Tiltrotor whirl-flutter stability investigation using Lyapunov Characteristic Exponents and multibody dynamics

Abstract

This work discusses the use of Lyapunov Characteristic Exponents to assess the stability of nonlinear, time-dependent mechanical systems. Specific attention is dedicated to methods capable of estimating the largest exponent without requiring the Jacobian matrix of the problem, which can be applied to time histories resulting from existing multibody solvers. Tiltrotor whirl-flutter stability is analyzed. With respect to the available literature, the proposed method does not require the system to be strictly periodic, no linearization is required about a reference steady solution, and characteristic nonlinear aspects of stationary solutions like limit cycle oscillations are correctly identified and pointed out. A limitation lies in the ability to correctly identify the stability but no information is inferred about the related characteristic frequencies/periods, if any.