Nonlinear free vibrations of porous composite microplates incorporating various microstructural-dependent strain gradient tensors

doi:10.1007/s10483-022-2851-7

Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (6): 825-844.doi: https://doi.org/10.1007/s10483-022-2851-7

Nonlinear free vibrations of porous composite microplates incorporating various microstructural-dependent strain gradient tensors

Duquan ZUO^1,2, B. SAFAEI³, S. SAHMANI⁴, Guoling MA¹

1. Aviation Engineering College, Civil Aviation Flight University of China, Guanghan 618307, Sichuan Province, China;
2. Chongqing Engineering Research Center for Advanced Intelligent Manufacturing Technology, Chongqing Three Gorges University, Chongqing 404100, China;
3. Department of Mechanical Engineering, Eastern Mediterranean University, Famagusta 99628, North Cyprus via Mersin 10, Turkey;
4. School of Science and Technology, The University of Georgia, Tbilisi 0171, Georgia

收稿日期:2021-12-31 修回日期:2022-03-28 发布日期:2022-06-11
通讯作者: Duquan ZUO, E-mail:taiyanghefeng@cafuc.edu.cn
基金资助:
the Sichuan Province Engineering Technology Research Center of General Aircraft Maintenance (No. ZDXM2021001), the Chongqing Natural Science Foundation (No. cstc2021jcyj-msxmX0072), the Science and Technology Research Program of Chongqing Education Commission of China (No. KJQN202101202), and the Chongqing Engineering Research Center for Advanced Intelligent Manufacturing Technology (No. ZNZZXDJS202002)

Nonlinear free vibrations of porous composite microplates incorporating various microstructural-dependent strain gradient tensors

Duquan ZUO^1,2, B. SAFAEI³, S. SAHMANI⁴, Guoling MA¹

1. Aviation Engineering College, Civil Aviation Flight University of China, Guanghan 618307, Sichuan Province, China;
2. Chongqing Engineering Research Center for Advanced Intelligent Manufacturing Technology, Chongqing Three Gorges University, Chongqing 404100, China;
3. Department of Mechanical Engineering, Eastern Mediterranean University, Famagusta 99628, North Cyprus via Mersin 10, Turkey;
4. School of Science and Technology, The University of Georgia, Tbilisi 0171, Georgia

Received:2021-12-31 Revised:2022-03-28 Published:2022-06-11
Contact: Duquan ZUO, E-mail:taiyanghefeng@cafuc.edu.cn
Supported by:
the Sichuan Province Engineering Technology Research Center of General Aircraft Maintenance (No. ZDXM2021001), the Chongqing Natural Science Foundation (No. cstc2021jcyj-msxmX0072), the Science and Technology Research Program of Chongqing Education Commission of China (No. KJQN202101202), and the Chongqing Engineering Research Center for Advanced Intelligent Manufacturing Technology (No. ZNZZXDJS202002)

摘要/Abstract

摘要： The main objective of the present numerical analysis is to predict the nonlinear frequency ratios associated with the nonlinear free vibration response of porous composite plates at microscale in the presence of different microstructural gradient tensors. To achieve this end, by taking cubic-type elements into account, isogeometric models of porous composite microplates are obtained with and without a central cutout and relevant to various porosity patterns of distribution along the plate thickness. The established unconventional models have the capability to capture the effects of various unconventional gradient tensors continuity on the basis of a refined shear deformable plate formulation. For the simply supported microsized uniform porous functionally graded material (UPFGM) plate having the oscillation amplitude equal to the plate thickness, it is revealed that the rotation gradient tensor causes to reduce the frequency ratio about 0.73%, the dilatation gradient tensor causes to reduce it about 1.93%, and the deviatoric stretch gradient tensor leads to a decrease of it about 5.19%. On the other hand, for the clamped microsized U-PFGM plate having the oscillation amplitude equal to the plate thickness, these percentages are equal to 0.62%, 1.64%, and 4.40%, respectively. Accordingly, it is found that by changing the boundary conditions from clamped to simply supported, the effect of microsize on the reduction of frequency ratio decreases a bit.

关键词: size dependency, isogeometric approach, nonlinear dynamics, geometric approximation, micromechanics

Abstract: The main objective of the present numerical analysis is to predict the nonlinear frequency ratios associated with the nonlinear free vibration response of porous composite plates at microscale in the presence of different microstructural gradient tensors. To achieve this end, by taking cubic-type elements into account, isogeometric models of porous composite microplates are obtained with and without a central cutout and relevant to various porosity patterns of distribution along the plate thickness. The established unconventional models have the capability to capture the effects of various unconventional gradient tensors continuity on the basis of a refined shear deformable plate formulation. For the simply supported microsized uniform porous functionally graded material (UPFGM) plate having the oscillation amplitude equal to the plate thickness, it is revealed that the rotation gradient tensor causes to reduce the frequency ratio about 0.73%, the dilatation gradient tensor causes to reduce it about 1.93%, and the deviatoric stretch gradient tensor leads to a decrease of it about 5.19%. On the other hand, for the clamped microsized U-PFGM plate having the oscillation amplitude equal to the plate thickness, these percentages are equal to 0.62%, 1.64%, and 4.40%, respectively. Accordingly, it is found that by changing the boundary conditions from clamped to simply supported, the effect of microsize on the reduction of frequency ratio decreases a bit.

Key words: size dependency, isogeometric approach, nonlinear dynamics, geometric approximation, micromechanics

中图分类号:

74H60

Duquan ZUO, B. SAFAEI, S. SAHMANI, Guoling MA. Nonlinear free vibrations of porous composite microplates incorporating various microstructural-dependent strain gradient tensors[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(6): 825-844.

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Nonlinear free vibrations of porous composite microplates incorporating various microstructural-dependent strain gradient tensors

Nonlinear free vibrations of porous composite microplates incorporating various microstructural-dependent strain gradient tensors

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