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The solvability of the 3-D elastic wave equations in inhomogeneous media

In this research, the three-dimensional elastic wave equations with variable coefficients (i.e. propagate through inhomogeneous media) are solved with the application of the Fourier transform in the spatial coordinates. The wave equation is coupled variable coefficients PDEs whose solutions may have...

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Main Authors: Tavioc,, Purwadi A. Darwitoa,, Gunawan Nugroho,, Murry Raditya,
Format: Article
Language:English
Published: Penerbit Universiti Kebangsaan Malaysia 2022
Online Access:http://journalarticle.ukm.my/21108/7/Jk_7.pdf
http://journalarticle.ukm.my/21108/
https://www.ukm.my/jkukm/volume-3406-2022/
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spelling my-ukm.journal.211082023-02-14T04:42:13Z http://journalarticle.ukm.my/21108/ The solvability of the 3-D elastic wave equations in inhomogeneous media Tavioc, Purwadi A. Darwitoa, Gunawan Nugroho, Murry Raditya, In this research, the three-dimensional elastic wave equations with variable coefficients (i.e. propagate through inhomogeneous media) are solved with the application of the Fourier transform in the spatial coordinates. The wave equation is coupled variable coefficients PDEs whose solutions may have significant in engineering applications. The method utilizes the second order ODE as the baseline for obtaining the complete solution. The solution of second order ODEs is expressed in one integration because the variable coefficients are broken down into several functions and resulted in first order reduction. Moreover, the coupled equations are performed by the order reduction of the higher order ODEs into the second order. The extended procedure for integral equation is implemented for the solutions from the transformed wave equations to generate the explicit expression. It is shown that the proposed method of integral evaluation is resulted in finding the roots of polynomials. Hence, it is concluded that the solvability of the elastic wave equations is ensured by the proposed method. Penerbit Universiti Kebangsaan Malaysia 2022 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/21108/7/Jk_7.pdf Tavioc, and Purwadi A. Darwitoa, and Gunawan Nugroho, and Murry Raditya, (2022) The solvability of the 3-D elastic wave equations in inhomogeneous media. Jurnal Kejuruteraan, 34 (6). pp. 1063-1075. ISSN 0128-0198 https://www.ukm.my/jkukm/volume-3406-2022/
institution Universiti Kebangsaan Malaysia
building Tun Sri Lanang Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Kebangsaan Malaysia
content_source UKM Journal Article Repository
url_provider http://journalarticle.ukm.my/
language English
description In this research, the three-dimensional elastic wave equations with variable coefficients (i.e. propagate through inhomogeneous media) are solved with the application of the Fourier transform in the spatial coordinates. The wave equation is coupled variable coefficients PDEs whose solutions may have significant in engineering applications. The method utilizes the second order ODE as the baseline for obtaining the complete solution. The solution of second order ODEs is expressed in one integration because the variable coefficients are broken down into several functions and resulted in first order reduction. Moreover, the coupled equations are performed by the order reduction of the higher order ODEs into the second order. The extended procedure for integral equation is implemented for the solutions from the transformed wave equations to generate the explicit expression. It is shown that the proposed method of integral evaluation is resulted in finding the roots of polynomials. Hence, it is concluded that the solvability of the elastic wave equations is ensured by the proposed method.
format Article
author Tavioc,
Purwadi A. Darwitoa,
Gunawan Nugroho,
Murry Raditya,
spellingShingle Tavioc,
Purwadi A. Darwitoa,
Gunawan Nugroho,
Murry Raditya,
The solvability of the 3-D elastic wave equations in inhomogeneous media
author_facet Tavioc,
Purwadi A. Darwitoa,
Gunawan Nugroho,
Murry Raditya,
author_sort Tavioc,
title The solvability of the 3-D elastic wave equations in inhomogeneous media
title_short The solvability of the 3-D elastic wave equations in inhomogeneous media
title_full The solvability of the 3-D elastic wave equations in inhomogeneous media
title_fullStr The solvability of the 3-D elastic wave equations in inhomogeneous media
title_full_unstemmed The solvability of the 3-D elastic wave equations in inhomogeneous media
title_sort solvability of the 3-d elastic wave equations in inhomogeneous media
publisher Penerbit Universiti Kebangsaan Malaysia
publishDate 2022
url http://journalarticle.ukm.my/21108/7/Jk_7.pdf
http://journalarticle.ukm.my/21108/
https://www.ukm.my/jkukm/volume-3406-2022/
_version_ 1758579334144065536
score 13.211869

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