Stability Analysis of Complex Multibody Systems

The linearized stability analysis of dynamical systems modeled using finite element based multibody formulations is addressed in this paper. The use of classical methods for stability analysis of these system, such as the characteristic exponent method or Floquet theory, results in computationally prohibitive costs. Since comprehensive multibody models are “virtual prototypes” of actual systems, the applicability to numerical models of the stability analysis tools that are used in experimental settings is investigated in this work. Various experimental tools for stability analysis are reviewed. It is proved that Prony’s method, generally regarded as a curve fitting method, is equivalent, and sometimes identical, to Floquet theory and to the partial Floquet method. This observation gives Prony’s method a sound theoretical, footing, and considerably improves the robustness of its predictions when applied to comprehensive models of complex multibody system. Numerical applications are presented to demonstrate the efficiency of the proposed procedure.