ABSTRACT
In many problems of the vibration of structural or mechanical systems, the quantity of primary interest is the predominant frequency of vibration. When the system has only one degree of freedom, the frequency of vibration is easily determined by the methods described in earlier chapters. Very often, however, the system under consideration is in fact a multi-degree-of-freedom system. Frequency determination of such systems is complex and time consuming. On the other hand, if a reasonable estimate can be made of the vibration shape, the system can be represented by an equivalent single-degreeof-freedom model whose frequency of vibration is more easily determined. Because we cannot expect the estimated vibration shape to be the same as the true vibration shape, the frequency determined by this method is in error. The practical utility of the method, however, lies in the fact that even with a crude estimate of the vibration shape, the error in the calculated frequency is generally small enough so that the frequency estimate is acceptable for all practical purposes.
