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中南大学学报(自然科学版)

Journal of Central South University

第51卷    第5期    总第309期    2020年5月

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文章编号:1672-7207(2020)05-1200-11
正交各向异性功能梯度微板的自由振动行为
康泽天,张岩,周博,薛世峰

(中国石油大学(华东) 储运与建筑工程学院,山东 青岛,266580)

摘 要: 基于新修正偶应力理论,利用哈密顿原理推导正交各向异性功能梯度Kirchhoff微板的控制微分方程和边界条件,建立微板动力学模型,并利用纳维解法对其进行求解。利用建立的模型,对正交各向异性功能梯度四边简支微板的自由振动和受双向正弦分布横向载荷作用下的弯曲行为进行研究,分析材料各向异性,尺度参数与板厚比以及功能梯度参数对微板挠度、偶应力和前三阶固有频率尺度效应的影响。研究结果表明:应用本文模型求解的微板挠度比经典弹性板理论解的小,而其固有频率比经典弹性板理论解的大;板厚与材料尺度参数比越小,微板挠度、偶应力和固有频率的尺度效应越明显;功能梯度参数对微板挠度、偶应力和固有频率的尺度效应有一定影响;沿2个正交方向的材料尺度参数对微板挠度、偶应力和固有频率的尺度效应影响程度不同。

 

关键字: 正交各向异性;功能梯度;尺度效应;能量法;偶应力理论

Free vibration behaviors of orthotropic functionally graded microplates
KANG Zetian, ZHANG Yan, ZHOU Bo, XUE Shifeng

College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao 266580, China

Abstract:Based on the new modified couple stress theory, the kinetic model, which includes the governing differential equations and boundary conditions of the Kirchhoff microplate was derived utilizing the Hamilton’s principle. The dynamic differential equation was solved by the Navier method. According to the presented model, the free vibration of a four-sided simply supported microplate and its bending behavior under bidirectional sinusoidal distributed loads were studied. The effects of material anisotropy, the ratio of length scale parameters to the plate thickness and functionally graded parameters on the size effects of deflection, couple stress and the first three orders of natural frequency were analyzed. The results show that the solution of the deflection of the microplates are always smaller than the classical elastic plate solution, but the solution of the natural frequencyies are always larger than the classical elastic plate solutions. The smaller the ratio of plate thickness to material length scale parameters is, the more obvious the size effects of the deflection, couple stress and natural frequency are. The functionally graded parameter has specific impacts on the size effects of deflection, couple stress and natural frequency of the microplate. The length scale parameters in the two orthogonal directions have different effects on the scale effects of deflection, couple stress and natural frequency of the microplate.

 

Key words: orthotropic; functionally gradient; size effect; energy method; couple stress theory

中南大学学报(自然科学版)
  ISSN 1672-7207
CN 43-1426/N
ZDXZAC
中南大学学报(英文版)
  ISSN 2095-2899
CN 43-1516/TB
JCSTFT
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