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本文利用高阶位移模式,确定了复合材料层合板的正应变和切应变。根据本构关系得到了相应的应力,给出了复合材料层合板的应变能和动能表达式。基于Hamilton原理分别对位移分量求变分,推导出了5个振动控制方程,求出了简支角铺矩形层合板的各阶固有频率。以[0°/90°/90°/0°]正交对称铺设简支板为算例,分别讨论了跨厚比、主轴弹性模量比及长宽比对无量纲固有频率的影响。数值结果表明:当跨厚比小于20时,无量纲固有频率变化较大;无量纲固有频率与主弹性模量比之间几乎成线性变化关系。
In this paper, using the high-order displacement mode, the normal strain and shear strain of the composite laminates are determined. The corresponding stress is obtained according to the constitutive relation, and the strain energy and kinetic energy expression of the composite laminates are given. Based on the principle of Hamilton, the displacement components were separately variationally derived, and five vibration control equations were deduced. The natural frequencies of each rectangular section of simply supported rectangular pavements were calculated. The effect of cross-section ratio, principal-axis elastic modulus ratio and aspect ratio on the dimensionless natural frequency was discussed with a simple symmetrical support plate [0 ° / 90 ° / 90 ° / 0 °]. The numerical results show that when the ratio of cross-section thickness is less than 20, the dimensionless natural frequency changes greatly. The relationship between the dimensionless natural frequency and the principal elastic modulus ratio changes almost linearly.