A simple method for designing structural models with closely spaced modes of vibration

Vehicle structures often have closely spaced modes of vibration within the frequency spectrum of applied loads. Such modes are important since they tend to be the source of vibration problems. In order to study the effects that closely spaced modes have on structural response in such situations as modal testing and self-excited vibrations, it is useful to be able to design a mathematical structural model having closely spaced modes. In this paper, a method for designing such a model is presented and illustrated with examples. Given a reference model with specified geometry and degrees of freedom, the lumped inertias and stiffnesses of the model are perturbed in such a manner as to force together two of its natural frequencies. With a slight alteration, the method is also applicable to the inverse problem of separating undesirable closely spaced modes which appear in a structural design.