Mass and stiffness modifications without changing any specified natural frequency of a structure

Abstract

The dynamic properties of an existing structure are altered when the mass and stiffness properties of the structure are modified. In some cases it can be desired that a specific natural frequency of the structure should not change after modifications. In case of adding a number of masses on the structure, one of the pre-specified natural frequencies can be preserved by attaching a grounded spring on it. In the present study, a new method is developed based on the Sherman-Morrison formula in order to determine the necessary spring coefficient. The performance of the developed method for damped structures is also investigated. Furthermore, an approach based on minimization of the described objective function is introduced for prediction of the best spring location.