非线性弹性矩形板的自由振动精确解研究  

STUDY ON EXACT SOLUTION TO FREE VIBRATION OF A NONLINEAR ELASTIC RECTANGULAR PLATE

作　　者：钟炜辉[1] 郝际平[1] 雷蕾[1] 颜心力[2] 

机构地区：[1]西安建筑科技大学土木工程学院,西安710055 [2]西安建筑科技大学理学院,西安710055

出　　处：《振动与冲击》2008年第1期46-48,60,共4页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(50378078)

摘　　要：板作为工程结构中的基本单元得到了人们的广泛研究,板在承受动力荷载作用下的动力响应问题受到了普遍关注。对非线性弹性矩形板的自由振动进行了研究,考虑了材料非线性和面内静载对板动力特性的影响,并根据半序空间的不动点理论求得该矩形板在自由振动时各阶模态的精确解,描绘了其自由振动的全过程。通过算例指出材料非线性和面内静载都对板的自由振动产生一定影响,在不同模态间可能出现"跳阶"现象。A linear elastic plate as a basic element in engineering stractures has been extensively studied.And its dynamic response under dynamic loads is universally concerned.The free vibration of a nonlinear elastic rectangular plate is explored,considering influence of material nonlinearity and static-load in plane on its dynamic characteristics.Exact solution to free vibration of each mode of the rectangular plate is obtained according to the fixed point theory of partially ordered space.So the whole process of free vibration is described.The effect of material nonlinearity and static load in plane on the free vibration of the plate is analyzed by numerical examples.The phenomenon 'order jumping' between different modes may appear.

关 键 词：非线性弹性矩形板 自由振动 不动点理论 算子 自振频率 

分 类 号：O322[理学—一般力学与力学基础] TU311.3[理学—力学]