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The Solvability of the 3-D Elastic Wave Equations in Inhomogeneous Media

Purwadi A. Darwito, Department of Engineering Physics, Institut Teknologi Sepuluh Nopember, Kampus ITS Sukolilo, Indonesia 60111, Gunawan Nugroho, Murry Raditya, Tavio ., Department of Engineering Physics, Institut Teknologi Sepuluh Nopember, Kampus ITS Sukolilo, Indonesia 60111, Department of Instrumentation Engineering, Institut Teknologi Sepuluh Nopember, Kampus ITS Sukolilo, Indonesia 60111, Department of Civil Engineering, Institut Teknologi Sepuluh Nopember, Kampus ITS Sukolilo, Indonesia 60111
2022 Jurnal Kejuruteraan  

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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
more » ... n 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.
doi:10.17576/jkukm-2022-34(6)-07 fatcat:hdj6khxuonft7kalkmzsh7p4su
DOAJ
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Purwadi A. Darwito, Department of Engineering Physics, Institut Teknologi Sepuluh Nopember, Kampus ITS Sukolilo, Indonesia 60111, Gunawan Nugroho, Murry Raditya, Tavio ., Department of Engineering Physics, Institut Teknologi Sepuluh Nopember, Kampus ITS Sukolilo, Indonesia 60111, Department of Instrumentation Engineering, Institut Teknologi Sepuluh Nopember, Kampus ITS Sukolilo, Indonesia 60111, Department of Civil Engineering, Institut Teknologi Sepuluh Nopember, Kampus ITS Sukolilo, Indonesia 60111. "The Solvability of the 3-D Elastic Wave Equations in Inhomogeneous Media." Jurnal Kejuruteraan 34.6 (2022) 1063-1075