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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Main Authors: Bui Thanh Tu, Pham Chi Vinh, Nguyen Thi Khanh Linh
Format: Article
Language:English
Published: Publishing House for Science and Technology 2009-03-01
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).
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language English
publishDate 2009-03-01
publisher Publishing House for Science and Technology
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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
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AT phamchivinh asymptoticexpansionofthedispersionequationoflambwavesinperiodicallylayeredelasticmedia
AT nguyenthikhanhlinh asymptoticexpansionofthedispersionequationoflambwavesinperiodicallylayeredelasticmedia