance on any substrate, offering a fast and streamlined approach to assess acoustic behaviors across diverse materials, thereby paving the way for efficient exploration of novel materials in SAW technology.
Near-surface defect detection in ultrasonic testing using domain-knowledge-informed self-supervised learning
Jeon M, Choi M, Choi W, Ha JM and Oh H
Recently, significant research efforts have been made to enhance ultrasonic testing (UT) by employing artificial intelligence (AI). However, collecting an extensive amount of labeled data across various testing environments to train the AI model poses significant challenges. Moreover, conventional UT typically focuses on detecting deep-depth defects, which limits the effectiveness of such methods in detecting near-surface defects. To this end, this paper proposes a novel near-surface defect detection method for ultrasonic testing that can be employed without collecting labeled data. We propose a self-supervised anomaly detection model that incorporates domain knowledge. First, synthetic faulty samples are generated by fusing the measured UT signals with the back-wall UT reflection signals, to simulate real faulty features. Unlike the CutPaste method used for computer vision applications, this synthesis method adds the back-wall echo signal to random locations by incorporating the physical principles of the superposition of ultrasonic signals. Next, a de-anomaly network is devised to isolate subtle defect features within the measured UT signals. The presence of defects was determined using the three-sigma rule of the mean absolute value of the residual output. The defect depth is determined by a time-of-flight calculation from the residual output. The effectiveness of the proposed method was evaluated through the UT of aluminum blocks with near-surface defects of varying depths under different surface conditions. Both qualitative and quantitative comparison studies demonstrated that the proposed method outperformed existing methods in detecting the presence and depth of near-surface defects.
Second-order nonlinear mixing processes involving a leaky guided acoustic wave
Pupyrev PD, Nedospasov IA and Mayer AP
Quasi-phasematched mixing processes of acoustic waves via second-order nonlinearity are analyzed with two perfectly guided waves generating a leaky wave. The efficiency of such processes is quantified by an acoustic nonlinearity parameter (ANP), defined as the linear growth rate of the leaky wave's amplitude in the initial stage of its spatial evolution. Two approximate ways of estimating the ANP of such processes are suggested. The first starts from a stationary solution of the equation of motion and boundary conditions for the displacement field, obtained within perturbation theory. This approach requires the solution of a near-singular linear system of equations. The second is based on the resonant state expansion of the displacement field generated in the mixing process. It allows to express the ANP in the form of an overlap integral, requiring normalization of the displacement field associated with the leaky wave. For leaky output waves with a high degree of localization at the waveguide, both methods yield results in good agreement, as demonstrated for an example system with generalized (2D) plate modes. The first approach has also been applied to finite element calculations of the ANP for nonlinear mixing processes of (1D) edge waves in an elastic plate with rigid faces.
Optimal transport assisted full waveform inversion for multiparameter imaging of soft tissues in ultrasound computed tomography
Wu X, Li Y, Su C, Li P and Lin W
Ultrasound computed tomography (USCT) has emerged as a promising platform for imaging tissue properties, offering non-ionizing and operator-independent capabilities. In this work, we demonstrate the feasibility of obtaining quantitative images of multiple acoustic parameters (sound speed and impedance) for soft tissues using full waveform inversion (FWI), which are justified with both numerical and experimental cases. A 3D reconstruction based on a series of 2D slice images is presented for the experimental case of ex vivo soft tissues. To improve the robustness of the reconstruction process, a hierarchical FWI strategy is adopted, gradually iterating from low to high frequencies. In parallel, we employ a graph-space optimal transport misfit function, avoiding convergence into local minima and minimizing inversion artifacts caused by skin-related supercritical reflections. Our method first carries out sound speed inversion based on transmitted waves in the low and middle frequency bands, and then uses all types of waves in the high frequency band for simultaneous inversion of both sound speed and impedance. Compared to conventional strategies, the proposed approach can accurately reconstruct physical models consistent with the actual soft tissue sample. These high-resolution ultrasound images of acoustic parameters are promising to allow for quantitative differentiation among different types of tissues (e.g., muscles and fats). These results have significant implications for advancing our understanding of tissue properties and for potentially contributing to disease diagnosis through USCT, which is a flexible and cost-effective alternative to X-ray computed tomography or magnetic resonance imaging at no significant sacrifices for resolution.
A noninvasive ultrasound vibro-elastography technique for assessing ocular lesions
Bui NT, Dalvin LA, Howard SL, Hall JP, Sit AJ and Zhang X
This research aims to develop a noninvasive ultrasound vibro-elastography technique for assessing ocular lesions including intraocular melanoma and nevus lesions.
Development of signal processing algorithms for delamination detection in composite laminates using non-contact excited Lamb waves
Lecointre LAC, Higuchi R, Yokozeki T, Hosoya N and Takeda SI
A novel Signal Processing algorithm based on the combination of a Wavelet Transform Analysis and Image Processing techniques is designed for assessing the delamination detectability of Lamb Waves generated with an innovative fully non-contact system in CFRP plates. Several Damage Indexes are extracted from the wavefields in spatial-time-frequency domain and plotted as surface cartographies to visualise their ability to size and localise artificial delaminations. Results show that the algorithm is efficient for characterising the waves propagation and that sophisticated Image comparison indexes show better ability to detect the artificial defects and to recognise healthy zones despite signal measurement and calculation uncertainties.
Ultrafast 3D synthetic aperture imaging with Hadamard-encoded aperiodic interval codes and aperiodic sparse arrays with separate transmitters and receivers
Kaddoura T, Masoumi MH and Zemp R
3D synthetic aperture (SA) imaging of volumes can be obtained using sparse 2D ultrasound arrays. However, even with just 256 elements, the volumetric imaging rate can be relatively slow due to having to transmit on each element in succession. Hadamard Aperiodic Interval (HAPI) codes can be used to image the full SA dataset in one extended transmit to speed up the synthetic aperture imaging, but their long nature produces large deadzones if the same elements are used as both transmitters and receivers. In this simulation study, we use a 2D Costas sparse array with separate transmitters and receivers to remedy the deadzone problem, and use it with the HAPI-coded imaging scheme to obtain fully transmit-receive focused, wide field-of-view 3D volumes with high-resolution and high SNR at ultrafast volumetric imaging rates of more than 500 volumes per second, almost nine times faster than non-coded SA imaging with the same imaging parameters. We show similar PSF performance compared to non-coded SA, and a 26 dB improvement in SNR with order-256 HAPI codes. We also present cyst simulations showing similar contrast for the HAPI-coded SA method compared to non-coded SA in the context of no noise, and improved contrast in the context of noise.
Influence of moisture on the diffusion of ultrasound in concrete
Ahn E, Song H, Shin M and Popovics JS
This study aimed to investigate the effects of internal moisture migration and subsequent drying-shrinkage-induced micro-cracking in concrete on diffuse ultrasound, through a series of experiments that comprised multiple drying and rewetting cycles carried out over the long-term. Cyclic drying and wetting phenomena in concrete were physically established following a predefined protocol and were traced measuring the mass change of specimens. Diffuse-wave tests were conducted using a pair of PZT patches bonded to cylindrical specimens, which acted as the ultrasonic transmitter and receiver in the range of 250-550 kHz. The results present that measured diffuse-wave parameters, diffusivity and dissipation, showed distinct varying and cyclic behaviors to drying and wetting processes, but they did not recover their original values in the saturated condition, revealing possible micro-cracking damage caused by the drying process, which should be understood to improve the reliability of diffuse ultrasound measurements in concrete subjected to environmental changes.
Lamb wave imaging via dual-frequency fusion for grating lobe effect compensation
Gao X, Yang T, Li D, Fang Y, Zhang J and Ta D
In Lamb wave imaging based on a phased array, higher frequencies narrowband excitation pulses enable more precise damage detection and localization. However, due to the size constraints of individual transducer elements, the spacing between array elements may exceed half the wavelength of the excitation signal. This can lead to a grating lobe effect. To overcome this limitation, a Lamb wave imaging method via dual-frequency fusion for grating lobe effect compensation is proposed in this study. Analyses indicate that the grating lobe effect may introduce artifacts or distortions in the imaging results. This method utilizes two frequencies of narrowband excitation pulses for imaging and subsequently fuses the results. By doing so, the imaging artifacts caused by the grating lobes produced by high-frequency narrowband excitation pulses are effectively compensated. The proposed method is validated through simulations and experiments on an aluminum plate, showing superior accuracy, contrast, and imaging quality.
High-cycle fatigue damage evaluation based on hysteresis nonlinearity using ultrasonic guided waves
Zhou T, Xue C, Lv X and Li B
This paper presents a novel approach utilizing nonlinear ultrasonic guided waves for the detection and evaluation of high-cycle fatigue damage in aluminum alloy plates. Through high-cycle fatigue testing, specimens with varying degrees of fatigue damage were created and evaluated using ultrasonic-guided wave measurement technology. The integration of time-frequency analyses effectively reduced the impact of wave dispersion and resonance effects, establishing a reliable operational frequency bandwidth. The results identified a positive correlation between the amplitude of odd harmonic components caused by hysteresis nonlinearity and fatigue crack length, while an inverse correlation was observed with specimen resonance frequency. The results confirm the high sensitivity and accuracy of this approach for early fatigue damage detection, offering a significant advancement in the non-destructive evaluation of engineering structures and a foundation for structural failure prevention.
Generation of broadband airborne ultrasound using an Harmonic Acoustic Pneumatic Source
Rousseau R, Grandjean P, Quaegebeur N, Charlebois-Vachon L and Micheau P
This paper presents a new type of airborne transducer for generating broadband ultrasound with a high Sound Pressure Level (SPL). The concept is based on the Harmonic Acoustic Pneumatic Source (HAPS) that uses pressurized air in conjunction with a flow chopper made up of a rotating cage with slots connected to a specific exhaust. The fundamental frequency depends on the number of slots and the rotation speed of the cage. An analytical model of the HAPS coupled with a numerical model of the exhaust is used to predict the radiated acoustic pressure and to estimate the influence of dimensional parameters on pressure level generated by the source. Experiments are conducted with two cages: one with one slot in order to generate pulses periodically and one with 122 slots to generate periodic sound. The level of sound pressure is measured as a function of distance (0.004 to 0.5 m), the cage rotation (up to 11 krpm) and directivity (0 to 90°). For the fundamental frequency at 22 kHz, the maximum SPL of 150 dB (632 Pa rms) is /measured at 0.004 m, and decreases to 122 dB (35 Pa rms) at 0.5 m. At 0.5 m, the second and third harmonics can generate a SPL equal or greater than 115 dB above 22 kHz and up to 66 kHz. Discrepancies between the experiments results and numerical model are observed in terms of SPL, directivity and in-axis pressure.
A new FEM-based approach on the modeling of stress-induced velocity shift of piezoelectric surface acoustic wave resonators
Naghdi M, Zhang H, Sreedharan SV, Ju S and Desai MH
A novel methodology is introduced for the computation of stress-induced surface acoustic wave velocity shifts in piezoelectric resonators including quartz, lithium niobate and langasite resonators. The numerical framework has been verified through a comparative analysis of experimental and Finite Element Method (FEM) results for quartz resonators. This approach introduces the combined capabilities of COMSOL Multiphysics and MATLAB, facilitated by LiveLink, to systematically calculate all parameters contributing to the perturbation integral. The findings have a better accuracy using the LiveLink methodology in this study compared to prior approaches that rely on average stress and strain calculations in the central point of the resonator. Moreover, the utilization of LiveLink not only enhances accuracy but also establishes MATLAB as a fundamental software platform for interfacing with COMSOL Multiphysics. The proposed approach in this paper can extend to complex strain sensors or investigations into the influence of temperature and imbalanced loading effects in future research endeavors. Furthermore, the LiveLink approach introduced herein can be extended to optimize crystal orientation and identify premium wave directions, thereby contributing to the enhanced design of Surface Acoustic Wave (SAW) resonators. This innovative methodology is used to advance the understanding and application of stress-induced velocity shifts in SAW devices, presenting future developments in sensor technologies and resonator designs. © 2024 Elsevier Science. All rights reserved.