Asymptotic expansion of the dispersion equation of Lamb waves in periodically layered elastic media
The present paper deals with the problem on Lamb waves propagation in periodically layered, compressible elastic media with initial deformations, in the case of long wavelength approximation (i.e. E = k.h < < 1, where k is the wave number, h is the thickness of one periodicity cell). With the...
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| Language: | English |
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Publishing House for Science and Technology
2009-03-01
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| Series: | Vietnam Journal of Mechanics |
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| Online Access: | https://vjs.ac.vn/index.php/vjmech/article/view/5492 |
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| author | Bui Thanh Tu Pham Chi Vinh Nguyen Thi Khanh Linh |
| author_facet | Bui Thanh Tu Pham Chi Vinh Nguyen Thi Khanh Linh |
| author_sort | Bui Thanh Tu |
| collection | DOAJ |
| description | The present paper deals with the problem on Lamb waves propagation in periodically layered, compressible elastic media with initial deformations, in the case of long wavelength approximation (i.e. E = k.h < < 1, where k is the wave number, h is the thickness of one periodicity cell). With the assumption that E < < 1, the dispersion equation is written as: 2 = 2 = [h + c!"h + c2D3 + ... = L cmDm+l·m=0. The main aim of this paper is to find formulae for determining the coefficients Di, ( i 2'. 1). In particular, we prove that D2n = 0 (n 2'. 1), derive formulae for D1 , D3, and construct recurrent formulae for D2n+i (n 2'. 2). Based on these formulae, the solution with any order of accuracy can be obtained. This research is an extension of the investigation by Norris and Santosa [Norris A. and Santosa F., Wave Motion 16 (1992), 33-55] from SH waves (one-component waves) to Lamb waves (two-component waves). |
| format | Article |
| id | doaj-art-7e20ff08003e484fa5ef629687fa0921 |
| institution | DOAJ |
| issn | 0866-7136 2815-5882 |
| language | English |
| publishDate | 2009-03-01 |
| publisher | Publishing House for Science and Technology |
| record_format | Article |
| series | Vietnam Journal of Mechanics |
| spelling | doaj-art-7e20ff08003e484fa5ef629687fa09212025-08-20T03:04:44ZengPublishing House for Science and TechnologyVietnam Journal of Mechanics0866-71362815-58822009-03-0131110.15625/0866-7136/31/1/5492Asymptotic expansion of the dispersion equation of Lamb waves in periodically layered elastic mediaBui Thanh Tu0Pham Chi Vinh1Nguyen Thi Khanh Linh2Hanoi University of ScienceHanoi University of SciencePublishing House for Science and TechnologyThe present paper deals with the problem on Lamb waves propagation in periodically layered, compressible elastic media with initial deformations, in the case of long wavelength approximation (i.e. E = k.h < < 1, where k is the wave number, h is the thickness of one periodicity cell). With the assumption that E < < 1, the dispersion equation is written as: 2 = 2 = [h + c!"h + c2D3 + ... = L cmDm+l·m=0. The main aim of this paper is to find formulae for determining the coefficients Di, ( i 2'. 1). In particular, we prove that D2n = 0 (n 2'. 1), derive formulae for D1 , D3, and construct recurrent formulae for D2n+i (n 2'. 2). Based on these formulae, the solution with any order of accuracy can be obtained. This research is an extension of the investigation by Norris and Santosa [Norris A. and Santosa F., Wave Motion 16 (1992), 33-55] from SH waves (one-component waves) to Lamb waves (two-component waves).https://vjs.ac.vn/index.php/vjmech/article/view/5492Lamb wavesWave propagationPeriodically layered mediaAsymptotic expansion. |
| spellingShingle | Bui Thanh Tu Pham Chi Vinh Nguyen Thi Khanh Linh Asymptotic expansion of the dispersion equation of Lamb waves in periodically layered elastic media Vietnam Journal of Mechanics Lamb waves Wave propagation Periodically layered media Asymptotic expansion. |
| title | Asymptotic expansion of the dispersion equation of Lamb waves in periodically layered elastic media |
| title_full | Asymptotic expansion of the dispersion equation of Lamb waves in periodically layered elastic media |
| title_fullStr | Asymptotic expansion of the dispersion equation of Lamb waves in periodically layered elastic media |
| title_full_unstemmed | Asymptotic expansion of the dispersion equation of Lamb waves in periodically layered elastic media |
| title_short | Asymptotic expansion of the dispersion equation of Lamb waves in periodically layered elastic media |
| title_sort | asymptotic expansion of the dispersion equation of lamb waves in periodically layered elastic media |
| topic | Lamb waves Wave propagation Periodically layered media Asymptotic expansion. |
| url | https://vjs.ac.vn/index.php/vjmech/article/view/5492 |
| work_keys_str_mv | AT buithanhtu asymptoticexpansionofthedispersionequationoflambwavesinperiodicallylayeredelasticmedia AT phamchivinh asymptoticexpansionofthedispersionequationoflambwavesinperiodicallylayeredelasticmedia AT nguyenthikhanhlinh asymptoticexpansionofthedispersionequationoflambwavesinperiodicallylayeredelasticmedia |