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This study considers the wave phenomena and fundamental solution in swelling porous elastic solids consisting of a mixture of solid, liquid, and gas. There exist three dilatational and two transversal waves which vibrate at distinct speeds. The basic characteristics of waves (phase velocity and attenuation coefficient) are computed numerically and displayed in the form of graphs. Also, a fundamental solution is explored for steady oscillation and some preliminary features are explored in this model. The obtained results for both waves are analyzed with and without swelling porous elastic solid. This new model enables us to improve the efficacy of swelling porous elastic solid which involves solid and fluid and find it applicable in exploration industries and to investigate various wave propagation problems.

Fundamental solution in a swelling porous medium containing a mixture of solid, liquid, and gas