The problem of the natural oscillations of a rectangle in the micropolar theory of elasticity

Abstract

We consider the plane problem of natural harmonic oscillations of a rectangle with mixed boundary conditions within the framework of the linear theory of micropolar elasticity. The exact analytical solution of the problem under consideration was obtained by the new method. A parametric analysis of the obtained exact solution is carried out according to which there is a “size effect”. It consists in an increase in micropolar effects with a decrease in the size of the rectangle compared with the classical case. The proposed method can be developed for the case of other boundary conditions and for the three-dimensional case.