Helicopter rotor aeroelastic stability evaluation using Lyapunov Exponents

This work presents the application of Lyapunov Characteristic Exponents (LCEs), or in short Lyapunov Exponents, to the evaluation of rotorcraft aeroelastic stability. Current state of art literature on rotorcraft aeroelastic stability analysis approaches the problem by either using a constant coefficient approximation or by computing the eigenvalues of the monodromy matrix according to Floquet Theory. The former neglects periodicity and the latter is only applicable to the perturbation of the problem about a periodic orbit. Often such approximations are acceptable; however, LCEs can be applied to generic trajectories of non-linear systems to produce an estimate of the stability properties without the need to reach a steady orbit or determine the period of the system. Being more general, LCEs can provide a common environment in rotorcraft aeroelastic stability among both linear and non-linear systems, and be applicable to all problems that can be proficiently analyzed by time marching analysis, including experimental data. This work presents the evaluation of the stability of an isolated rotor formulated as a linear time-periodic system by computing the LCEs from arbitrary fiducial trajectories. The method is illustrated in relation with the problem of rigid helicopter blade flapping, and ground resonance with one damper inoperative and with non-linear dampers.