振动杆有限差分模型的一类特征值反问题  

AN INVERSE EIGENVALUE PROBLEM FOR THE FINITE DIFFERENCE MODEL OF A VIBRATING ROD

作　　者：毛晓彬[1] 戴华[1] 

机构地区：[1]南京航空航天大学理学院,南京210016

出　　处：《高等学校计算数学学报》2008年第2期159-168,共10页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(10271055)

摘　　要：1 引言 杆是重要的工程构件之一，具有分布质量的杆的纵向振动由下面的偏微分方程描述：In this paper, an inverse eigenvalue problem for the finite difference model of a vibrating rod is proposed, i.e., constructing the discrete model of a vibrating rod from partial physical parameters and two defective eigenpairs of the rod. The solvability of the problem is discussed for the discrete model. The necessary and sufficient conditions for the construction of a physically realizable rod with positive parameters are derived. A numerical method for solving the problem is presented. A numerical example is given.

关 键 词：特征值反问题 有限差分模型 振动杆 偏微分方程 工程构件 纵向振动 分布质量 

分 类 号：O151.21[理学—数学] TV122[理学—基础数学]