基于高阶位移模式的层合板自由振动问题研究  

Free Vibration of Composite Laminated Plates Basd on the Higher-order Displacement Mode

作　　者：杨加明[1] 盛佳[1] 孙超[1] 

机构地区：[1]南昌航空大学飞行器工程学院,南昌330063

出　　处：《力学季刊》2012年第2期309-316,共8页Chinese Quarterly of Mechanics

基　　金：江西省教育厅科技项目(GJJ11514);南昌航空大学无损检测技术教育部重点实验室基金(ZD201129006)

摘　　要：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。Abstract： Normal and shear strains of composite laminated plates are formed using a higher-order displace- ment mode. The corresponding stress is found out according to the constitutive relations. The strain ener- gy and kinetic energy of composite laminated plates are obtained. Through the Hamiltonian principle, the governing equations are derived by variations of displacement components. The natural frequencies are acquired for simply supported angle-ply laminated plates. As an example, numerical results are presented for [0°/90°/90°/0°] symmetric cross-ply plates. The influence of thickness, elastic modulus and aspect ra- tios are discussed on the nondimensional natural frequency. The numerical results show that the nondi- mensional natural frequency of symmetric cross-ply plates has been greatly changed when the length/ height ratio is less than 20, and there are almost linear relations between the nondimensional natural fre- quency and the main elastic modulus ratios.

关 键 词：高阶位移模式 复合材料层合板 固有频率 自由振动 HAMILTON原理 

分 类 号：V214.8[航空宇航科学与技术—航空宇航推进理论与工程]