基于各向异性修正偶应力理论的Reddy型层合板的自由振动

Free Vibration of Composite Laminated Reddy Plate Based on Anisotropic Modified Couple Stress Theory

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.

In this study,based on the anisotropic modified couple stress theory,a free vibration model of composite laminated Reddy plate containing only one internal material length scale parameter was developed.The presented model predicted the frequency of free vibration of composite laminated plate in micro scale more accurately than the Kirchhoff model in published literature.The Hamilton’s principle was employed to derive the governing equations of motion and the boundary conditions.A simply supported square plate was taken as an illustrative example,the problem of which was solved analytically.Influence of the length scale parameter on natural frequency of material was analyzed,and differences between the results obtained using the Kirchhoff,Mindlin and Reddy plate theories were discussed.Numerical results showed that the presented model was capable of capturing the scale effects.The natural frequencies were always shown to be overestimated by the Kirchhoff theory,especially in thick plate cases,when comparing with the more accurate results obtained using the Mindlin or Reddy theory.