梁的离散模型的模态反问题  

INVERSE MODE PROBLEMS FOR THE DISCRETE MODEL OF BEAM

作　　者：田霞[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：《振动与冲击》2005年第6期29-31,共3页Journal of Vibration and Shock

基　　金：国家自然科学基金(10271055)资助项目

摘　　要：采用集中质量法或有限差分法对梁进行离散,得到横向振动梁的弹簧-质点-刚杆模型,其质量矩阵为对角矩阵而刚度矩阵为对称五对角矩阵。已知(λ,x)、(μ,y)为梁的两个特征对,W为梁的总质量,考虑由这些数据构造离散梁的物理参数,得出构造具有正的质量和刚度的真实系统的充要条件。如果这些条件得到满足,则系统的构造是唯一的。因为构造梁的离散系统需要的数据可由测试得到,所以其结果适用于模态分析应用。A simple discrete spring-mass-rod model for the transverse vibration of a beam is derived by the concentrated mass method or the finite difference method. It consists of mass matrix which is diagonal and stiffness matrix which is pentadiagonal. Let (λ, x) and (μ, y) be two eigenpairs of the discrete beam and W the total weight of the beam, the physical parameters of the system can be constructed by (λ, x), (μ, x) and W. The necessary and sufficient conditions for the construction of a physical realizable system with positive mass and spring elements are established. It is shown that if these conditions are satisfied, the discrete system of the beam 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.

关 键 词：特征对 集中质量法 有限差分法 弹簧-质点-刚杆模型 梁 

分 类 号：O327[理学—一般力学与力学基础]