Inverse Vibration Problems Of The Rod And Beam

This dissertation studies the inverse mode problems for the spring-mass system, the discrete model of the rod, the finite element model of the rod, the discrete model and the continuous model of the beam. The main contribution is as follows.The inverse mode problems of the spring-mass system are studied. The simply connected spring-mass system and the modified systems (a simple oscillator of mass and/or spring is attached to one end of the system) are considered. Given two eigenpairs of a simply connected spring-mass system and the modified system respectively, one additional mass and/or additional spring, three classes of the inverse mode problems constructing the spring-mass systems are presented. The problems are transferred into inverse eigenvalue problems for Jacobi matrices. The necessary and sufficient conditions for the reconstruction of a physical realizable system with positive mass and stiffness elements from the known eigenpairs, the additional mass and /or stiffness are established. If these conditions are satisfied, the simply connected spring-mass system may be constructed uniquely. An algorithm is presented for constructing the physical realizable system from the data. The inverse mode problem of the spring-mass system with the partial masses connected to the ground by the spring is considered. Given two eigenpairs of the system and the masses connected to the ground, construct the physical parameters of the spring-mass system. The necessary and sufficient conditions for the construction of a physical realizable system with positive mass and stiffness elements are given.An inverse vibration problem for the discrete model of a vibrating rod is considered. Suppose that the rod is connected to the elastic basic along its axis. Given the frequencies of the axial vibrating rod, fixed at one end and free at the other, and the frequencies of the rod, fixed at two ends, and a mode corresponding to the lowest frequency of the fixed-free rod and the total mass of the rod, the...