Abstract
A mathematical model representing the dynamics of geometrically nonlinear (flexible) micropolar elastic thin plates in Cartesian and curvilinear coordinates is constructed (the approach is generalized to the case of micropolar flexible shallow shells as well). The model is developed under the assumption that the elastic deflection of a plate is comparable with the plate thickness but is small compared to the characteristic plate size in plan. Based on the given model of micropolar elastic flexible plates, the problem on free vibrations is solved for rectangular and circular plates and shallow shells. Effective manifestations of characteristic features of a micropolar material are considered in comparison with the corresponding classical material.
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