杆有限元模型的特征值反问题  

INVERSE EIGENVALUE PROBLEMS FOR THE FINITE ELEMENT MODEL OF THE ROD

作　　者：田霞[1] 戴华[1] 

机构地区：[1]南京航空航天大学数学系,南京210016

出　　处：《高等学校计算数学学报》2007年第2期146-156,共11页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金资助项目(10271055).

摘　　要：1引言非均匀杆的轴向自由振动方程为其中L为杆的长度,A(x)为杆的横截面积,E(x)为弹性模量,ρ(x)是杆的密度．杆的主振动的一般形式为u(x,t)=u(x)sin(wt+φ), (2)其中u(x)满足d/dx[E(x)A(x)du/dx]+λρ(x)A(x)u=0,λ=ω2．(3)The finite element model, based on linear shape functions, for rods under longitudinal vibrations, consists of mass and stiffness matrices which are both tridiagonal. Let （λ, x） and （μ, y） be two eigenpairs of the rod, W the total mass of the rod. The problem of constructing the physical parameters of the model from （λ, x）,（μ, y） and W is considered. The necessary and sufficient conditions for the construction of a physical realizable system with positive mass and positive spring elements are established. If these conditions are satisfied, the construction of the model is unique.

关 键 词：杆 有限元模型 特征值 反问题 振动 

分 类 号：O242.25[理学—计算数学] O327[理学—数学]