Understanding Floquet frequency indeterminacy in time-periodic systems: Application to anisotropic helicopter ground resonance
Abstract
While Floquet-Lyapunov theory provides a robust mathematical framework for analysing the stability of linear systems with periodic coefficients, it inherently suffers from frequency indeterminacy due to the multiplicity of mode harmonics. To understand this ambiguity, this article introduces the harmonic continuation method, a computational approach that bridges continuous modal tracking and periodic eigenvector analysis. To demonstrate its broad theoretical applicability, the proposed method is first validated against the canonical Mathieu equation and subsequently extended to capture the local dynamics of a weakly non-linear Duffing oscillator, effectively mapping its perturbation harmonics continuously across fold bifurcations. The methodology is then applied to complex, multidimensional rotordynamics, specifically an asymmetric Jeffcott rotor and an anisotropic helicopter ground resonance model. By successfully exhibiting the spectral content of these systems, the proposed approach highlights how severe structural anisotropy and critical faults-such as the loss of a lead-lag damper-trigger complex parametric resonances, thereby offering a comprehensive, continuous frequency analysis tool for modal analysis of time-periodic systems.
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BibTeX
@article{golleville2026understanding,
title = {{Understanding Floquet frequency indeterminacy in time-periodic systems: Application to anisotropic helicopter ground resonance}},
author = {Paul Pinel de Golleville and Benjamin Chouvion and Rémi Coisnon and Jérôme Montagny and Paul Cranga and Olivier Montagnier},
journal = {Journal of Sound and Vibration},
year = {2026},
month = oct,
doi = {10.1016/j.jsv.2026.120198},
url = {https://hal.science/hal-05825872v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - Understanding Floquet frequency indeterminacy in time-periodic systems: Application to anisotropic helicopter ground resonance
AU - Paul Pinel de Golleville
AU - Benjamin Chouvion
AU - Rémi Coisnon
AU - Jérôme Montagny
AU - Paul Cranga
AU - Olivier Montagnier
PY - 2026
DA - 2026/10/20
JO - Journal of Sound and Vibration
DO - 10.1016/j.jsv.2026.120198
UR - https://hal.science/hal-05825872v1
AB - While Floquet-Lyapunov theory provides a robust mathematical framework for analysing the stability of linear systems with periodic coefficients, it inherently suffers from frequency indeterminacy due to the multiplicity of mode harmonics. To understand this ambiguity, this article introduces the harmonic continuation method, a computational approach that bridges continuous modal tracking and periodic eigenvector analysis. To demonstrate its broad theoretical applicability, the proposed method is first validated against the canonical Mathieu equation and subsequently extended to capture the local dynamics of a weakly non-linear Duffing oscillator, effectively mapping its perturbation harmonics continuously across fold bifurcations. The methodology is then applied to complex, multidimensional rotordynamics, specifically an asymmetric Jeffcott rotor and an anisotropic helicopter ground resonance model. By successfully exhibiting the spectral content of these systems, the proposed approach highlights how severe structural anisotropy and critical faults-such as the loss of a lead-lag damper-trigger complex parametric resonances, thereby offering a comprehensive, continuous frequency analysis tool for modal analysis of time-periodic systems.
SN - 0022-460X
SN - 1095-8568
ER -