Proper Motions of the Flat Structure of Cosserat Type

The problem on natural vibrations of a flat strip of anisotropic two-dimensional Cosserat medium under the assumption of small deformations and in the absence of external forces and moments is investigated. It is shown that two natural frequencies correspond to each wave number. The natural forms of oscillations and the relation between them are found. It is concluded that at oscillations with the lower of the two frequencies the inclusion rotations accompany the longitudinal displacement of the strip, and at oscillations with a higher frequency they prevent it. The obtained results are illustrated on the example of a medium model with specific parameter values. The plots show the dependences of natural frequencies, phase and group velocities on the wave number, and their asymptotic behavior is studied.