Analytical Modeling of Vibration of Micropolar Plates

Lev Steinberg; Roman Kvasov

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Analytical Modeling of Vibration of Micropolar Plates

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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.

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《应用数学（英文）》 |2015年第5期|817-836|共20页
作者
Lev Steinberg; Roman Kvasov;
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作者单位

Department of Mathematical Sciences;

University of Puerto Rico at Mayagüez;

Mayagü

ez;

USA;

Department of Mathematics;

University of Puerto Rico at Aguadilla;

Aguadilla;

USA;

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原文格式 PDF
正文语种 chi
中图分类数学;
关键词
Cosserat; Materials; Plate; Vibration; Frequencies; of; Transverse; Micro-Vibration; Variational; Principle;

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1. Analytical analysis for vibration of longitudinally moving plate submerged in infinite liquid domain [J] . Yanqing WANG ,J.W.ZU . 应用数学和力学：英文版 . 2017,第5期
2. NONLINEAR MINDLIN PLATE EQUATIONSFOR THE THICKNESS-SHEAR VIBRATIONS OF CRYSTAL PLATES [C] . Ji WANG ,Rong-xing WU ,Jian-ke DU . 第三届全国压电和声波理论及器件技术研讨会 . 2008
3. The study of nonlinear vibration properties in parallel-plate assemblies [A] . fuchao . 2008

Analytical Modeling of Vibration of Micropolar Plates

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