Maintaining Specific Natural Frequency of Damped System despite Mass Modification

Abstract

In aerospace engineering, structural modifications play an essential role in design of structures. In some cases, it is necessary to guarantee that a specific natural frequency of the structure remains unchanged when additional masses are attached. The methods based on the Sherman-Morrison formula are proposed in this paper, called the optimal selection method and the absolute value method, to maintain the specific natural frequency. The methods are both implemented by installing a spring on the system and can eliminate the effect of the additional mass on the specific frequency. The proposed methods were verified to be effective and accurate through numerical simulations. Results show that the optimal selection method has similar applicability as the existing real value method, and both methods are applicable only in cases of small damping. In addition, the absolute value method has extensive applicability in systems with either small or large damping.