This paper concerns with the coupled linear theory of viscoelasticity for porous materials. In this theory the coupled phenomenon of the concepts of Darcy’s law and the volume fraction is considered. The basic internal and external boundary value problems (BVPs) of steady vibrations are investigated. Indeed, the fundamental solution of the system of steady vibration equations is constructed explicitly by means of elementary functions and its basic properties are presented. Green’s identities are obtained and the uniqueness theorems for the regular (classical) solutions of the BVPs of steady vibrations are proved. The surface and volume potentials are constructed and the basic properties of these potentials are given. Finally, the existence theorems for classical solutions of the BVPs of steady vibrations are proved by means of the potential method and the theory of singular integral equations.

本文涉及多孔材料粘弹性的耦合线性理论。在该理论中，考虑了达西定律概念与体积分数的耦合现象。研究了稳态振动的基本内部和外部边界值问题（BVP）。确实，利用基本函数明确构造了稳态振动方程组的基本解，并给出了其基本性质。获得了格林的恒等式，并证明了稳态振动BVP的正则（经典）解的唯一性定理。构造了表面和体积电势，并给出了这些电势的基本性质。最后，