弹性混合板的振动和稳定问题  

Vibration and Stability of Hybrid Plate Based on Elasticity Theory

作　　者：吕和祥[1,2] 李俊永 

机构地区：[1]大连理工大学工程力学系 [2]工业装备结构分析国家重点试验室,辽宁大连116023

出　　处：《应用数学和力学》2009年第4期388-398,共11页Applied Mathematics and Mechanics

摘　　要：通过将非线性应变位移关系引入Hellinger-Reissner变分原理,推导出了各向异性板基于弹性理论下的振动和屈曲控制方程.用精细积分法研究了四边简支混合矩形板.精细积分法与传统的有限差分法相比,可以给出计算机精度允许的很精确的数值结果.所以,给出的混合板的振动和稳定的结果可以看作是近似解析的.这些结果可以作为衡量各种板理论准确性的一个标准.而且,非对称层合板中出现的各种耦合影响,比如弯扭耦合,拉弯耦合等在同一组控制方程里被考虑了.The governing equations of elasticity theory for natural vibration and buckling of anisotropic plate were derived from Hellinger-Reissner＇s variational principle with nonlinear strain-displacement relations. Simply supported rectangular hybrid pLates were studied by p.recise integration method. This method, in contrast to the traditional finite difference approximation, gives highly precise numerical results which approach the full computer precision. So the results for natural vibration and stability of hybrid plates presented can be regarded as approximate analytical solutions. Furthermore, the several types of coupling effects , such as coupling between bending and twisting, coupling between extension and bending, etc. when the layer stacldng sequence is not syminetric, are considered by only one set of governing equations.

关 键 词：振动 屈曲 精细积分 混合板 状态空间 

分 类 号：O343.8[理学—固体力学]