Shifting Natural Frequencies of Mechanical Systems to Desired Values Using Frequency Response Functions

One of the important problems encountered in engineering structures is resonance. One way to avoid this situation is to shift the natural frequencies of the system out of the dangerous frequency zone. In this regard, the problem of shifting the natural frequencies of a system to the desired values is an important study subject. Shifting the natural frequencies of a system to other values can be achieved by changing the physical properties of this system, such as mass and stiffness. The problem is that there are changes that need to be made to shift the natural frequencies to the desired values. For this purpose, various methods have been developed using modal properties of the system or Frequency Response Functions (FRF). However, researchers are working to develop more effective and practically feasible methods. In this context, the purpose of this thesis is to develop an effective method for calculating the mass and spring changes that must be made on the system in order to shift a certain number of natural frequencies of a system to the desired values. For this purpose, a method has been developed by using the FRF's of the main system and by using the Sherman-Morrison (SM) formula known from the matrix theory. This method has been used in the literature to shift the natural frequencies of the system to desired values by adding only mass or only spring. However, in some cases, it is not possible to apply the changes obtained in practice, as there is no solution. In this study, different situations where mass and spring changes are made together are also considered. Thus, for example, in cases where mass change cannot be practiced, the problem can be solved by spring changes. On the other hand, in previous studies, the number of frequencies to be shifted and the number of changes were selected equally. Thus, equations are obtained as many as unknown numbers. In this study, the number of changes and the number of frequencies to be shifted were chosen differently, and less specific or excessively non-linear equation sets were obtained. By solving these equations numerically, necessary changes are obtained. The validity of the developed method has been demonstrated by numerical simulation studies on a five degrees of freedom (DOF) discrete system. An experimental model of the same system was made and applications were made for this system. Mass change, spring change, mass and spring change are considered together and very successful results are obtained. It has been shown that the method can also be used in real applications.