基于新修正偶应力理论的Mindlin层合板自由振动分析

该文基于各向异性修正偶应力理论建立一个Mindlin层合板（跨厚比10~20的中厚板）自由振动模型。该理论偶应力曲率张量不对称，但偶应力弯矩对称。利用Hamilton原理推导振动微分方程和边界条件。新模型可退化为修正偶应力层合薄板振动模型和经典Mindlin层合板振动模型。以正交铺设简支方板为例计算了偶应力模型的自振频率，分析偶应力Mindlin层合板的自由振动尺度效应。算例表明，该文建立的新修正偶应力层合板模型能够用于分析细观尺度下Mindlin层合板的自由振动及尺度效应。

FREE VIBRATION ANALYSIS OF A LAMINATED COMPOSITE MINDLIN PLATE BASED ON NEW MODIFIED COUPLE STRESS THEORY

A free vibration model for a composite laminated Mindlin plate (span-depth ratio at 10~20) is established based on new modified couple stress theory for anisotropic material. In this theory, the curvature tensor is asymmetric, while the couple stress bending moment is symmetry. A Hamiltonian principle is employed to derive the governing equations of motion and boundary conditions. This new model can be reduced to the model for a composite laminated thin plate based on modified couple stress theory, and also to the model for a composite laminated Mindlin plate based on classical theory. An example of natural frequencies analysis with a cross-ply simple supported square-plate is used to show the scale effects of natural frequencies. Numerical results show that the present model can capture the scale effects of the free vibration of a micro-scale composite laminated Mindlin plate.