Abstract
This report presents a comprehensive analysis of the flap mode stability for a two-bladed teetering rotor using Floquet theory, focusing on the parameter space defined by the advance ratio (μ) and lock number (𝛾𝛾). The study employs numerical integration to compute the monodromy matrix and Floquet multipliers over a grid of μ from 0 to 3.0 and γ from 0 to 20. Key findings include distinct regions of instability where the maximum magnitude of the Floquet multipliers (|ρ|_{\max}) exceeds 1, primarily at higher μ values. Instability boundaries are identified, revealing two primary unstable lobes: one at lower 𝛾𝛾 (approximately 1.0–12.0) starting around μ ≈ 1.5, and another at higher 𝛾𝛾 (≥14) with onset at progressively lower μ (decreasing from ≈2.9 to 2.6). Eigenvalues are predominantly real in unstable regions and complex in stable ones, consistent with divergencetype instabilities.
Document Type
Final Report
Class Name
Mechanical Engineering and Material Sciences Independent Study
Date of Submission
12-2-2025
Recommended Citation
Cachero, Jose T., "The Floquet Stability of Two-Bladed Teetering Rotors in Forward Flight" (2025). Mechanical Engineering and Materials Science Independent Study. 317.
https://openscholarship.wustl.edu/mems500/317