杆的离散系统的振动反问题

Inverse vibration problem for the discrete system of a rod

研究杆的一类离散系统的振动反问题,假定杆沿轴向与弹性基础相连,设{ωi}i=1n为杆一端固定、另一端自由时的频率,{μi}i=1n-1为杆两端固定时的频率,u为固定—自由杆对应于最低频率ωi的模态,W为杆的总质量。考虑由给定的两组频率、一个模态和系统的总质量来构造杆的离散系统的参数。本文将问题转化为Jacobi矩阵的特征值反问题,给出由{ωi}i=1n、{μi}i=1n-1、u和W构造具有正的质量和刚度的可实现物理系统的充分必要条件,并且证明如果这些条件得到满足,则可唯一地构造杆离散系统。因为构造杆的离散系统需要的数据可由测试得到,其结果适用于模态分析应用。

Consider an inverse vibration problem for the discrete system of a rod. Suppose that the rod is connected to the elastic basic along tits axial. Let {wi}i^n=1 be the frequencies of the axial vibrating rod, fixed at one end and free at the other, {μi}i=1^n-1 the frequencies of the rod, fixed at two ends, and a mode corresponding to the lowest frequency Wi of the fixed-free rod and W the total mass of the rod. The problem of constructing the physical parameters of the discrete system of the rod from {wi}i^n=1、{μi}i=1^n-1,u and W is considered. The problem is transferred into inverse eigenvalue problems for Jacobi matrices. The necessary and sufficient conditions for the construction of a physical realizable discrete system of the rod with positive mass and stiffness elements are derived. It is further shown that if these conditions are satisfied the discrete system of the rod may be constructed uniquely. Since the data required for the construction may be available from measurements, the presented approach is well suited for modal analysis applications.