Ring Transducer Research Articles

Smart structural health monitoring (SHM) system for on-board localization of defects in pipes using torsional ultrasonic guided waves

Most reported research for monitoring health of pipelines using ultrasonic guided waves (GW) typically utilize bulky piezoelectric transducer rings and laboratory-grade ultrasonic non-destructive testing (NDT) equipment. Consequently, the translation of these approaches from laboratory settings to field-deployable systems for real-time structural health monitoring (SHM) becomes challenging. In this work, we present an innovative algorithm for damage identification and localization in pipes, implemented on a compact FPGA-based smart GW-SHM system. The custom-designed board, featuring a Xilinx Artix-7 FPGA and front-end electronics, is capable of actuating the PZT thickness shear mode transducers, data acquisition and recording from PZT sensors and generating a damage index (DI) map for localizing the damage on the structure. The algorithm is a variation of the common source method adapted for cylindrical geometry. The utility of the algorithm is demonstrated for detection and localization of defects such as notch and mass loading on a steel pipe, through extensive finite element (FE) method simulations. Experimental results obtained using a C-clamp for applying mass loading on the pipe show good agreement with the FE simulations. The localization error values for experimental data analysed using C code on a processor implemented on the FPGA are consistent with algorithm results generated on a computer running Python code. The system presented in this study is suitable for a wide range of GW-SHM applications, especially in cost-sensitive scenarios that benefit from on-node signal processing over cloud-based solutions.

Enhancing Image Contrast in Breast USCT Reflection Imaging Using Coherence Factor Beamforming

Abstract Breast cancer is the most common cancer worldwide, and early screening is essential. Existing breast ultrasound is affordable and convenient, but its 2D image quality is poor, and it heavily relies on the doctor’s skills. The novel breast ultrasound computed tomography (USCT) can use a ring array probe to implement hundreds of single transducer emission for full-view focusing synthetic aperture reflection imaging, thereby obtaining high-resolution 3D images. However, single transducer emission results in low acoustic intensity, which further leads to low signal-to-noise ratio and low contrast of reflection images. To improve image contrast, this study incorporated beamforming with coherence factor (CF) into reflection imaging using ring transducers, promising to produce high-contrast USCT reflection images. For evaluation, we developed a USCT prototype with 2048 elements and conducted phantom experiments. We conducted phantom experiments. Results showed that the contrast achieved by the coherence factor method of the breast phantom image is improved from 24.54 dB to 63.18 dB, and the artifacts are significantly suppressed. It can be seen that the CF method could significantly improve the contrast of the breast USCT reflection image.

Demonstration Study of Reflector-Based Volumetric Speed-of-Sound Imaging With Linear Ultrasound Arrays

Conventional B-mode ultrasound imaging has difficulty in delineating homogeneous soft tissues with similar acoustic impedances, as the reflectivity depends on the acoustic impedance at the interface. As a quantitative imaging biomarker sensitive to alteration of biomechanical properties, speed-of-sound (SoS) holds promising potential for tissue and disease differentiation such as delineation of different breast tissue types with similar acoustic impedance. Compared to two-dimensional (2D) SoS images, three-dimensional (3D) volumetric SoS images achieved through a full-angle ultrasound scan can reveal more intricate morphological structures of tissues; however, they generally require a ring transducer. In this study, we introduce a 3D SoS reconstruction system that utilizes hand-held linear arrays instead. This system employs a passive reflector positioned opposite the linear arrays, serving as an echogenic reference for time-of-flight (ToF) measurements, and a high-definition camera to track the location corresponding to each group of transmit-receive data. To merge these two streams of ToF measurements and location tracking, a voxel-based reconstruction algorithm is implemented. Experimental results with gelatin phantom and ex vivo tissue have demonstrated the stability of our proposed method. Moreover, the results underscore the potential of this system as a complementary diagnostic modality, particularly in the context of diseases such as breast cancer.

A miniature swimmer actuated by a PZT ring ultrasonic underwater propulsion system

This study investigates a scheme utilizing a ring transducer for an acoustic underwater propulsion system. Acoustic underwater propulsion systems are well suited for the inspection and repair of underwater robots due to their small size, high power density, and simple structure. Previous research has focused on self-propelled swimmers utilizing disc transducers. However, the radial vibration component of disc transducers makes it difficult to provide propulsion for an acoustic underwater propulsion system driven by an acoustic driving force. Pure longitudinal vibration requires a greater thickness to achieve the same vibration area, resulting in higher impedance and reduced driving efficiency. In this paper, simulation, and measurements of vibration distribution demonstrate that a ring transducer exhibits a vibration distribution closely resembling pure longitudinal vibration. A prototype swimmer using a ring transducer was fabricated for experimental evaluation through measurements of admittance characteristics, zero-speed propulsion, and no-load speed in water.

A lumped-parameter model of the free-flooded ring transducer array.

The free-flooded ring (FFR) transducer is an extensively used ring-type acoustic transducer in underwater environments owing to its broad operating frequency bandwidth and small size. However, achieving high sound pressure levels with a single FFR transducer is often difficult, thus necessitating the construction of vertically arranged FFR transducer arrays. This study presents a comprehensive analysis of the electrical and acoustic characteristics of an FFR transducer array by considering the mutual radiation load and the effects of gaps between adjacent piezoelectric rings. The lumped-parameter models of the piezoelectric ring, cylindrical cavity, cylindrical gap, and radiation impedance constitute an entire impedance matrix. The radiation impedance matrix for the FFR transducer array is calculated using the Helmholtz-Kirchhoff integral formula by considering the interaction of the FFR surfaces with the surrounding fluid medium. The proposed model predicts the resonance peaks in the admittance and transmitted voltage response (TVR) with a relative error of 5%, and the TVR level within a 3 dB range. Detailed analyses of a four-FFR transducer array reveal that a wider gap between each FFR leads to a decreased chance of negative conductance and broader operating bandwidth. The proposed model offers valuable insights into the design of FFR transducer arrays.

Radial sandwich radial-bending composite transducer designed based on acoustic black hole theory

A novel radial sandwich radial bending composite transducer is proposed based on the increasing amplitude of bending waves in the structure of an acoustic black hole (ABH). The transducer consists of a radial sandwich circular ring transducer and an outer acoustic black hole structure. The existence of the ABH structure realizes the conversion between radial vibration and bending vibration of the transducer, and improves the acoustic radiation performance of the transducer. Based on the one-dimensional acoustic black hole bending vibration theory, the bending vibration equation of the circular ABH structure is given. An analytical model of the ABH structure bending vibration is established by using the method of geometrical-acoustics, and the eigen frequency of its bending vibration is given. The relationship between the electromechanical conversion performance and the size of the transducer is discussed by using the finite element method, and the results show that when the eigen frequency of the bending vibration of the ABH structure is close to the resonant frequency of the transducer, the electromechanical coupling coefficient of the transducer reaches a maximum value. The radiation sound pressure field, radiation sound intensity, and radiation directionality of the transducer in the air are also analyzed by the finite element method. The results indicate that the presence of the ABH structure can improve the electromechanical conversion performance of the bending vibration of the transducer, enhance the acoustic radiation performance of the transducer, make the transducer exhibit radiation directionality and the lower order of the bending vibration mode of the ABH structure, the stronger radiation directionality of the transducer towards the left side and the right side. Finally, in order to verify the accuracy of the simulation and theory, we made a prototype transducer and carried out the experimental test of transducer electrical impedance and vibration mode. The measured results are in good agreement with the simulation results. The displacement distribution of the radiation surface of the transducer at resonance frequency is measured, which verifies the bending vibration mode of the ABH structure. This type of transducer is expected to be used as acoustic projector in the air or water.

Ultrasound computed tomography image reconstruction with multi-mode aperture matching of ring array

Ultrasound computed tomography (USCT) imaging with a ring array holds significant potential for the inspection of small animals, breast tissue, and industrial components. Despite its promise, current techniques face challenges in terms of image quality. This paper presents a multi-mode aperture matching method for USCT image reconstruction with a ring array, aiming to enhance imaging performance. The proposed method utilizes a full ring transducer to transmit signals with a designated sub-aperture, while the receiving sub-aperture is adjusted based on the reference center element. By altering the transmitting and receiving sub-apertures under different conditions, specific imaging effects can be achieved. Experimental validation was conducted using a hair strand of 0.03 mm diameter placed at both center and eccentric positions within the ring array, in conjunction a breast phantom. Image resolution and contrast were assessed using full width at half maximum and contrast-to-noise ratio metrics. The results identified optimal transmitting and receiving sub-aperture matching modes for imaging the hair strand at various positions, and demonstrated the impact of this method on imaging targets at different positions within the breast phantom. These findings and experimental validations provide significant implications for enhancing imaging performance in USCT with a ring array.

Design and realization of directivity adjustable ring transducer

In this paper, a directional segmented ring transmitting transducer, which can radiate sound waves in any horizontal region, has been developed. First, we introduce the structure of the segmented ring transducer and the characteristics of its radiation sound field, investigate the transmitting beam pattern control method based on the modal synthesis, and propose orthogonal beam pattern functions to adjust steering angles. Then, the three-dimensional finite element model of the segmented ring transducer is established, and the amplitude and phase of sound pressure excited by the first three modes, respectively, are calculated as a function of the frequency. We can combine each mode to obtain the desired beam patterns, and simulate the transmitting beam patterns steering to different directions. Finally, we manufacture the segmented ring transducer and measure its transmitting directivity in an anechoic water tank, and the first three modes are also calibrated according to the measured sound pressure. The experimental results show that the beam pattern synthesized by the first two modes has a 3 dB down beam width of about 156◦ at 15 kHz after calibration, and the maximum source level is approximately 24 dB higher than the minimum. The −3 dB beam width synthesized by the first three modes is about 84◦ at 17 kHz after calibration. In addition, we also carry out the experimental test on the proposed beam control method, and the driving-voltage weighting vectors are designed to obtain good transmitting beam patterns steering to different angles.

An improved lumped parameter model of the single free-flooded ring transducer using Helmholtz–Kirchhoff integral solution

The Helmholtz-Kirchhoff integral (HKI) may be considered as the boundary element method (BEM) used to calculate the acoustic pressure at any position in the 3D-radiation problem from a vibrating surface. This method provides valuable insights into the radiation characteristics of vibrating structures, which may offer significant information and tools to underwater transducer design engineers during the early stages of development. It may save considerable computational costs in the design processes for the underwater transducer such as Hull Mount Sonar. This study illustrates usefulness of the HKI-based approach by developing a simple model of the Free Flooded Ring (FFR) transducer using a piezoelectric ring model and the HKI solution on the surface acoustic pressure of the ring through their physical conditions on their connected interfaces. The FFR transducer is widely utilized as a low-frequency acoustic source in underwater environments due to its broad operating frequency bandwidth and relatively small size. The developed approach aims to construct a precise model that considers the sound-structure interactions between the piezoelectric ring and the acoustic medium around it. To validate the accuracy of the proposed method, the acoustic pressure and electrical admittance are compared with those obtained through finite element method (FEM) simulations.

Analysis and Optimization of Bending Vibration Modes of a Trilaminar Bending Ring Transducer with Unequal Diameters

In this study, we propose a fast calculation method that utilizes Kirchhoff’s hypotheses and electroelasticity theory to derive the resonant frequency, antiresonant frequency, and effective electromechanical coupling coefficient of a trilaminar bending ring transducer with unequal diameters. The accuracy of the theoretical method is validated through finite element analysis (FEM) and experimental tests. Furthermore, we perform optimization of the effective electromechanical coupling coefficient of the first-order bending vibration of the trilaminar bending ring transducer. Our optimization results indicate that, under the free inner and fixed outer boundary conditions, the effective electromechanical coupling coefficient initially increases to a maximum value and then rapidly decreases as r1/r2 increases. This behavior can be attributed to the out-of-phase vibrations and the in-phase electric field excitation on both sides of the bending ring vibration nodal circle. Finally, we present the optimized size configuration required to achieve the maximum effective electromechanical coupling coefficient. This study provides theoretical guidance for the design and optimization of trilaminar bending ring transducers with unequal diameters and has the potential to significantly advance the field of crosswell seismic source technology.

Biaxial ultrasound driving technique for small animal blood–brain barrier opening

Biaxial driving can more efficiently convert electrical power to forward acoustic power in piezoelectric materials, and the interaction between the orthogonal electric fields can produce a combination of extensional and shear deformations as a function of the phase difference between them to allow dynamic steering of the beam with a single-element. In this study, we demonstrate for the first time the application of a single-element biaxially driven ring transducer in vivo for blood–brain barrier opening in mice, and compare it to that achieved with a conventional single-element highly focused (F# = 0.7) spherical transducer operating at a similar frequency. Transcranial focused ultrasound (0.45 MPa, 10 ms pulse length, 1 Hz repetition frequency, 30 s duration) was applied bilaterally to mice with a 40 μl/kg bolus of DefinityTM microbubbles, employing either a single-element biaxial ring (1.482 MHz, 10 mm inner diameter, 13.75 mm outer diameter) or spherical (1.5 MHz, 35 mm diameter, F# = 0.7; RK50, FUS Instruments) transducer on each side. Follow-up MRI scans (T1 pre- and post- 0.2 mmol/kg Gd injection, T2) were acquired to assess blood–brain barrier opening volume and potential damage. Compared to blood–brain barrier opening achieved with a conventional single-element spherical focused transducer, the opening volume achieved with a single-element biaxial ring transducer was 35% smaller (p = 0.002) with a device of a ring diameter of 40% the aperture size. Axial refocusing was further demonstrated with the single-element biaxial ring transducer, yielding a 1.63 mm deeper, five-fold larger opening volume (p = 0.048) relative to its small-focus mode. The biaxial ring transducer achieved a more localized opening compared to the spherical focused transducer under the same parameters, and further enabled dynamic axial refocusing with a single-element transducer with a smaller fabrication footprint.

Open-UST: An Open-Source Ultrasound Tomography Transducer Array System.

Fast imaging methods are needed to promote clinical adoption of ultrasound tomography (UST), and more widely available UST hardware could support the experimental validation of new measurement configurations. In this work, an open-source 256-element transducer ring array was developed (morganjroberts.github. io/open-UST) and manufactured using rapid prototyping, for only £2k. Novel manufacturing techniques were used, resulting in a 1.17° mean beam axis skew angle, a [Formula: see text] mean element position error, and a [Formula: see text] deviation in matching layer thickness. The nominal acoustic performance was measured using hydrophone scans and watershot data, and the 61.2 dB signal-to-noise ratio (SNR), 55.4° opening angle, 10.2 mm beamwidth, and 54% transmit-receive bandwidth (-12 dB) were found to be similar to existing systems and compatible with state-of-the-art full-waveform-inversion image reconstruction methods. The interelement variation in acoustic performance was typically < 10% without using normalization, meaning that the elements can be modeled identically during image reconstruction, removing the need for individual source definitions based on hydrophone measurements. Finally, data from a phantom experiment were successfully reconstructed. These results demonstrate that the open-UST system is accessible for users and is suitable for UST imaging research.

Higher harmonics dynamic focalization in single-element ring transducers using biaxial driving

Biaxial driving is a new driving technique that allows the steering of the ultrasound field generated by a single-element piezoceramic transducer. Because of their natural axisymmetric geometry, ultrasound generation with ring transducers can take advantage of the biaxial driving to change the focus of the beam generated by this type of transducer using only two driving signals. In this study, we applied the biaxial driving technique into a single-element PZT ring transducer operating at 500 kHz to produce a change in size and position of the focal spot while using the 1st (482 kHz), 3rd (1.362 MHz) and 5th (2.62 MHz) harmonic excitation. The transducer had a thickness of 2.85 mm, an inner diameter of 9.75 mm and a ring width of 2.0 mm, and two pairs of electrodes as required for biaxial driving. Simulation and experimental results showed that both the focal area and the distance at which the focal area centre was located changed as a function of the phase and power difference between the two driving signals. Experimental results showed that the focal area could be reduced from 31.6 mm2 (conventional driving) to 3.4 mm2 (89 % reduction) when using the first harmonic excitation. For the third harmonic, the focal area could be reduced from 4.0 mm2 (conventional driving) to 3.3 mm2 (17.5 % reduction). For the fifth harmonic, the focal area could be reduced from 1.7 mm2 (conventional driving) to 1 mm2 (41.7 % reduction). Results also demonstrated the centre of the focus could be displaced between 3.0 mm and 9.3 mm from the surface of the transducer when using the first harmonic, between 7.3 mm and 8.4 mm at the third harmonic, and between 4.9 mm and 8.2 mm at the fifth harmonic. The reduction in the focus area, as well as the possibility to displace the focus dynamically will be advantageous for preclinical applications of focused ultrasound, especially on drug delivery and neuromodulation studies in small rodents.

Real-Time Intravital Imaging of Acoustic Cluster Therapy-Induced Vascular Effects in the Murine Brain.

The blood-brain barrier (BBB) is an obstacle for cerebral drug delivery. Controlled permeabilization of the barrier by external stimuli can facilitate the delivery of drugs to the brain. Acoustic Cluster Therapy (ACT®) is a promising strategy for transiently and locally increasing the permeability of the BBB to macromolecules and nanoparticles. However, the mechanism underlying the induced permeability change and subsequent enhanced accumulation of co-injected molecules requires further elucidation. In this study, the behavior of ACT® bubbles in microcapillaries in the murine brain was observed using real-time intravital multiphoton microscopy. For this purpose, cranial windows aligned with a ring transducer centered around an objective were mounted to the skull of mice. Dextrans labeled with 2 MDa fluorescein isothiocyanate (FITC) were injected to delineate the blood vessels and to visualize extravasation. Activated ACT® bubbles were observed to alter the blood flow, inducing transient and local increases in the fluorescence intensity of 2 MDa FITC-dextran and subsequent extravasation in the form of vascular outpouchings. The observations indicate that ACT® induced a transient vascular leakage without causing substantial damage to the vessels in the brain. The study gave novel insights into the mechanism underlying ACT®-induced enhanced BBB permeability which will be important considering treatment optimization for a safe and efficient clinical translation of ACT®.

Numerical analysis and experimental measurement on segmented ring transducer acoustic fields

In order to overcome the shortcomings of the two traditional methods of finite element method (FEM) and direct coupling of mechanical FEM and acoustic boundary element method (BEM) in the comprehensive simulation of acoustic characteristics of non-two-dimensional axisymmetrical transducers, the acoustic FEM and acoustic BEM coupling method is adopted in this study to model, calculate and analyze the three-dimensional (3D) model of the segmented ring transducer. Firstly, the basic theory of FEM, BEM and FEM-BEM coupling calculation of the transducer is introduced. Secondly, a 1/8 3D model of the segmented ring transducer is built to simulate the underwater electro-acoustic characteristics of the transducer. Finally, a transducer prototype is manufactured according to the numerical model, and the electro-acoustic performance of the transducer is measured in the anechoic tank. The numerical results of transmission voltage response (TVR), admittance and radiation directivity curves are in good agreement with the experimentally measured results, which indicate that the proposed method is correct and effective. Therefore, the method could be used to comprehensively calculate the acoustic characteristics of the segmented ring transducer. In addition, the method could be used not only to study the acoustic problems of other transducers or transducers arrays with complex structures that are non-two-dimensional axisymmetrical, but also to comprehensively analyze and predict the near-field and far-field acoustic characteristics of any transducers including two-dimensional (2D) axisymmetrical transducers.

An endoluminal cylindrical sectored-ring ultrasound phased-array applicator for minimally-invasive therapeutic ultrasound.

The size of catheter-based ultrasound devices for delivering ultrasound energy to deep-seated tumors is constrained by the access pathway which limits their therapeutic capabilities. To devise and investigate a deployable applicator suitable for minimally-invasive delivery of therapeutic ultrasound, consisting of a 2D cylindrical sectored-ring ultrasound phased array, integrated within an expandable paraboloid-shaped balloon-based reflector. The balloon can be collapsed for compact delivery and expanded close to the target position to mimic a larger-diameter concentric-ring sector-vortex array for enhanced dynamic control of focal depth and volume. Acoustic and biothermal simulations were employed in 3D generalized homogeneous and patient-specific heterogeneous models, for three-phased array transducers with 32, 64, and 128 elements, composed of sectored 4, 8, and 16 tubular ring transducers, respectively. The applicator performance was characterized as a function of array configuration, focal depth, phasing modes, and balloon reflector geometry. A 16-element proof-of-concept phased array applicator assembly, consisting of four tubular transducers each divided into four sectors, was fabricated, and characterized with hydrophone measurements along and across the axis, and ablations in ex vivo tissue. Simulation results indicated that transducer arrays (1.5 MHz, 9mm OD × 20mm long), balloon sizes (41-50 mm expanded diameter, 20-60 mm focal depth), phasing mode (0-4) and sonication duration (30s) can produce spatially localized acoustic intensity focal patterns (focal length: 3-22 mm, focal width: 0.7-8.7 mm) and ablative thermal lesions (width: 2.7-16 mm, length: 6-46 mm) in pancreatic tissue across a 10-90 mm focal depth range. Patient-specific studies indicated that 0.1, 0.46, and 1.2cm3 volume of tumor can be ablated in the body of the pancreas for 120s sonications using a single axial focus (Mode 0), or four, and eight simultaneous foci in a toroidal pattern (Mode 2 and 4, respectively). Hydrophone measurements demonstrated good agreement with simulation. Experiments in which chicken meat was thermally ablated indicated that volumetric ablation can be produced using single or multiple foci. The results of this study demonstrated the feasibility of a novel compact ultrasound applicator design capable of focusing, deep penetration, electronic steering, and volumetric thermal ablation. The proposed applicator can be used for compact endoluminal or laparoscopic delivery of localized ultrasound energy to deep-seated targets.

Concentric-ring arrays for forward-viewing ultrasound imaging.

Current ultrasound (US)-image-guided needle insertions often require an expertized technique for clinicians because the performance of tasks in a three-dimensional space using two-dimensional images requires operators to cognitively maintain the spatial relationships between the US probe, the needle, and the lesion. This work presents forward-viewing US imaging with a ring array configuration to enable needle interventions without requiring the registration between tools and targets. The center-open ring array configuration allows the needle to be inserted from the center of the visualized US image, providing simple and intuitive guidance. To establish the feasibility of the ring array configuration, the design parameters causing the image quality, including the radius of the center hole and the number of ring layers and transducer elements, were investigated. Experimental results showed successful visualization, even with a hole in the transducer elements, and the target visibility was improved by increasing the number of ring layers and the number of transducer elements in each ring layer. Reducing the hole radius improved the region's image quality at a shallow depth. Forward-viewing US imaging with a ring array configuration has the potential to be a viable alternative to conventional US image-guided needle insertion methods.

Design and Simulation of a Ring Transducer Array for Ultrasound Retinal Stimulation.

Argus II retinal prosthesis is the US Food and Drug Administration (FDA) approved medical device intended to restore sight to a patient’s blind secondary to retinal degeneration (i.e., retinitis pigmentosa). However, Argus II and most reported retinal prostheses require invasive surgery to implant electrodes in the eye. Recent studies have shown that focused ultrasound can be developed into a non-invasive retinal prosthesis technology. Ultrasound energy focused on retinal neurons can trigger the activities of retinal neurons with high spatial-temporal resolution. This paper introduces a novel design and simulation of a ring array transducer that could be used as non-invasive ultrasonic retinal stimulation. The array transducer is designed in the shape of a racing ring with a hemisphere surface that mimics a contact lens to acoustically couple with the eye via the tear film and directs the ultrasound to avoid the high acoustic absorption from the crystalline lens. We will describe the design methods and simulation of the two-dimensional pattern stimulation. Finally, compared with other existing retinal prostheses, we show that the ultrasound ring array is practical and safe and could be potentially used as a non-invasive retinal prosthesis.

압전 단결정을 이용한 고감도 광대역 링 트랜스듀서의 수중 음향특성 분석

In this study, the design and underwater acoustic characteristics of a ring transducer composed of a piezoelectric single crystal as the active material was reported. The PIN-PMN-PT piezoelectric single crystals with improved thermal durability have superior piezoelectric performance compared to PZT-4, widely used in underwater acoustic sensors. A 33-mode ring transducer was designed and its acoustic characteristics were estimated through electro-mechanical-acoustic coupled analysis. Furthermore, the acoustic characteristics of the ring transducers, composed of piezoelectric single crystals or PZT-4, were compared. The piezoelectric single crystals ring transducer is expected to have a higher transmitting voltage response (TVR) and receiving voltage sensitivity (RVS) compared to the PZT-4 ring transducer due to a high electro-mechanical coupling coefficient. It is also expected to have wideband performance due to a low mechanical quality factor. The acoustic characteristics of the fabricated piezoelectric single crystals ring transducer were measured and analyzed with the results of the electro-mechanical-acoustic coupled analysis. Upon applying piezoelectric single crystals as active materials, the ring transducer provided high sensitivity and broadband performance.

Control of low-frequency guided elastic wave modes in a hollow pipe using a meta-surface

A locally resonant meta-surface for preferential excitation of a guided mode in a hollow pipe can improve ultrasonic guided wave inspection of pipelines. The proposed meta-surface comprises a periodic arrangement of bonded prismatic rod-like resonators in the circumferential and axial directions of the pipe. We demonstrate the presence of bandgaps for the low-frequency axisymmetric longitudinal modes L(0,1) and L(0,2) and the torsional mode T(0,1). The generated bandgaps can be used to filter the higher harmonics associated with the system nonlinearity to improve nonlinear ultrasonic measurements on pipes. These bandgaps exist even for the non-axisymmetric flexural modes but with their hybridized dispersion curves exhibiting mode-coupling for higher circumferential orders. Moreover, a “partial” bandgap is obtained where preferential transmission of the L(0,2) mode over L(0,1) is possible. We discuss the potential advantages of this partial bandgap to improve pipeline inspections using the L(0,2) mode. Time-domain finite element analyses are used to validate the presence of these bandgaps under radial, circumferential, and axial excitation that mimics the excitation using a ring of piezoelectric transducers. Finally, we discuss the influence of resonator spacing, filling fraction, and the number of resonator rings on the bandgaps for an informed meta-surface design.