Abstract
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.
Highlights
Shifting the natural frequency of a system is an important issue in the structural modification
The motivation of this paper can be clarified as follows: to develop a method for shifting the natural frequencies of a system to the desired values by the mass modifications, which uses measured frequency response function (FRF) of the original system without needing the physical or modal parameters; to advance Sherman-Morrison (SM) formula [20], for the inverse structural modification aim, which is successfully used for the solution of various structural modification problems in the past
This paper focuses on the shifting of a certain number of natural frequencies of a dynamic system to desired values with the concentrated mass modifications
Summary
Shifting the natural frequency of a system is an important issue in the structural modification. Sivan and Ram [5] developed a method for determining mass and stiffness modifications to achieve desired natural frequencies by using modal analysis. The suggested method was applied to estimation of spring stiffness values in a spring supported plate Li and He [7] proposed a method based upon use of FRF data in order to determine mass and stiffness modifications of an undamped structural system that are needed to change the dynamic characteristics of the system. Their approach formulates the structural modification problem using a set of linear equations.
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