Performance and Robustness of Nonlinear Systems Using Bifurcation Analysis

Nonlinear vibrations can be frequently encountered in engineering applications, and take their origin from different sources including contact, friction or large displacements. Other manifestations of nonlinearities are peculiar phenomena such as amplitude jumps, quasi-periodic oscillations and isolated response curves. These phenomena are closely related to the presence of bifurcations in the frequency response, which dictate the system's dynamics. While recent progress has been achieved to develop tools for nonlinear modal analysis of industrial applications, bifurcation analysis was still limited to reduced models and academic case studies. Along with the lack of an efficient algorithm to detect and study bifurcations, bifurcation analysis for design purposes also remained unexplored.

The fundamental contribution of this doctoral thesis is the development of a new methodology for the detection, characterization and tracking of bifurcations of large-scale mechanical systems. To this end, an extension of the harmonic balance (HB) method is proposed. Taking advantage of the efficiency of the HB method for the continuation of nonlinear normal modes and frequency responses, this extension allows for robust computation of bifurcation curves in the system's parameter space. A validation of the methodology is performed on the strongly nonlinear model of an Airbus Defence & Space spacecraft, which possesses an impact-type nonlinear device consisting of multiple mechanical stops limiting the motion of an inertia wheel mounted on an elastomeric interface.

The second main contribution is the development of a new vibration absorber, the nonlinear tuned vibration absorber (NLTVA), which generalizes Den Hartog's equal-peak method to nonlinear systems. The absorber is demonstrated to exhibit unprecedented performance for the mitigation of nonlinear resonances. In a second step, the HB-based bifurcation methodology is utilized to characterize the performance regions of the NLTVA, and to ensure its robustness with respect to parameter uncertainties.