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Research on vibration characteristics of strain gradient higher-order shear deformable microplates
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Weijia KONG1, 2, Bo ZHANG1, 2, Yuhang DUAN1, 2, Huoming SHEN1, 2, Xu ZHANG1, 2
Chinese Journal of Applied Mechanics | 2025, 42(6) : 1397 - 1409
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Chinese Journal of Applied Mechanics | 2025, 42(6): 1397-1409
• Dynamic and Control •
Research on vibration characteristics of strain gradient higher-order shear deformable microplates
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Weijia KONG1, 2, Bo ZHANG1, 2, Yuhang DUAN1, 2, Huoming SHEN1, 2, Xu ZHANG1, 2
Affiliations
  • 1.Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, 610031 Chengdu, China
  • 2.School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, 610031 Chengdu, China
Published: 2025-12-15 doi: 10.11776/j.issn.1000-4939.2025.06.019
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This paper develops a free vibration model of rectangular microplates including three material length scale parameters and two displacement field variables using the modified strain gradient theory and a refined higher-order shear deformation theory, and presented the related governing differential equations. The analytical vibration frequencies of a four-edge supported rectangular microplate were obtained via the Navier method. Combining the Gauss-Lobatto quadrature and differential quadrature rules, a four-node seventy-two-DOF differential quadrature finite element was constructed to solve the free vibration of rectangular microplates with general boundary conditions. Through typical numerical examples, the effectiveness of the present model was established, and the effects of boundary conditions, material length scale parameters, aspect ratio and length-thickness ratio on the vibration frequencies and mode shapes of rectangular microplates were revealed. The results indicate that the vibration frequencies and some mode shapes of rectangular microplates exhibit significant size effect, and its intensity is associated with the boundary conditions and geometric dimensions.

modified strain gradient theory  /  refined higher-order shear deformation theory  /  rectangular microplate  /  free vibration  /  differential quadrature finite element
Weijia KONG, Bo ZHANG, Yuhang DUAN, Huoming SHEN, Xu ZHANG. Research on vibration characteristics of strain gradient higher-order shear deformable microplates[J]. Chinese Journal of Applied Mechanics, 2025 , 42 (6) : 1397 -1409 . DOI: 10.11776/j.issn.1000-4939.2025.06.019
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Article Info
doi: 10.11776/j.issn.1000-4939.2025.06.019
  • Receive Date：2023-06-12
  • Online Date：2026-03-27
  • Published：2025-12-15
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  • Received：2023-06-12
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Affiliations
    1.Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, 610031 Chengdu, China
    2.School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, 610031 Chengdu, China
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https://castjournals.cast.org.cn/joweb/yylxxb/EN/10.11776/j.issn.1000-4939.2025.06.019
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表12种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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