The main research aims of this project are:

• To present the six-coupled mathematical models for elastic materials with double and triple porosity, thermoelastic materials with double porosity, viscoelastic materials with single, double and triple porosity, which is based on the coupled concepts of Darcy’s law and the volume fractions;
• To investigate the non-classical problems of steady vibrations of these models.

In these new models the following problems will be investigated:

• a) The fundamental solutions of the systems of steady vibration equations will be constructed by elementary functions and their basic properties will be established;
• b) Green’s formulae for the systems of steady vibration equations will be obtained;
• c) The uniqueness theorems for classical solutions of the internal and external boundary value problems (BVPs) of steady vibrations will be proved;
• d) The basic properties of surface and volume potentials will be established. The BVPs of steady vibrations will be reduced to the equivalent singular integral equations;
• e) The existence theorems for classical solutions of the internal and external BVPs of steady vibrations will be proved by using the potential method (the boundary integral equation method) and the theory of singular integral equations.

Principal investigator: Merab Svanadze