Inverse Eigenvalue Problems Of Mass-Damper-Spring Systems

This dissertation studies the inverse mode problems for the spring-mass system and the mass-damper-spring system. The main contributions are as follows.An inverse mode problem of constructing the remaining physical parameters of spring-mass system from its partial physical parameters and two defective eigenpairs is considered. The problem is transferred into inverse eigenvalue problem for Jacobi matrix. The necessary and sufficient conditions for the construction of a physically realizable spring-mass system with positive parameters are derived.An inverse mode problem of constructing the physical parameters of mass-damper-spring system from its complex mode, a real mode of the associated undamped system and the total mass is considered. The problem is transferred into inverse eigenvalue problem for quadratic Jacobi pencil. The necessary and sufficient conditions for constructing the mass-damper-spring system uniquely with positive parameters are derived.The simply connected spring-mass system and the modified systems (a single vicious damper is attached to between one mass and the ground or between two masses) are considered. Given one eigenpair of the simply connected spring-mass system and one eigenpair of its modified system respectively, two classes of the inverse mode problems are presented. The necessary and sufficient conditions for the reconstruction of a physical realizable system with positive mass and stiffness elements from the known data are derived. If these conditions are satisfied, the simply connected spring-mass system may be constructed uniquely.