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During the design and development process of complex technical systems like buildings, aircraft, spacecraft and engines the analysis of the dynamics and vibrations is an important task. The dynamic analysis requires computational models which need to be setup with adequate methods and have to be validated by experiments e.g. on components or prototypes of the structures. In the dynamic analyses also nonlinear effects have to be taken into account. Thus, the experimental validation of computational models has to be able to identify, characterize and quantify nonlinearities.   Equations of motion for structures:  The discretization and modeling of complex structures is briefly described. The linear basic dynamic equations are setup and discussed. The solutions for dynamic vibrations are derived in modal coordinates and are explained. The occurrence of typical nonlinearities is described and the nonlinear equations as well as the finding of solutions are derived and discussed.   Dynamic identification and modal analysis:  The modal identification of complex technical structures is explained. A concept, suitable for the identification and characterization of typical nonlinearities, is described. The concept consists in dividing the occurring nonlinearities in different groups and using different identification methods.   Nonlinear modal identification:  The basic equations for the nonlinear modal identification are derived and discussed in general. Single mode identification In the following, the case of single mode identification is considered in detail and the required steps are described.   Coupled mode identification:  Next, the coupled mode identification is explained. Both identification types are illustrated by applying them to an analytical vibration system with a low number of degrees of freedom.   Application to a real structure:  The modal identification as wells as the detection, characterization and quantification of nonlinearities in practice is shown by applying the methods to an aerospace structure.

Non-Linearity in Structural Dynamics and Experimental Modal Analysis