結(jié)構(gòu)動力學(xué)中的特征值反問題.pdf

1、南京航空航天大學(xué)博士學(xué)位論文結(jié)構(gòu)動力學(xué)中的特征值反問題姓名：王正盛申請學(xué)位級別：博士專業(yè)：一般力學(xué)與力學(xué)基礎(chǔ)指導(dǎo)教師：戴華20060601結(jié)構(gòu)動力學(xué)中的特征值反問題 iiABSTRACT This dissertation studies the inverse eigenvalue problems in structural dynamics, including vibration inverse problems for the

2、 spring-mass system, the discrete beam, damped systems and the damage detection in rods. The main contribution is as follows. First of all, the inverse eigenvalue problems of the spring-mass systems are studied. The sim

3、ply connected spring-mass system of two freedoms and the modified system with a simple oscillator of mass or spring attached to one end of the system are considered. For simply connected spring-mass system of n freedoms,

4、 the necessary and sufficient conditions for the reconstruction of a physical realizable system from the known four and five eigenpairs are established. Also, the inverse eigenvalue problems of the hybrid connected spri

5、ng-mass system are considered. The necessary and sufficient conditions for the solvability of the problems are obtained. Numerical methods and numerical experiments are given. Secondly， an inverse vibration problem for t

6、he discrete beam is considered. Given the three frequencies and corresponding modes of the axial vibrating beam, the problem of constructing the structural physical parameters of the discrete model of the beam from the k

7、nown data is considered. The problem is transferred into inverse eigenvalue problems for real symmetric pentadiagonal matrices. The necessary and sufficient conditions for the solvability of the problem are obtained. Num

8、erical methods and numerical experiments are presented. Afterwards, the inverse quadratic eigenvalue problems in damped vibration system are studied. These problems include the construction of the stiffness matrix and da

9、mped matrix of the damped vibration systems from the full frequencies and corresponding modes, the construction of the stiffness matrix and damped matrix of damped vibration systems with proportional damping from the som