摘要
运用Fourier分析方法,建立了对边简支的矩形中厚板弯曲问题的完备的辛本征展开.借助于Math-ematica软件的帮助,得到了来源于矩形中厚板问题的Hamilton算子的本征函数.接着证明了本征函数系的完备性,这为使用分离变量法求解相应问题提供了理论保证;进而运用完备性定理,得到了问题的解析解;一个数值算例验证了结果的正确性.
A complete symplectic eigenfunction expansion for rectangular moderately thick plate with two simply-supported opposite sides is proposed by using Fourier analysis method. The eigenfunctions of the Hamiltonian operator arising from considered problem are solved. The completeness of the eigenfunctions is then proved,providing the theoretical guarantee of using separation of variables to solve the problems. The analytic solution is obtained with the proved expansion theorem,and a numerical example shows the correctness of the result.
出处
《固体力学学报》
CAS
CSCD
北大核心
2011年第6期611-618,共8页
Chinese Journal of Solid Mechanics
基金
国家自然科学基金项目(10962004)
内蒙古自然科学基金项目(20080404MS0104)
国家大学生创新性实验计划项目(091012609)资助
关键词
中厚板
HAMILTON体系
辛特征展开
解析解
analytic solution moderately thick plate, Hamiltonian system, symplectic eigenfunction expansion,
