{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,25]],"date-time":"2025-10-25T12:49:08Z","timestamp":1761396548749,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T00:00:00Z","timestamp":1686268800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004504","name":"Research Foundation of the Research Council of Lithuania","doi-asserted-by":"publisher","award":["MIP-23-119"],"award-info":[{"award-number":["MIP-23-119"]}],"id":[{"id":"10.13039\/501100004504","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The application of non-stationary Lamb wave signals is a promising tool in various industrial applications where information about changes inside a structure is required. Phase velocity is one of the Lamb wave parameters that can be used for inhomogeneities detection. The possibility of reconstructing the segment of the phase velocity in a strong dispersion range using only two signals is proposed. The theoretical study is performed using signals of the A0 mode propagating in an aluminium plate at a frequency of 150 kHz, 300 kHz, 500 kHz and 900 kHz. The experiment was carried out at a value of 300 kHz. The studies conducted indicated that the maximum distance between two signals, at which the time-of-flight can be measured between the same phase points, is the main parameter for the two signals technique application. Theoretical and experimental studies were performed, and the mean relative error was calculated by comparing the obtained results with those calculated via the SAFE method. In the theoretical study, the mean relative error of 0.33% was obtained at 150 kHz, 0.22% at 300 kHz, 0.23% at 500 kHz and 0.11% at 900 kHz. The calculated mean relative errors \u03b4cph=0.91% and \u03b4cph=1.36% were obtained at different distances in the experimental study. The results obtained show that the estimation of the phase velocity in dispersion ranges using only two received signals was a useful tool that saved time and effort.<\/jats:p>","DOI":"10.3390\/sym15061236","type":"journal-article","created":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T08:37:33Z","timestamp":1686299853000},"page":"1236","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Estimation of Lamb Wave Anti-Symmetric Mode Phase Velocity in Various Dispersion Ranges Using Only Two Signals"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8057-5802","authenticated-orcid":false,"given":"Lina","family":"Draudvilien\u0117","sequence":"first","affiliation":[{"name":"Ultrasound Research Institute, Kaunas University of Technology, LT-51423 Kaunas, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2408-5427","authenticated-orcid":false,"given":"Renaldas","family":"Rai\u0161utis","sequence":"additional","affiliation":[{"name":"Ultrasound Research Institute, Kaunas University of Technology, LT-51423 Kaunas, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1720","DOI":"10.1016\/j.ultras.2014.04.023","article-title":"High-frequency guided ultrasonic waves for hidden defect detection in multi-layered aircraft structures","volume":"54","author":"Masserey","year":"2014","journal-title":"Ultrasonics"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"052001","DOI":"10.1088\/1361-6501\/acae27","article-title":"Guided ultrasonic waves propagation imaging: A review","volume":"34","author":"Chia","year":"2023","journal-title":"Meas. Sci. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"107014","DOI":"10.1016\/j.ultras.2023.107014","article-title":"A review in guided-ultrasonic-wave-based structural health monitoring: From fundamental theory to machine learning techniques","volume":"133","author":"Yang","year":"2023","journal-title":"Ultrasonics"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1590","DOI":"10.1177\/1475921719890590","article-title":"Dispersion curve analysis method for Lamb wave mode separation","volume":"19","author":"Hu","year":"2020","journal-title":"Struct. Health Monit."},{"key":"ref_5","first-page":"183","article-title":"Time-frequency characterization of lamb waves for material evaluation and damage inspection of plates","volume":"62\u201363","author":"Pai","year":"2015","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"106114","DOI":"10.1016\/j.ultras.2020.106114","article-title":"Environmental and operational conditions effects on Lamb wave based structural health monitoring systems: A review","volume":"105","author":"Gorgin","year":"2020","journal-title":"Ultrasonics"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Yang, T., Zhou, W., and Yu, L. (2023). Guided Wave-Based Damage Detection of Square Steel Tubes Utilizing Structure Symmetry. Symmetry, 15.","DOI":"10.3390\/sym15040805"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Xie, J., Ding, W., Zou, W., Wang, T., and Yang, J. (2022). Defect Detection inside a Rail Head by Ultrasonic Guided Waves. Symmetry, 14.","DOI":"10.21203\/rs.3.rs-1817243\/v1"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"108026","DOI":"10.1016\/j.measurement.2020.108026","article-title":"Nonlinear Lamb wave analysis for microdefect identification in mechanical structural health assessment","volume":"164","author":"Chen","year":"2020","journal-title":"Measurement"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1007\/s10921-017-0404-x","article-title":"Assessment of Quantitative and Qualitative Characteristics of Ultrasonic Guided Wave Phase Velocity Measurement Technique","volume":"36","author":"Draudviliene","year":"2017","journal-title":"J. Nondestr. Eval."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"111318","DOI":"10.1016\/j.oceaneng.2022.111318","article-title":"Corrosion degradation monitoring of ship stiffened plates using guided wave phase velocity and constrained convex optimization method","volume":"253","author":"Zima","year":"2022","journal-title":"Ocean. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Olisa, S.C., Khan, M.A., and Starr, A. (2021). Review of Current Guided Wave Ultrasonic Testing (GWUT) Limitations and Future Directions. Sensors, 21.","DOI":"10.3390\/s21030811"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/j.ymssp.2018.10.020","article-title":"An approach based on expectation-maximization algorithm for parameter estimation of Lamb wave signals","volume":"120","author":"Jia","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1109\/TUFFC.2003.1197965","article-title":"A rapid signal processing technique to remove the effect of dispersion from guided wave signals","volume":"50","author":"Wilcox","year":"2003","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1016\/j.jsv.2006.01.020","article-title":"Guided Lamb waves for identification of damage in composite structures: A review","volume":"295","author":"Su","year":"2006","journal-title":"J. Sound Vib."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.sigpro.2013.05.025","article-title":"Structure damage localization with ultrasonic guided waves based on a time\u2013frequency method","volume":"96","author":"Dai","year":"2014","journal-title":"Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Golub, M.V., Doroshenko, O.V., Arsenov, M.A., Bareiko, I.A., and Eremin, A.A. (2022). Identification of Material Properties of Elastic Plate Using Guided Waves Based on the Matrix Pencil Method and Laser Doppler Vibrometry. Symmetry, 14.","DOI":"10.20944\/preprints202204.0161.v1"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"124006","DOI":"10.1088\/1361-6501\/ac261b","article-title":"Phase velocity measurement of dispersive wave modes by Gaussian peak-tracing in the f-k transform domain","volume":"32","author":"Ghose","year":"2021","journal-title":"Meas. Sci. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"115029","DOI":"10.1088\/1361-665X\/ab47e1","article-title":"Determination of Lamb wave phase velocity dispersion using time\u2013frequency analysis","volume":"28","author":"Zeng","year":"2019","journal-title":"Smart Mater. Struct."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"107387","DOI":"10.1016\/j.ymssp.2020.107387","article-title":"The measurement of Lamb wave phase velocity using analytic cross-correlation method","volume":"151","author":"Zeng","year":"2021","journal-title":"Mech. Syst. Signal Process"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Crespo, B.H., Courtney, C., and Engineer, B. (2018). Calculation of Guided Wave Dispersion Characteristics Using a Three-Transducer Measurement System. Appl. Sci., 8.","DOI":"10.3390\/app8081253"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"113174","DOI":"10.1016\/j.compstruct.2020.113174","article-title":"Estimation of the Lamb wave phase velocity dispersion curves using only two adjacent signals","volume":"258","author":"Draudviliene","year":"2021","journal-title":"Compos. Struct."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"111739","DOI":"10.1016\/j.oceaneng.2022.111739","article-title":"Experimental and numerical identification of corrosion degradation of ageing structural components","volume":"258","author":"Zima","year":"2022","journal-title":"Ocean Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1016\/j.jsv.2006.01.021","article-title":"Modeling wave propagation in damped waveguides of arbitrary cross-section","volume":"295","author":"Bartoli","year":"2006","journal-title":"J. Sound Vib."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/S0041-624X(03)00097-0","article-title":"Guided wave dispersion curves for a bar with an arbitrary cross-section, a rod and rail example","volume":"41","author":"Hayashi","year":"2003","journal-title":"Ultrasonics"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1109\/58.646916","article-title":"Simulation of ultrasound pulse propagation in lossy media obeying a frequency power law","volume":"45","author":"He","year":"1998","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control."},{"key":"ref_27","first-page":"30","article-title":"Contact ultrasonic transducers for mechanical scanning systems","volume":"65","year":"2010","journal-title":"Ultragarsas"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/6\/1236\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:51:49Z","timestamp":1760125909000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/6\/1236"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,9]]},"references-count":27,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["sym15061236"],"URL":"https:\/\/doi.org\/10.3390\/sym15061236","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,6,9]]}}}