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

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


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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 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.

Item Type:Article
Keywords:Wave equation; Inhomogeneous media; Reduction of order; Integral evaluation; Reduction of polynomial order
Journal:Jurnal Kejuruteraan
ID Code:21108
Deposited By: Mohd Hamka Md. Nasir
Deposited On:09 Feb 2023 04:33
Last Modified:14 Feb 2023 04:42

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