| All real vibrating systems are nonlinear; however, nonlinear behaviors are not always observed in the system dynamics. Input types and levels, boundary conditions, and other characteristics of the experimental environment determine whether or not the nonlinearities surface during testing. Traditional techniques for characterizing nonlinear vibrating systems and identifying models of these systems are temporal in nature. Although these techniques work well in single degree of freedom and/or single input, single output applications, they are not generally applicable to multiple degree of freedom systems and/or multiple input, multiple output applications with multiple nonlinearities because they only use temporal data, which contains coupled linear and nonlinear dynamics. A new spatial approach is used in the research here to derive new and powerful characterization and identification methods for nonlinear vibrating systems. The premise is that models of nonlinear systems should describe the dynamics as a function of time, frequency, and space. By utilizing spatial data, the new techniques decouple the linear and nonlinear vibrations. It is demonstrated through experimental verification that the new techniques can be used to analyze complicated nonlinear vibrating systems.; The dissertation begins by reviewing many behaviors of nonlinear vibrating systems and the experimental issues with testing nonlinear systems. Then a comprehensive theoretical and applied database of the traditional temporal nonlinear analysis techniques is given. Next, the importance of spatial data is discussed and new nonlinear vibration analysis techniques are derived. The techniques are then applied to characterize and identify complicated nonlinear systems with many different types of nonlinearities. Finally, the research is summarized and suggestions and plans for future research in this area are given. |
