Fundamental and Generalized Solutions of the Equations of Motion of a Two-Component Biot Medium and Their Properties

摘要

We consider wave propagation processes generated by forces of various types in a two-component Biot medium. Based on the Fourier transform of generalized functions, we construct a Green tensor describing the process of propagation of waves in spaces of dimension {-69pt} begin{document}$$N=1,2,3 $$end{document} acted upon by pulsed sources of force that are lumped at the coordinate origin and given by the singular Dirac delta function. Based on this tensor, generalized solutions are constructed to these equations under various disturbance sources that are described by both regular and singular generalized functions. For the regular acting forces, we provide integral representations of the solutions that can be used to calculate the stress-strain state of a porous water-saturated medium.