Mechanical Engineering

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Solution Methodology for Constrained Eigenvalue Problems and Its Applications with Experimental Validation in Structural Characteristics Identification
(2021-11-15) Chen, Longhan; Gu, Randy; Yang, Lianxiang; Mourelatos, Zissimos P.; Spagnuolo, Anna
A numerical reverse algorithm was developed in this dissertation to find some unknown parameters of an object. For example, if the natural frequency of an object is known, find the mass of the particle placed at a specific place in the object. There is nos such direct formula or algorithm that can solve this kind of problem, we can use the reverse algorithm to solve it. Since the objective function can be built after the structure's stiffness matrix and mass matrix were obtained using the finite element method, and the structure's natural frequencies are known, this kind of problem becomes a constrained eigenvalue problem. The constrained eigenvalue problem can be solved by minimizing the objective function and executed using numerical methods. In this dissertation, we developed Newton's iteration to solve it and also developed the Genetic Algorithm as an alternative algorithm when Newton's iteration cannot find unknown parameters. Several numerical examples, such as beam, plane frame, three-dimensional frame, and plate structure, were chosen to test the proposed algorithm's feasibility, accuracy, and solving time. Furthermore, some groups of experimental validation were also provided to testify to it.