受压对称迭层矩形板的自由振动分析  

FREE VIBRATION ANALYSIS OF COMPRESSED SYMMETRICALLY LAMINATED RECTANGULAR PLATES

作　　者：杨端生[1] 袁端才[2] 黄炎[2] 

机构地区：[1]长沙理工大学桥梁与结构工程学院,长沙410076 [2]国防科技大学航天与材料工程学院,长沙410073

出　　处：《工程力学》2007年第4期41-45,共5页Engineering Mechanics

基　　金：国家自然科学基金资助项目(19872076)

摘　　要：根据受压的对称迭层矩形板自由振动的微分方程可以求得各种解析解来求解各种边值问题。迭层板有两种,一种是正交铺设,其方向与坐标轴平行,属正交异性板,当板的四边为简支时,可用双正弦级数来求解自由振动的各阶频率及其振型以及均匀受压的各阶临界载荷及其屈型。另一种是角铺设,属各向异性板,当两相邻边为自由,另两边为简支或固支时可用复数级数来求解其最低频率及其振型以及最低临界载荷及其屈型。此时其特征方程的根为两对复根,且可表成三角级数和双曲线级数,以满足边界条件。另外用代数多项式和双正弦级数组成的解来满足角点条件。在算例中计算了若干板受压或不受压的振动频率和临界载荷,并与其他文献进行了对比。According to the differential equation of compressed symmetrically laminated rectangular plates in free vibration, various analytical solutions can be obtained to solve different boundary value problems. There exist two kinds of laminated plates. One is cross-ply, the directions of which are parallel with the coordinate axes. This belongs to the orthotropic plate. When the plate is simply supported on four edges, it can be solved by double sine series to obtain not only each frequency and its vibration mode while vibrating freely, but also each critical load and its buckling mode when compressed uniformly. The other is angle-ply, which belongs to anisotropic plate. When the plate is free on two adjacent edges and the other two are simply supported or fixed, it can be solved by complex series to obtain the lowest frequency, the vibration mode, the lowest critical load and the buckling mode. The roots of the characteristic equation are two pairs of complex ones, which can be expressed by trigonometric function and hyperbolic function that can satisfy the boundary conditions. Moreover, the solution composed by algebraic polynomial with double sine series is used to satisfy the comer conditions. The compressed or non-compressed vibration frequency and the critical loads for some example plates were calculated and compared with the results in other references.

关 键 词：对称迭层板 解析法 自由振动 频率 屈曲 临界载荷 

分 类 号：O326[理学—一般力学与力学基础] O343.9[理学—力学]