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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Penerbit Universiti Kebangsaan Malaysia
2022
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| Online Access: | http://journalarticle.ukm.my/21108/ http://journalarticle.ukm.my/21108/7/Jk_7.pdf |
| _version_ | 1848815273039101952 |
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| author | Tavioc, Purwadi A. Darwitoa, Gunawan Nugroho, Murry Raditya, |
| author_facet | Tavioc, Purwadi A. Darwitoa, Gunawan Nugroho, Murry Raditya, |
| author_sort | Tavioc, |
| building | UKM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T00:47:21Z |
| format | Article |
| id | oai:generic.eprints.org:21108 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T00:47:21Z |
| publishDate | 2022 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:generic.eprints.org: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/ |
| spellingShingle | Tavioc, Purwadi A. Darwitoa, Gunawan Nugroho, Murry Raditya, The solvability of the 3-D elastic wave equations in inhomogeneous media |
| title | 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_short | 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 |
| url | http://journalarticle.ukm.my/21108/ http://journalarticle.ukm.my/21108/ http://journalarticle.ukm.my/21108/7/Jk_7.pdf |