Abstract

Airframe flexibility effects have typically been captured by modal reduction of the airframe. Although efficient, this model may still be prohibitively expensive for preliminary design studies. This paper employs time- and frequency-domain system identification techniques to form a multi-objective optimization (MOO) problem to identify equivalent transfer functions representing airframe flexibility effects. Pareto-optimal sets are first identified for an equivalent transfer function of a force element between the landing gear (LG) attachment point and the center of gravity (CG) of a 150-passenger regional jet, and a second transfer function from the input LG force to the cockpit acceleration. The reduced models demonstrate the ability to generally capture flexibility effects with reduced computation times. The combination of time-domain and frequency-domain information ensures the positive time-history matches while the model remains physically realizable as it is rooted to frequency response obtained from the finite element model (FEM). It is hypothesized that this physical link allowed the model to be robust to the landing initial conditions.

References

References
1.
International Civil Aviation Organization
,
2020
, “
Accident Statistics
,”
International Civil Aviation Organization
, Montreal, QC, Canada.
2.
Cook
,
F. E.
, and
Milwitzky
,
B.
,
1956
, “
Effect of Interaction of Landing-Gear Behavior and Dynamic Loads in a Flexible Airplane Structure
,” National Advisory Committee for Aeronautics, Langley Field, VA, Report No. NACA-TR-1278.
3.
Craig
,
R. R.
, and
Bampton
,
M. C.
,
1968
, “
Coupling of Substructures for Dynamic Analyses
,”
AIAA J.
,
6
(
7
), pp.
1313
1319
.10.2514/3.4741
4.
Pritchard
,
J.
,
2001
, “
Overview of Landing Gear Dynamics
,”
J. Aircr.
,
38
(
1
), pp.
130
137
.10.2514/2.2744
5.
Krüger
,
W. R.
, and
Morandini
,
M.
,
2011
, “
Recent Developments at the Numerical Simulation of Landing Gear Dynamics
,”
CEAS Aeronaut. J.
,
1
(
1–4
), pp.
55
68
.10.1007/s13272-011-0003-y
6.
Khapane
,
P. D.
,
2003
, “
Simulation of Asymmetric Landing and Typical Ground Maneuvers for Large Transport Aircraft
,”
Aerosp. Sci. Technol.
,
7
(
8
), pp.
611
619
.10.1016/S1270-9638(03)00066-X
7.
Bronstein
,
M.
,
Feldman
,
E.
,
Vescovini
,
R.
, and
Bisagni
,
C.
,
2015
, “
Assessment of Dynamic Effects on Aircraft Design Loads: The Landing Impact Case
,”
Prog. Aerosp. Sci.
,
78
, pp.
131
139
.10.1016/j.paerosci.2015.06.003
8.
Cumnuantip
,
S.
, and
Krüger
,
W.
,
2018
, “
Assessment of Dynamic Landing Loads by a Hybrid Multibody/Full Finite Element Simulation Approach
,”
Deutscher Luft- und Raumfahrtkongress 2018, Friedrichshafen, Germany, Sept. 4–6, Paper No. 480116.
9.
Ijff
,
J.
,
1972
, “
Analysis of Dynamic Aircraft Landing Loads, and a Proposal for Rational Design Landing Load Requirements
,” Ph.D. thesis,
Delft University of Technology
, Delft, The Netherlands.
10.
Castrichini
,
A.
,
Cooper
,
J. E.
,
Benoit
,
T.
, and
Lemmens
,
Y.
,
2017
, “
Gust and Ground Loads Integration for Aircraft Landing Loads Prediction
,”
J. Aircraft
, 55(1), pp.
184
194
.10.2514/1.c034369
11.
Allen
,
M. S.
,
2009
, “
Frequency-Domain Identification of Linear Time-Periodic Systems Using LTI Techniques
,”
ASME J. Comput. Nonlinear Dyn.
, 4(4), p.
041004
.10.1115/1.3187151
12.
Doranga
,
S.
, and
Wu
,
C. Q.
,
2016
, “
Nonlinear System Identification Technique for a Base-Excited Structure Based on Modal Space Formulation
,”
ASME J. Comput. Nonlinear Dyn.
,
11
(
6
), p.
061016
.10.1115/1.4034394
13.
Bittanti
,
S.
, and
Lovera
,
M.
,
1997
, “
Identification of Linear Models for a Flexible Structure
,”
IFAC Proc. Vol.
,
30
(
27
), pp.
123
127
.10.1016/S1474-6670(17)41168-2
14.
Balas
,
G.
, and
Doyle
,
J.
,
1990
, “
Identification of Flexible Structures for Robust Control
,”
IEEE Control Syst. Mag.
,
10
(
4
), pp.
51
58
.10.1109/37.56278
15.
Lew
,
J. S.
,
Juang
,
J. N.
, and
Longman
,
R. W.
,
1993
, “
Comparison of Several System Identification Methods for Flexible Structures
,”
J. Sound Vib.
,
167
(
3
), pp.
461
480
.10.1006/jsvi.1993.1348
16.
Estes
,
A.
,
Majji
,
M.
, and
Juang
,
J.-N.
,
2014
, “
Time-Varying Methods for Identification of Constrained Flexible Structures
,”
AIAA
Paper No. 2014–4305.10.2514/6.2014-4305
17.
Vanpaemel
,
S.
,
Naets
,
F.
,
Vermaut
,
M.
, and
Desmet
,
W.
,
2020
, “
Parameter Identification on Flexible Multibody Models Using the Adjoint Variable Method and Flexible Natural Coordinate Formulation
,”
ASME J. Comput. Nonlinear Dyn.
,
15
(
7
), p.
071006
.10.1115/1.4047086
18.
de Abreu
,
G. L. C. M.
,
da Conceição
,
S. M.
,
Lopes
,
V.
, Jr.
,
Brennan
,
M. J.
, and
Alves
,
M. T. S.
,
2012
, “
System Identification and Active Vibration Control of a Flexible Structure
,”
J. Braz. Soc. Mech. Sci. Eng.
,
34
, pp.
386
392
.10.1590/S1678-58782012000500007
19.
Chierichetti
,
M.
,
2014
, “
Load and Response Identification for a Nonlinear Flexible Structure Subject to Harmonic Loads
,”
ASME J. Comput. Nonlinear Dyn.
,
9
(
1
), p.
011009
.10.1115/1.4025505
20.
Giordano
,
B.
, and
Silva
,
O.
,
2011
, “
Data Gathering and Preliminary Results of the System Identification of a Flexible Aircraft Model
,”
AIAA
Paper No. 2011–6355. 10.2514/6.2011-6355
21.
Stachiw
,
T.
,
2020
, “
Synthesis and Optimization of Mechanical Networks With Inverters in Landing Gear for Improved Landing Performance and Vibration Control at Touchdown Considering Airframe Flexibility
,”
Master of Applied Science
,
Carleton University
,
Ottawa, ON, Canada
.https://curve.carleton.ca/71301035-1fb0-4ccf-8861-4dfa1c46a8d6
22.
Federal Aviation Administration, and Department of Transportation
,
2020
, “Part 25—Airworthiness Standards: Transport Category Airplanes,”
Federal Aviation Administration, and Department of Transportation
, Washington, DC.
23.
Fiala
,
E.
,
1954
, “
Seitenkraften Am Rollenden Luftreifen
,”
VDI
,
96
, pp.
973
979
.
24.
Daugherty
,
R. H.
,
2003
, “
A Study of the Mechanical Properties of Modern Radial Aircraft Tires
,” National Aeronautics and Space Administration, Hampton, VA, Report No. NASA/TM-2003-212415.
25.
Lanczos
,
C.
,
1950
, “
An Iteration Method for the Solution of the Eigenvalue Problem of Linear Differential and Integral Operators
,”
J. Res. Natl. Bur. Stand.
,
45
(
4
), p.
255
.10.6028/jres.045.026
26.
Marler
,
R. T.
, and
Arora
,
J. S.
,
2004
, “
Survey of Multi-Objective Optimization Methods for Engineering
,”
Struct. Multidiscip. Optim.
,
26
(
6
), pp.
369
395
.10.1007/s00158-003-0368-6
27.
Allemang
,
D. R. J.
, and
Brown
,
D. D. L.
,
1987
, “
Experimental Modal Analysis and Dynamic Component Synthesis
,” Air Force Wright Aeronautical Laboratories, Wright-Patterson Air Force Base, Report No. AFWAL-TR-87-3069.
28.
Byrd
,
R. H.
,
Gilbert
,
J. C.
, and
Nocedal
,
J.
,
2000
, “
A Trust Region Method Based on Interior Point Techniques for Nonlinear Programming
,”
Math. Program., Ser. B
,
89
(
1
), pp.
149
185
.10.1007/PL00011391
29.
Audet
,
C.
, and
Dennis
,
J. E.
,
2002
, “
Analysis of Generalized Pattern Searches
,”
SIAM J. Optim.
,
13
(
3
), pp.
889
903
.10.1137/S1052623400378742
30.
Custódio
,
A. L.
,
Madeira
,
J. F.
,
Vaz
,
A. I.
, and
Vicente
,
L. N.
,
2011
, “
Direct Multisearch for Multiobjective Optimization
,”
SIAM J. Optim.
,
21
(
3
), pp.
1109
1140
.10.1137/10079731X
31.
Deb
,
K.
,
2001
,
Multi-Objective Optimization Using Evolutionary Algorithms
,
Wiley
, Chichester, UK.
32.
Ghiringhelli
,
G.
, and
Boschetto
,
M.
,
1990
, “
Design Landing Loads Evaluation by Dynamic Simulation of Flexible Aircraft
,” Landing Gear Design Loads Conference, Povoa de Varzim, Portugal, Oct. 8–12, AGARD CP-484, N. 16, pp. 16.1–16.22.
You do not currently have access to this content.