Modal Derivatives for Efficient Vibration Prediction of Geometrically Nonlinear Structures with Friction Contact

Abstract

This paper evaluates the performance of the Rubin reduction methods, enhanced with static modal derivatives, for vibration analysis of geometrically nonlinear structures with friction contact. Static modal derivatives are computed numerically based on Rubin reduction, which includes free interface normal modes and residual flexibility attachment modes, by introducing a finite displacement around these modes. Then, the most relevant static modal derivatives are selected using an improved strategy that incorporates weighting factors derived from both a nonlinear static analysis and a geometrically linear transient run. This enhanced Rubin method is also compared with the previously used enhanced Craig–Bampton method, which is based on fixed normal modes, constraint modes, and their static derivatives. The effectiveness of these methods is demonstrated through vibration analysis of a geometrically nonlinear beam in different contact configurations. Both methods proved their robustness, achieving accurate results with a relatively small number of modes in the reduced space, thus ensuring low online computation times. Furthermore, the analyses show the significant impact of using a geometrically nonlinear model on the accurate prediction of a contact state.