TY - JOUR
T1 - Stability Analysis of Nonlinear Rotating Systems Using Lyapunov Characteristic Exponents Estimated From Multibody Dynamics
AU - Cassoni, Gianni
AU - Zanoni, Andrea
AU - Tamer, Aykut
AU - Masarati, Pierangelo
PY - 2023/8/1
Y1 - 2023/8/1
N2 - The use of Lyapunov Characteristic Exponents to assess the stability of nonlinear, time-dependent mechanical systems is discussed. 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 simulations performed with existing multibody solvers. Helicopter ground resonance is analyzed as the reference application. Improvements over the available literature are: the problem is formulated in physical coordinates, without eliminating periodicity through multiblade coordinates; the rotation of the blades is not linearized; the problem is modeled considering absolute positions and orientations of parts. The dynamic instability that arises at some angular velocities when the isotropy of the rotor is broken (e.g., caused by the failure of one lead-lag damper, a design test condition) is observed to evolve into a large amplitude limit cycle, where the usual Floquet-Lyapunov analysis of the linearized time-periodic simply predicts instability.
AB - The use of Lyapunov Characteristic Exponents to assess the stability of nonlinear, time-dependent mechanical systems is discussed. 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 simulations performed with existing multibody solvers. Helicopter ground resonance is analyzed as the reference application. Improvements over the available literature are: the problem is formulated in physical coordinates, without eliminating periodicity through multiblade coordinates; the rotation of the blades is not linearized; the problem is modeled considering absolute positions and orientations of parts. The dynamic instability that arises at some angular velocities when the isotropy of the rotor is broken (e.g., caused by the failure of one lead-lag damper, a design test condition) is observed to evolve into a large amplitude limit cycle, where the usual Floquet-Lyapunov analysis of the linearized time-periodic simply predicts instability.
UR - http://www.scopus.com/inward/record.url?scp=85159124803&partnerID=8YFLogxK
U2 - 10.1115/1.4056591
DO - 10.1115/1.4056591
M3 - Article
SN - 1555-1415
VL - 18
SP - 1
EP - 11
JO - Journal of Computational and Nonlinear Dynamics
JF - Journal of Computational and Nonlinear Dynamics
IS - 8
M1 - 081002
ER -