Analysis of the wave solution of the elastokinetic equations of a Cosserat continuum for the case of bulk plane waves

A study is made of waves in a Cosserat continuum, whose strain state is characterized by independent displacement and rotation vectors. The propagation of longitudinal and transverse bulk waves is considered. Wave solutions are sought in the form of wave trains specified by a Fourier spectrum of arbitrary shape. It is shown that if the solution is sought in the form of three components of the displacement vector and three components of the rotation vector which depend on time and the longitudinal coordinate, the initial system is split into two systems, one of which describes longitudinal waves, and the other transverse waves. For waves of both types, dispersion relations and analytical solutions in displacement are obtained. The dispersion characteristics of the solutions obtained differ from the dispersion characteristics of the corresponding classical elastic solutions.