Generalized Quantitative Stability Analysis of Time-Dependent Comprehensive Rotorcraft Systems
Abstract
:1. Introduction
- alternating loads that excite the fuselage, and
- alternating system properties leading to a time-dependent system.
2. Method
2.1. Lyapunov Characteristic Exponents
- First, the time response of the system converges to zero, which happens when all eigenvalues have a negative real part.
- Second, the system responds in a divergent manner when some eigenvalues have a positive real part.
- Third, a periodic orbit can be the resulting motion in the presence of purely imaginary eigenvalues.
2.2. Application to LTP Problems
2.3. Numerical Estimation of LCEs
2.4. Computation of State Transition Matrix
2.5. Analytical Sensitivity of LCEs
2.5.1. Sensitivity of QR Decomposition
2.5.2. Sensitivity of the State Transition Matrix
3. Numerical Results
3.1. Verification with an Analytical Solution
3.2. Complex LTP Rotorcraft Model
3.2.1. Model Description
- all six rigid body modes (Fore/Aft, Lateral, Plunge, Roll, Pitch, and Yaw);
- flight mechanics derivatives of the fuselage determined by fuselage/wing-body, horizontal tail, and the vertical tail;
- ten elastic airframe modes captured at airframe and connection locations (such as airframe rotor connection); additionally, % modal damping was also added;
- three bending modes of the rotor in multiblade coordinates, formulated using a linerazized finite volume approach [26];
- three main rotor servo-actuators modelled as transfer function from the force applied by controls () and requested displacement () to the servoactuator displacement (), namely ;
- lead-lag dampers for the main rotor blades.
3.2.2. Analysis
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
Abbreviations
LCE | Lyapunov Characteristic Exponents |
LTI | Linear, Time-Invariant |
LTP | Linear, Time-Periodic |
LTV | Linear, Time-Variant |
STM | State Transition Matrix |
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Parameter | Value | Units |
---|---|---|
Helicopter | ||
Gross Weight | 7400 | kg |
Max Speed | 140 | kn |
Main Rotor | ||
Number of blades | 4 | |
Radius | 7.49 | m |
Solidity | 0.0913 | (n.d.) |
Lock number | 8.70 | (n.d.) |
Speed | 270 | rpm |
Flap frequency | 1.03 | /rev |
Lag Frequency | 0.26 | /rev |
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Tamer, A.; Masarati, P. Generalized Quantitative Stability Analysis of Time-Dependent Comprehensive Rotorcraft Systems. Aerospace 2022, 9, 10. https://doi.org/10.3390/aerospace9010010
Tamer A, Masarati P. Generalized Quantitative Stability Analysis of Time-Dependent Comprehensive Rotorcraft Systems. Aerospace. 2022; 9(1):10. https://doi.org/10.3390/aerospace9010010
Chicago/Turabian StyleTamer, Aykut, and Pierangelo Masarati. 2022. "Generalized Quantitative Stability Analysis of Time-Dependent Comprehensive Rotorcraft Systems" Aerospace 9, no. 1: 10. https://doi.org/10.3390/aerospace9010010