摘要
恰当地选择对偶变量得出矩形中厚板弯曲问题的可分Hamilton系统.利用斜对角无穷维Hamilton算子的结构特性结合典型的力学边界条件导出了相应Hamilton算子本征函数系之间的双正交关系.运用双正交关系得到了对边简支矩形中厚板弯曲问题完备的双正交展开解.文章最后应用数值算例验证了双正交展开定理的正确性.
The moderately thick rectangular plate bending problem is derived to a septarable Hamiltonian system by choosing proper dual vectors. Using the structural characteristics of off- diagonal Hamiltonian operators and the typical mechanical boundary conditions, the biorthogonal relationships of the eigenfunctions are presented. Applying the biorthogonal relationships, a com- plete biorthogonal expansion of the moderately thick rectangular plate bending problems with two opposites simply supported is established. Finally, the numerical example shows the correctness of the biorthogonal expansion method.
出处
《内蒙古大学学报（自然科学版）》
CAS
CSCD
北大核心
2014年第5期462-469,共8页
Journal of Inner Mongolia University：Natural Science Edition
基金
国家自然科学基金资助项目(11361034)
内蒙古自然科学基金资助项目(2012MS0105)
关键词
本征函数系
完备性
双正交展开
可分Hamilton系统
中厚板
eigenfunction system
completeness
biorthogonal expansion
Septarable Hamiltoni-an system
moderately thick rectangular plate
