接地弹簧-质点系统的逆特征值问题

考虑接地的简单连接的弹簧—质点系统,设(λ,X)和(μ,Y)为只有部分质量(j个)接地的弹簧—质点系统的2个特征对,考虑由这2个特征对、前j个质量构造接地的弹簧—质点系统的特征值反问题。将问题转化为Jacobi矩阵特征值反问题,给出由已知条件构造具有正的质量和正的刚度物理系统的充分必要条件。如果这些条件得到满足,则可惟一地构造接地的弹簧—质点系统。

An inverse eigenvalue problem for grounding spring-mass systems

Consider a simply connected grounding spring mass system, it is supposed that j mass is connected to the ground. Let (λ,X) and (μ,Y) be two eigenpairs of a simply connected grounding spring mass system. The inverse eigenvalue problem of constructing the physical elements of the system from (λ,X),(μ,Y) and j mass was studied. This problem was transferred into an inverse eigenvalue problem for Jacobi matrices. The necessary and sufficient conditions for the construction of a physical realizable system with positive mass and stiffness elements were established. If these conditions were satisfied, the grounding spring-mass system can be uniquely constructed.