| Finite Element Model Updating has emerged in the 1990's as a significant subject to the design, construction and maintenance of mechanical systems. Currently, finite element analysis techniques in the field of engineering technology used widely to develop rapidly. Model updating, at its ambitions, is used to correct inaccurate analytical models by measured data, such as natural frequencies, damping ratios and model shapes, which can usually be obtained by vibration test. Updating the analytical mass, damping and stiffness matrices by measured frenquencies (eigenvaluesλ1,...,λk) and model shapes (eigenvectors X1,..., Xk) is the finite element model updating problem, which we will discuss in this paper. That is also the problem about finding the best closest solution for the inverse quadratic eigenvalue problem. According to updating different object, there are many model updating methods. We will mainly introduce two types of updating methods: One is based on the optimization theory, has used classics dual theory; Another is a reference based method, using mass matrix as a reference basic and through minimization of the objective function for updating model.In this paper, we look back many scholars' works in this area and give a method for the inverse quadratic eigenvalue problems. We also develop a new method for the model updating problems.This paper includes five chapters. Chapter 1 gives us an introduction of the background and content about the inverse quadratic eigenvalue problems and the finite element model updating problems. In chapter 2, we mainly constructe the solution for the inverse quadratic eigenvalue problems. Chapter 3 introduce the model updating method basic on optimization theory. In chapter 4, we introduce the model updating method by updating the damping and stiffness matrices simultaneously. Numerical experiments are given in the last chapter.
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