A new method of passive modifications for partial frequency assignment of general structures

The assignment of a subset of natural frequencies to vibrating systems can be conveniently achieved by means of suitable structural modifications. It has been observed that such an approach usually leads to the undesired change of the unassigned natural frequencies, which is a phenomenon known as frequency spill-over. Such an issue has been dealt with in the literature only in simple specific cases. In this paper, a new and general method is proposed that aims to assign a subset of natural frequencies with low spill-over. The optimal structural modifications are determined through a three-step procedure that considers both the prescribed eigenvalues and the feasibility constraints, assuring that the obtained solution is physically realizable. The proposed method is therefore applicable to very general vibrating systems, such as those obtained through the finite element method. The numerical difficulties that may occur as a result of employing the method are also carefully addressed. Finally, the capabilities of the method are validated in three test-cases in which both lumped and distributed parameters are modified to obtain the desired eigenvalues