| Due to increased available computer power, the analysis of nonlinear flexible multi-body systems, fixed-wing aircraft and rotary-wing vehicles is relying on increasingly complex, large scale models. An important aspect of the dynamic response of flexible multi-body systems is the potential presence of instabilities. Stability analysis is typically performed on simplified models with the smallest number of degrees of freedom required to capture the physical phenomena that cause the instability. The system stability boundaries are then evaluated using the characteristic exponent method or Floquet theory for systems with constant or periodic coefficients, respectively. As the number of degrees of freedom used to represent the system increases, these methods become increasingly cumbersome, and quickly unmanageable. In this work, a novel approach is proposed, the Implicit Floquet Analysis, which evaluates the largest eigenvalues of the transition matrix using the Arnoldi algorithm, without the explicit computation of this matrix. This method is far more computationally efficient than the classical approach and is ideally suited for systems involving a large number of degrees of freedom. The proposed approach is conveniently implemented as a postprocessing step to any existing simulation tool. The application of the method to a geometrically nonlinear multi-body dynamics code is presented. This work also focuses on the implementation of trimming algorithms and the development of tools for the graphical representation of numerical simulations and stability information for multi-body systems. |
