基于各向异性修正偶应力理论的Reddy型层合板的自由振动

发布时间：2018-03-27 15:21

本文选题：各向异性修正偶应力理论　切入点：尺度效应　出处：《固体力学学报》2016年02期

【摘要】：论文基于各向异性修正偶应力理论建立了只含一个尺度参数的Reddy型复合材料层合板的自由振动模型.同见诸于文献的细观尺度Kirchhoff薄板偶应力模型相比,论文提出的新模型能够更精确的预测细观尺度下的中、厚层合板的自振频率.基于Hamilton原理推导了细观尺度下Reddy型复合材料层合板的运动微分方程以及边界条件,并以正交铺设的四边简支复合材料层合方板为例进行了解析求解,分析了尺度参数对自振频率的影响并对比了Kirchhoff、Mindlin和Reddy等三种板模型计算结果的异同.算例结果表明论文所给出的模型能够捕捉到复合材料层合板自由振动问题的尺度效应.另外,在细观尺度下Kirchhoff板模型所预测的自振频率相对于Mindlin板模型和Reddy板模型总是过高,且越接近厚板三者的差别就越大,这与经典理论中三种板模型的对比情况是一致的.
[Abstract]:Based on the anisotropic modified couple stress theory, the free vibration model of Reddy composite laminated plates with only one parameter is established, which is compared with the mesoscale Kirchhoff thin plate coupling stress model. The new model proposed in this paper can more accurately predict the natural frequencies of mesoscale thick laminated plates. Based on the Hamilton principle, the differential equations of motion and boundary conditions of Reddy composite laminated plates at mesoscale scale are derived. Taking the quadrilateral simply supported composite laminated square plate as an example, the analytical solution is given. The influence of scale parameters on the natural vibration frequency is analyzed, and the differences and similarities between Kirchhoff Mindlin and Reddy model are compared. The numerical results show that the model presented in this paper can capture the scale effect of the free vibration problem of composite laminated plates. The natural vibration frequency predicted by the Kirchhoff plate model is always too high than that of the Mindlin plate model and the Reddy plate model at the mesoscale scale, and the closer it is to the thick plate, the greater the difference among them is, which is consistent with the comparison of the three kinds of plate models in the classical theory.
【作者单位】：沈阳航空航天大学辽宁省飞行器复合材料结构分析与仿真重点实验室;
【基金】：国家自然科学基金资助项目(No.11572204)资助
【分类号】：O323

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