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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。
In this paper, a free-vibration model of Mindlin laminates (medium-thick plates with cross-section thickness ratio of 10-20) is established based on the anisotropic modified even-stress theory. The theoretical even stress tensor tensor is asymmetric, but the even stress moment is symmetrical. Derivation of Vibration Differential Equation and Boundary Condition by Hamilton Principle. The new model can degenerate into a modified vibration model for even-stress laminated sheets and a classical Mindlin laminate vibration model. The natural frequency of the even-stress model was calculated by the orthogonal laying of a simple square, and the free-vibration scaling effect of the even-stress Mindlin laminate was analyzed. The results show that the new modified even-stress laminate model established in this paper can be used to analyze the free vibration and scale effects of Mindlin laminates at the mesoscopic scale.