Reconstruction of Lamb Wave Dispersion Curves in Different Objects Using Signals Measured at Two Different Distances
The possibilities of an effective method of two adjacent signals are investigated for the evaluation of Lamb waves phase velocity dispersion in objects of different types, namely polyvinyl chloride (PVC) film and wind turbine blade (WTB). A new algorithm based on peaks of spectrum magnitude is prese...
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| Format: | Article |
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MDPI AG
2021-11-01
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| Series: | Materials |
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| Online Access: | https://www.mdpi.com/1996-1944/14/22/6990 |
| _version_ | 1797509519754919936 |
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| author | Lina Draudvilienė Olgirdas Tumšys Renaldas Raišutis |
| author_facet | Lina Draudvilienė Olgirdas Tumšys Renaldas Raišutis |
| author_sort | Lina Draudvilienė |
| collection | DOAJ |
| description | The possibilities of an effective method of two adjacent signals are investigated for the evaluation of Lamb waves phase velocity dispersion in objects of different types, namely polyvinyl chloride (PVC) film and wind turbine blade (WTB). A new algorithm based on peaks of spectrum magnitude is presented and used for the comparison of the results. To use the presented method, the wavelength-dependent parameter is proposed to determine the optimal distance range, which is necessary in selecting two signals for analysis. It is determined that, in the range of 0.17–0.5 wavelength where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>δ</mi><mrow><msub><mi>c</mi><mrow><mi>p</mi><mi>h</mi></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula> is not higher than 5%, it is appropriate to use in the case of an A<sub>0</sub> mode in PVC film sample. The smallest error of 1.2%, in the distance greater than 1.5 wavelengths, is obtained in the case of the S<sub>0</sub> mode. Using the method of two signals analysis for PVC sample, the phase velocity dispersion curve of the A<sub>0</sub> mode is reconstructed using selected distances <i>x</i><sub>1</sub> = 70 mm and <i>x</i><sub>2</sub> = 70.5 mm between two spatial positions of a receiving transducer with a mean relative error <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>δ</mi><mrow><msub><mi>c</mi><mrow><mi>p</mi><mi>h</mi></mrow></msub></mrow></msub><mo>=</mo><mn>2.8</mn><mo>%</mo></mrow></semantics></math></inline-formula>, and for S<sub>0</sub> mode, <i>x</i><sub>1</sub> = 61 mm and <i>x</i><sub>2</sub> = 79.7 mm with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>δ</mi><mrow><msub><mi>c</mi><mrow><mi>p</mi><mi>h</mi></mrow></msub></mrow></msub><mo>=</mo><mn>0.99</mn><mo>%</mo></mrow></semantics></math></inline-formula>. In the case of the WTB sample, the range of 0.1–0.39 wavelength, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>δ</mi><mrow><msub><mi>c</mi><mrow><mi>p</mi><mi>h</mi></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula> is not higher than 3%, is determined as the optimal distance range between two adjacent signals. The phase velocity dispersion curve of the A<sub>0</sub> mode is reconstructed in two frequency ranges: first, using selected distances <i>x</i><sub>1</sub> = 225 mm and <i>x</i><sub>2</sub> = 231 mm with mean relative error <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>δ</mi><mrow><msub><mi>c</mi><mrow><mi>p</mi><mi>h</mi></mrow></msub></mrow></msub><mo>=</mo><mn>0.3</mn><mo>%</mo></mrow></semantics></math></inline-formula>; and second, <i>x</i><sub>1</sub> = 225 mm and <i>x</i><sub>2</sub> = 237 mm with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>δ</mi><mrow><msub><mi>c</mi><mrow><mi>p</mi><mi>h</mi></mrow></msub></mrow></msub><mo>=</mo><mn>1.3</mn><mo>%</mo></mrow></semantics></math></inline-formula>. |
| first_indexed | 2024-03-10T05:18:55Z |
| format | Article |
| id | doaj.art-85b9225f0d6541459afd3248234c7b3b |
| institution | Directory Open Access Journal |
| issn | 1996-1944 |
| language | English |
| last_indexed | 2024-03-10T05:18:55Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
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| series | Materials |
| spelling | doaj.art-85b9225f0d6541459afd3248234c7b3b2023-11-23T00:11:59ZengMDPI AGMaterials1996-19442021-11-011422699010.3390/ma14226990Reconstruction of Lamb Wave Dispersion Curves in Different Objects Using Signals Measured at Two Different DistancesLina Draudvilienė0Olgirdas Tumšys1Renaldas Raišutis2Ultrasound Research Institute, Kaunas University of Technology, K. Baršauskas St. 59, LT-51423 Kaunas, LithuaniaUltrasound Research Institute, Kaunas University of Technology, K. Baršauskas St. 59, LT-51423 Kaunas, LithuaniaUltrasound Research Institute, Kaunas University of Technology, K. Baršauskas St. 59, LT-51423 Kaunas, LithuaniaThe possibilities of an effective method of two adjacent signals are investigated for the evaluation of Lamb waves phase velocity dispersion in objects of different types, namely polyvinyl chloride (PVC) film and wind turbine blade (WTB). A new algorithm based on peaks of spectrum magnitude is presented and used for the comparison of the results. To use the presented method, the wavelength-dependent parameter is proposed to determine the optimal distance range, which is necessary in selecting two signals for analysis. It is determined that, in the range of 0.17–0.5 wavelength where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>δ</mi><mrow><msub><mi>c</mi><mrow><mi>p</mi><mi>h</mi></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula> is not higher than 5%, it is appropriate to use in the case of an A<sub>0</sub> mode in PVC film sample. The smallest error of 1.2%, in the distance greater than 1.5 wavelengths, is obtained in the case of the S<sub>0</sub> mode. Using the method of two signals analysis for PVC sample, the phase velocity dispersion curve of the A<sub>0</sub> mode is reconstructed using selected distances <i>x</i><sub>1</sub> = 70 mm and <i>x</i><sub>2</sub> = 70.5 mm between two spatial positions of a receiving transducer with a mean relative error <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>δ</mi><mrow><msub><mi>c</mi><mrow><mi>p</mi><mi>h</mi></mrow></msub></mrow></msub><mo>=</mo><mn>2.8</mn><mo>%</mo></mrow></semantics></math></inline-formula>, and for S<sub>0</sub> mode, <i>x</i><sub>1</sub> = 61 mm and <i>x</i><sub>2</sub> = 79.7 mm with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>δ</mi><mrow><msub><mi>c</mi><mrow><mi>p</mi><mi>h</mi></mrow></msub></mrow></msub><mo>=</mo><mn>0.99</mn><mo>%</mo></mrow></semantics></math></inline-formula>. In the case of the WTB sample, the range of 0.1–0.39 wavelength, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>δ</mi><mrow><msub><mi>c</mi><mrow><mi>p</mi><mi>h</mi></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula> is not higher than 3%, is determined as the optimal distance range between two adjacent signals. The phase velocity dispersion curve of the A<sub>0</sub> mode is reconstructed in two frequency ranges: first, using selected distances <i>x</i><sub>1</sub> = 225 mm and <i>x</i><sub>2</sub> = 231 mm with mean relative error <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>δ</mi><mrow><msub><mi>c</mi><mrow><mi>p</mi><mi>h</mi></mrow></msub></mrow></msub><mo>=</mo><mn>0.3</mn><mo>%</mo></mrow></semantics></math></inline-formula>; and second, <i>x</i><sub>1</sub> = 225 mm and <i>x</i><sub>2</sub> = 237 mm with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>δ</mi><mrow><msub><mi>c</mi><mrow><mi>p</mi><mi>h</mi></mrow></msub></mrow></msub><mo>=</mo><mn>1.3</mn><mo>%</mo></mrow></semantics></math></inline-formula>.https://www.mdpi.com/1996-1944/14/22/6990ultrasonic Lamb wavenon-destructive testingnon-homogeneous materialsignal processingLamb wave phase velocitydispersion curve reconstruction |
| spellingShingle | Lina Draudvilienė Olgirdas Tumšys Renaldas Raišutis Reconstruction of Lamb Wave Dispersion Curves in Different Objects Using Signals Measured at Two Different Distances Materials ultrasonic Lamb wave non-destructive testing non-homogeneous material signal processing Lamb wave phase velocity dispersion curve reconstruction |
| title | Reconstruction of Lamb Wave Dispersion Curves in Different Objects Using Signals Measured at Two Different Distances |
| title_full | Reconstruction of Lamb Wave Dispersion Curves in Different Objects Using Signals Measured at Two Different Distances |
| title_fullStr | Reconstruction of Lamb Wave Dispersion Curves in Different Objects Using Signals Measured at Two Different Distances |
| title_full_unstemmed | Reconstruction of Lamb Wave Dispersion Curves in Different Objects Using Signals Measured at Two Different Distances |
| title_short | Reconstruction of Lamb Wave Dispersion Curves in Different Objects Using Signals Measured at Two Different Distances |
| title_sort | reconstruction of lamb wave dispersion curves in different objects using signals measured at two different distances |
| topic | ultrasonic Lamb wave non-destructive testing non-homogeneous material signal processing Lamb wave phase velocity dispersion curve reconstruction |
| url | https://www.mdpi.com/1996-1944/14/22/6990 |
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