A method for shifting natural frequencies of a dynamic system to desired values with concentrated mass modifications

In this study, shifting a certain number of natural frequencies of a dynamic system to the desired values with the concentrated mass modifications is considered. A new method is proposed in order to determine the necessary mass modifications. The method proposed is based on the Sherman-Morrison formula and uses the receptances that are related to the modification coordinates of the original system. The system is sequentially modified at the predefined locations by a number of unknown masses which equal the number of frequencies that will be shifted. The method yields a set of nonlinear equations which equal the number of shifting frequencies, then the necessary masses are estimated by solving these equations numerically. The efficiency of the proposed method is shown by various numerical and experimental applications. It is shown that the method is very effective and can be used for real applications.