Analytical Modeling of Vibration of Micropolar Plates

Lev Steinberg¹, Roman Kvasov²

¹Department of Mathematical Sciences, University of Puerto Rico at Mayagüez, Mayagüez, USA.
²Department of Mathematics, University of Puerto Rico at Aguadilla, Aguadilla, USA.

DOI: 10.4236/am.2015.65077                

Abstract

This paper presents an extension of mathematical static model to dynamic problems of micropolar elastic plates, recently developed by the authors. The dynamic model is based on the generalization of Hellinger-Prange-Reissner (HPR) variational principle for the linearized micropolar (Cosserat) elastodynamics. The vibration model incorporates high accuracy assumptions of the micropolar plate deformation. The computations predict additional natural frequencies, related with the material microstructure. These results are consistent with the size-effect principle known from the micropolar plate deformation. The classic Mindlin-Reissner plate resonance frequencies appear as a limiting case for homogeneous materials with no microstructure.

Keywords

Cosserat Materials, Plate Vibration, Frequencies of Transverse Micro-Vibration, Variational Principle

Conflicts of Interest

The authors declare no conflicts of interest.

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