Fundamental solutions of poroelastodynamics in the frequency domain have been derived by Cheng et al. (1991, “Integral Equation for Dynamic Poroelasticity in Frequency Domain With BEM Solution,” J. Eng. Mech., 117(5), pp. 1136–1157) for the point force and fluid source singularities in 2D and 3D, using an analogy between poroelasticity and thermoelasticity. In this paper, a formal derivation is presented based on the decomposition of a Dirac δ function into a rotational and a dilatational part. The decomposition allows the derived fundamental solutions to be separated into a shear and two compressional wave components, before they are combined. For the point force solution, each of the isolated wave components contains a term that is not present in the combined wave field; hence can be observable only if the present approach is taken. These isolated wave fields may be useful in applications where it is desirable to separate the shear and compressional wave effects. These wave fields are evaluated and plotted.
Fundamental Solutions of Poroelastodynamics in Frequency Domain Based on Wave Decomposition
Manuscript received December 5, 2012; final manuscript received February 3, 2013; accepted manuscript posted February 19, 2013; published online August 21, 2013. Assoc. Editor: Younane Abousleiman.
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Ding, B., Cheng, A. H., and Chen, Z. (August 21, 2013). "Fundamental Solutions of Poroelastodynamics in Frequency Domain Based on Wave Decomposition." ASME. J. Appl. Mech. November 2013; 80(6): 061021. https://doi.org/10.1115/1.4023692
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