基于Hamilton体系的加载边简支矩形薄板稳定性分析  

Stability analysis of simply supported rectangular thin plate for loaded side based upon Hamilton system

作　　者：杨洪澜[1] 赵亚荣 郑俊[3] 周涛[1] 

机构地区：[1]齐齐哈尔大学机电工程学院,黑龙江齐齐哈尔161006 [2]长春迪瑞医疗科技股份有限公司,吉林长春130000 [3]江苏大学能源与动力工程学院,江苏镇江212013

出　　处：《高师理科学刊》2016年第11期36-40,共5页Journal of Science of Teachers＇College and University

基　　金：江苏省自然科学基金项目(BK20130478)

摘　　要：在板微弯曲最小势能变分原理的基础上,选用状态变量和对偶变量,导向一般变分原理.经过变分运算,得出全状态变量表示的微分方程组.采用分离变量法得到本征值方程,给出了本征值方程的解,导出加载边简支矩形薄板挠度的级数表达式.可以根据各种边界条件建立板稳定性问题方程.The variational principle for the micro bending plate was derived through the principle of the minimum potential energy with the state variables and dual variables. The differential sate equation set, was then obtained from the variational equation of the generalized functional. The characteristic equation of the equation set was derived by the method of separation of variables, which yields the series solution of the deflection of the thin square plate. Other stability problems of the plate could also be modeled for under different boundary conditions.

关 键 词：HAMILTON体系 弹性薄板 稳定性 分离变量法 

分 类 号：O343[理学—固体力学]