应变梯度高阶剪切变形微板的自由振动特性研究

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中图分类号：TB383；TB34 文献标志码：A 文章编号：1000-4939（2025）06-1397-13

Abstract：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 diferential 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 diferential 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.

Key words： modified strain gradient theory ;refined higher-order shear deformation theory;rectangular microplate ;free vibration;differential quadrature finite element

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