Shota Rustaveli National Science Foundation of GeorgiaStart Date: 2009-03-01 End Date: 2012-03-01
On the basis of this project the following results are obtained:
a) The 3D boundary value problems (BVPs) of steady vibrations and initial-BVPs of dynamics of the theories of elasticity and thermoelasticity for double porosity solids with microtemperatures are investigated by means of the potential method and the theory of singular integral equations. The existence of eigenfrequencies of the interior BVPs of steady vibration is studied. The connection between plane waves and these eigenfrequencies is established.
b) The existence and uniqueness theorems of solutions of the 2D and 3D BVPs in the equilibrium theories of elasticity and thermoelasticity for double porosity solids with microtemperatures are proved by means of the potential method and the theory of singular integral equations. The solutions of the BVPs for a half-space, half-plane and ball are constructed.
c) The solutions of the 2D BVPs in the equilibrium theories of elasticity and thermoelasticity of double porosity solids with microtemperatures for a circle, a circular ring and plane with a circular hole are constructed. Numerical solutions of the BVPs for a circle are obtained.