Updating and verification of the finite element models for structural dynamic analysis using frequency response functions

Finite Element (FE) method has become a powerful tool in engineering with the developments of computer technology. However, the original structure cannot be fully represented due to some assumptions and modeling errors made in FE models. For this reason, model updating methods are used to best overlap with the original structure of the FE models. The main objective of this thesis is to develop an effective FE updating method that uses directly measured or numerically computed Frequency Response Functions (FRFs). The Sherman-Morrison (SM) formula, known from matrix theory, is now used effectively in structural modification problems. An important advantage of this method is that it requires a limited number of FRFs related to modification coordinates. In this study, it is aimed to use this method for inverse structural modification. For this purpose, firstly a specific inverse structural modification problem is that preservation of natural frequencies of a system after structural modifications is investigated and a method based on the SM formula is developed. The method provides necessary spring modifications at selected coordinates for unchanged some natural frequencies after known mass modifications on a system. The spring modifications can be between the structure and the ground or between two coordinates on the structure, which is one of the original aspects of the study. This method was then applied to the problem of shifting natural frequencies to desired values. A new formulation is obtained for the calculation of the necessary structural modifications to shift the certain number of natural frequencies to desired values of a structure. Finally, a new FE updating method based on the Sherman-Morrison-Woodbury (SMW) formula and the inverse structural modification technique is developed. In the developed FE updating method, the difference between experimental and numerical (FE) FRFs is considered. The updating process is based on the calculation of the structural modifications that make up this difference. An important advantage of the developed method over some existing methods doesn't need the unmeasured FRF's in the experimental studies. The validity and applicability of the methods developed in the thesis are investigated via numerical simulations and experimental applications and successful results are obtained. It is seen that the performance of the methods was adversely affected if the noisy FRFs are used. If the frequency points are selected from noiseless regions, successful results are obtained in the updating process.