<p>A design method of a strongly coupled vibration system is required for improving noise and vibration performance of machinery. One of the authors proposed that analysis of the self-compliance matrix at interface degrees of freedom between two systems, called as kernel compliance matrix, gives the insight to work out satisfactory countermeasures for resonance frequency control of a strongly coupled vibration system. The approach, however, is only feasible for a two by two kernel compliance matrix. To expand this approach to an N by N kernel compliance matrix, a coordinate transform is available to reduce the matrix dimensions. However, the selection of the basis vector is not so easy. This paper presents a practical approach for the analysis of an N by N kernel compliance matrix. In this paper, it is shown that structural modification for resonance control can be derived using the Wedderburn's rank-one perturbation of a kernel compliance matrix. Finally, this approach was verified by a numerical case study.</p>