弹性理论中一类算子矩阵的本征向量展开定理及应用  

Eigen-vector expansion theorem of a class of operator matrices appearing in elasticity and applications

作　　者：张国亭[1] 黄俊杰[1] 阿拉坦仓[1] 

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《物理学报》2012年第14期24-32,共9页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11061019;11101200);教育部春晖计划项目(批准号:Z2009-1-01010);内蒙古自然科学基金项目(批准号:2010MS0110)资助的课题~~

摘　　要：研究弹性理论中一类非自伴算予矩阵的本征向量展开定理.证明了其本征向量组具有辛正交性,给出了本征向量组完备的充分必要条件,并将所得结果应用于板弯曲问题和矩形薄板均匀变压屈曲挠度方程中.For a class of operator matrices appearing in elasticity,the eigen-vector expansion theorem is considered.It is shown that the eigen-vectors possess the symplectic orthogonality.And a necessary and sufficient condition for the completeness of the eigen-vector system is further given.As concrete applications,the obtained results are tested for the plate bending equation and the buckling deflection problem of rectangular thin plates.

关 键 词：算子矩阵 本征向量展开定理 弹性理论 

分 类 号：O151.21[理学—数学]