ABSTRACT
This chapter discusses the method for solving a local problem for the heat conduction equation for a composite array with cylindrical square-section inclusions is proposed. The consideration includes membranes with a hexagonal array of circle inclusions, construction of analytical relations for eigenmodes and oscillation frequencies, composite membrane with a square lattice of circle inclusions, as well as composite membrane with square holes. The trend of modern technologies is focused on the creation of composite materials with a given combination of their physical properties and structural and geometric characteristics which is realized by varying the internal microstructure of the composite, using various constituent materials, and employing various technologies and production conditions. The solution of the homogenization problem is simpler for small inclusion sizes. In this case, the shape of the inclusions does significantly affect the averaged parameter, since its value is determined to a greater extent by the concentration of inclusions than by their shape.
