6. Conclusions

In this chapter, we presented a mathematical model of Cosserat plate vibrations. The dynamic model of the plates has been developed as a dynamic extension of the Reissner plate theory. The equations has been presented in both tensorial and the matrix forms. We also described the validation of the model, which is based on the comparison with the three-dimensional Cosserat elastodynamics exact solutions. Based on the presented results of the computer simulations we were able to detect and classify the additional high resonance frequencies of a plate. We have shown that the frequencies depend on the shape and orientation of microelements (ballshaped elements, horizontally and vertically stretched ellipsoids) incorporated into the Cosserat plates. We also have been able to identify that micro frequencies associated with the micro rotatory inertia and its transverse variation of the ellipsoid elements have higher micro frequencies than the ball-shaped elements. We also showed the dependence of the eigenfrequencies on the angles of rotation of the horizontal ellipsoid micro-elements. These results can be used to identify the characteristics of the plate micro-elements.

Distinctive Characteristics of Cosserat Plate Free Vibrations DOI: http://dx.doi.org/10.5772/intechopen.87044
