Acoustic-elastodynamic interaction in isotropic fractal media
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green St., Urbana, IL 61801, USA
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Received: 3 June 2013
Revised: 6 August 2013
Published online: 7 October 2013
This research explores the acoustic-elastodynamic interaction in isotropic fractal media. The analysis discusses the direct coupling of two constitutive models under dynamic loading: a continuous solid and an isotropic fractal medium. We consider two situations where in the first, the fractal medium is enclosed within a thin spherical shell (interior problem), while in the second, the fractal medium extends infinitely outside the shell (exterior problem). The two problems are simulated analytically, and the exact solution for the shell displacement is expressed in closed form in the Laplace domain. The formulation of the radiation condition for infinite fractal media is essential to derive the exterior problem's solution. This study represents a meaningful idealization of real-application problems involving the interaction of multi-constitutive media, e.g. the human brain, whereby fractal features affect the response of this body under various excitations.
© EDP Sciences, Springer-Verlag, 2013