Case Studies on the Use of Two and Three Degree of Freedom Models to Understand Fundamental Vibration Behavior of Complex Systems

Mathematical models of simple two and three degree of freedom vibrating systems are beneficial to ease understanding of a complex system by providing an opportunity to readily identify the effect of one degree of freedom on another. When dealing with short timelines in industry, simple models provide the opportunity to quickly develop potential solutions to excessive vibration issues or understand unexpected results. Simple models are not always appropriate and may have significant uncertainties but such an option may still add value when compared to the time and effort required to develop larger, detailed models. This paper presents two cases regarding the use of simple models to develop understanding of a complex system. In each case, the focus is on the insights that can be gained from a simple model rather than the detailed calculations and calibrations necessary to ensure its complete accuracy. Case 1 employs a two degree of freedom system to relate how an experimental modal test of an engine component can be affected by the base structure on which it is mounted. This study directly relates to the experimental modal testing of large engine components which are tested both in laboratories and on engines. Two charts are presented to evaluate the error of a measured natural frequency as a function of both the mass and natural frequency of the component to be tested and the base structure. Case 2 utilizes a three degree of freedom system built in a commercial finite element analysis (FEA) code and solved via a multi-disciplinary optimizer to determine the ideal parameters of a vibration absorber to effect the greatest possible reduction in vibration levels of a component. The lessons learned from this study are applicable to developing a vibration absorber to be installed on an engine component that is being excited by global modes of a generator set. Both cases display the significant lessons that can be learned from extremely simple systems.