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American Institute of Aeronautics and Astronautics
1
Integrated Structural, Flight Dynamics and Aeroelastic
Analysis of the ANCE X-3d as a Flexible Body
Luis A. Hernández1
Universidad Simón Bolívar, Caracas, Miranda, 1080-A, Venezuela
Pedro J. Boschetti2
Universidad Simón Bolívar, Naiguatá, Vargas, 1160, Venezuela
and
Pedro J. González3
Instituto Tecnológico de Aeronáutica, São José Dos Campos, SP, 12228-900, Brazil
The objective of this paper is to generate simplified structural configurations for the ANCE
X-3d by considering the influence of structural flexibility on the flight dynamic characteristics
and the aeroelastic phenomena. This aircraft consists of an unswept wing with double tail
boom structure and two vertical stabilizers. Two structures were designed by an analytical
approach and finite element models to create suitable structural arrangements for the wing,
tail booms, and stabilizers, and carbon-fiber composite materials were selected for this
purpose. Knowing the stiffness and mass properties of the main structural components,
reduced order aero-structural models were developed to quantify the influence of the
flexibility on the aircraft aerodynamics and stability characteristics. Flight dynamic
evaluation of the airplane considering the flexibility of the structure was performed at
different velocities and altitudes. The resultant flutter and divergence velocities fulfill the
design criteria.
Nomenclature
Ak = circulation Fourier mode coefficients
CD0 = minimum drag coefficient
CL0, CM0 = lift and pitching moment coefficients at zero angle of attack
CLq, CDq, CMq = variation of lift, drag, and pitching moment coefficients with pitch rate
CLα, CDα, CMα = lift, drag, and pitching moment slopes
CYβ, Cℓβ, Cnβ = variation of side force, rolling, yawing coefficients with sideslip angle
CYp, Cℓp, Cnp = variation of side force, rolling, yawing coefficients with roll rate
CYr, Cℓr, Cnr = variation of side force, rolling, yawing coefficients with yaw rate
D = control state vector
E = control error-integral vector
E = young modulus, Pa
EI = bending stiffness, Nm2
iF = beam force-stress resultant
JF = global beam force-stress resultant
G = shear modulus, Pa
GJ = torsional stiffness, Nm2
h0 = stick fixed neutral point
k = lift dependent drag factor or induced drag factor
1 Undergraduate student, Program in Mechanical Engineering, Sartenejas Valley. 2 Associate Professor, Department of Industrial Technology, Camurí Grande Valley, Senior Member AIAA. 3 PhD Candidate, Aerospace Engineering Division, São José dos Campos, Member AIAA.
Roll Real -16.946 -20.309 -58.223 16.56% 70.89% 186.68%
Spiral Real 0.01353 0.01213 0.01228 11.51% 10.18% 1.21%
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Figure 9. Eigenvalues obtained at Carson speed (45 m/s) at sea level.
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
-6 -5 -4 -3 -2 -1 0
Imag
inar
y p
art
Real part
Dutch Roll Rigid
Dutch Roll D1
Dutch Roll D2
Short Period Rigid
Short Period D1
Short Period D2
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
-0.03 -0.02 -0.01 0 0.01 0.02
Imag
inar
y p
art
Real part
Phugoid Rigid
Phugoid D1
Phugoid D2
Spiral rigid
Spiral D1
Spiral D2
Figure 10. Eigenvalues obtained at Carson speed (51 m/s) in cruise altitude (2438 m).
-13
-11
-9
-7
-5
-3
-1
1
3
5
7
9
11
13
-6 -5 -4 -3 -2 -1 0
Imag
inar
y p
art
Real part
Dutch Roll Rigid
Dutch Roll D1
Dutch Roll D2
Short Period Rigid
Short Period D1
Short Period D2
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
-0.03 -0.02 -0.01 0 0.01 0.02
Imag
inar
y p
art
Real part
Phugoid Rigid
Phugoid D1
Phugoid D2
Spiral rigid
Spiral D1
Spiral D2Dow
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Figure 11. Variation of Dutch roll eigenvalues with velocity at sea level (left) and cruise altitude (right).
0
2
4
6
8
10
12
14
16
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0
Imag
inar
y p
art
Real part
B.H Rigid
B.H Flexible D1
B.H Flexible D2
0
2
4
6
8
10
12
14
16
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0
Imag
inar
y p
art
Real part
B.H Rigid
B.H Flexible D1
B.H Flexible D2
Figure 12. Variation of short period eigenvalues with velocity for sea level (left) and cruise altitude (right).
0
5
10
15
20
25
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
Imag
inar
y p
art
Real part
S.P Rigid
S.P Flexible D1
S.P Flexible D2
0
2
4
6
8
10
12
14
16
18
20
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
Imag
inar
y p
art
Real part
S.P Rigid
S.P Flexible D1
S.P Flexible D2
Figure 13. Variation of phugoid eigenvalues with velocity at sea level (left) and cruise altitude (right).
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
-0.05 -0.04 -0.03 -0.02 -0.01 0.00
Imag
inar
y p
art
Real part
Phugoid Rigid
Phugoid D1
Phugoid Flexible D20.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
-0.06 -0.05 -0.04 -0.03 -0.02 -0.01
Imag
inar
y p
art
Real part
Phugoid Rigid
Phugoid D1
Phugoid Flexible D2
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Figure 14. Root-Locus of Dutch roll, short period and phugoid with velocity at sea level for the first structure
(D1).
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
-6 -5 -4 -3 -2 -1 0
Imag
inar
y p
art
Real Part
26 m/s
36 m/s
46 m/s
56 m/s
66 m/s
76 m/s
86 m/s
96 m/s
Dutch
Short period
-0.40
-0.35
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
-0.10 -0.08 -0.06 -0.04 -0.02 0.00
Imag
inar
y p
art
Real part
26 m/s
36 m/s
46 m/s
56 m/s
66 m/s
76 m/s
86 m/s
96 m/s
Phugoid
Figure 15. Root-Locus of Dutch roll, short period and phugoid with velocity at sea level for the second structure
(D2).
-25
-20
-15
-10
-5
0
5
10
15
20
25
-6 -5 -4 -3 -2 -1 0
Imag
inar
y p
art
Real part
26 m/s36 m/s46 m/s56 m/s66 m/s76 m/s86 m/s
Dutch roll
Short period
-0.40
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
-0.08 -0.06 -0.04 -0.02 0.00
Imag
inar
y p
art
Real part
26 m/s
36 m/s
46 m/s
56 m/s
66 m/s
76 m/s
86 m/s
96 m/s
Phugoid
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Figure 16. Root-Locus of Dutch roll, short period and phugoid with velocity for cruise altitude for the first
structure (D1).
-12
-7
-2
3
8
-5 -4 -3 -2 -1 0
Imag
inar
y p
art
Real part
30 m/s
40 m/s
50 m/s
60 m/s
70 m/s
80 m/s
90 m/s
Short period
Dutch roll
-0.40
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
-0.10 -0.08 -0.06 -0.04 -0.02 0.00Im
agin
ary p
art
Real part
30 m/s
40 m/s
50 m/s
60 m/s
70 m/s
80 m/s
90 m/s
Phugoid
Figure 17. Root-Locus of Dutch roll, short period and phugoid with velocity for cruise altitude for the second
structure (D2).
-25
-20
-15
-10
-5
0
5
10
15
20
25
-6 -5 -4 -3 -2 -1 0
Imag
inar
y p
art
Real part
30 m/s 40 m/s
50 m/s 60 m/s
70 m/s 80 m/s
90 m/s 100 m/s
Dutch roll
Short period
-0.40
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
-0.08 -0.06 -0.04 -0.02 0.00
Imag
inar
y p
art
Real part
30 m/s
40 m/s
50 m/s
60 m/s
70 m/s
80 m/s
90 m/s
100 m/s
Phugoid
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Figure 18. Dutch roll damping as a function of velocity at sea level (left) and cruise altitude (right).
-0.99
-0.97
-0.95
-0.93
-0.91
-0.89
-0.87
-0.85
20 40 60 80 100
Rea
l p
art
Velocity, m/s
Dutch Roll D1
Dutch Roll D2
-1.00
-0.98
-0.96
-0.94
-0.92
-0.90
-0.88
20 40 60 80 100
Rea
l p
art
Velocity, m/s
Dutch Roll D1
Dutch Roll D2
Figure 19. Short period damping with velocity at sea level (left) and cruise altitude (right).
-0.98
-0.96
-0.94
-0.92
-0.90
-0.88
-0.86
-0.84
-0.82
20 40 60 80 100
Rea
l p
art
Velocity, m/s
Short Period D1
Short Period D2
-1.00
-0.98
-0.96
-0.94
-0.92
-0.90
-0.88
-0.86
-0.84
-0.82
20 40 60 80 100
Rea
l p
art
Velocity, m/s
Short Period D1
Short Period D2
Figure 20. Phugoid damping with velocity at sea level (left) and cruise altitude (right).
-1.000
-0.998
-0.996
-0.994
-0.992
-0.990
-0.988
25 35 45 55 65 75 85
Rea
l p
art
Velocity, m/s
Phugoid D1
Phugoid D2
-1.000
-0.998
-0.996
-0.994
-0.992
-0.990
35 45 55 65 75 85
Rea
l p
art
Velocity, m/s
Phugoid D1
Phugoid D2Dow
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Figure 21. Root-locus as a function of velocity at sea level for the first structure (D1).
S.P, D.R, phugoid
0
25
50
75
100
125
150
175
200
-50 -40 -30 -20 -10 0
Imag
inar
y p
art
Real part
26 m/s
36 m/s
46 m/s
56 m/s
66 m/s
76 m/s
86 m/s
96 m/s
Wing asymmetric
torsion
Tailboom symmetric
bending
Unstable
40
42
44
46
48
50
52
54
56
-12 -8 -4 0 4 8 12
Imag
inar
y p
art
Real part
26 m/s
36 m/s
46 m/s
56 m/s
66 m/s
76 m/s
86 m/s
96 m/s
Figure 22. Damping as a function of velocity at sea level for the first structure (D1).
-10
-8
-6
-4
-2
0
2
4
0 10 20 30 40 50 60 70 80 90 100
Dam
pin
g,
s-1
Velocity, m/s
Tailboom symmetric bending
Wing asymmetric torsion
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Figure 23. Root-locus as a function of velocity for cruise altitude for the first structure (D1).
S.P, D.R, phugoid
0
25
50
75
100
125
150
175
200
-50 -40 -30 -20 -10 0 10
Imag
inar
y p
art
Real part
30 m/s
40 m/s
50 m/s
60 m/s
70 m/s
80 m/s
90 m/s
Wing asymmetric
torsion
Tailboom symmetric
bending
Unstable
40
42
44
46
48
50
52
54
56
-12 -8 -4 0 4 8 12
Imag
inar
y p
art
Real part
30 m/s
40 m/s
50 m/s
60 m/s
70 m/s
80 m/s
90 m/s
Figure 24. Damping as a function of velocity for cruise level for the first structure (D1).
-15
-10
-5
0
5
10
0 10 20 30 40 50 60 70 80 90 100
Dam
pin
g,
s-1
Velocity, m/s
Tailboom symmetric bending
Wing asymmetric torsion
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Figure 25. Root-locus as a function of velocity at service ceiling for the first structure (D1).
0
25
50
75
100
125
150
175
200
-125 -100 -75 -50 -25 0 25 50
Imag
inar
y p
art
Real part
47 m/s
57 m/s
67 m/s
77 m/s
87 m/s
97 m/s
107 m/s
Tailboom symmetric
bending
Wing asymmetric
torsion
Unstable
15
20
25
30
35
40
45
50
-10 -8 -6 -4 -2 0 2 4
Imag
inar
y p
art
Real part
47 m/s
57 m/s
67 m/s
77 m/s
78 m/s
Figure 26. Damping as a function of velocity at service ceiling for the first structure (D1).
-6
-5
-4
-3
-2
-1
0
1
2
40 45 50 55 60 65 70 75 80
Dam
pin
g,
s-1
Velocity, m/s
Tailboom symmetric bending
Wing symmetric torsion
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Figure 27. Root-locus as a function of velocity at sea level for the second structure (D2).
Unstable H.T
Torsion
40
60
80
100
120
140
160
180
-40 -30 -20 -10 0 10 20 30
Imag
inar
y p
art
Real part
26 m/s
36 m/s
46 m/s
56 m/s
66 m/s
76 m/s
79 m/s
96 m/s
Tailboom SYM.
B (IP)
Tailboom SYM. B (OP)
Tailboom
ASYM. B (OP)
Unstable
250
270
290
310
330
350
370
390
-10 -8 -6 -4 -2 0 2
Imag
inar
y p
art
Real part
26 m/s
36 m/s
46 m/s
56 m/s
66 m/s
76 m/s
86 m/s
96 m/s
Wing ASYM. B (IP)
Figure 28. Damping as a function of velocity at sea level for the second structure (D2).
-30
-25
-20
-15
-10
-5
0
5
0 10 20 30 40 50 60 70 80 90 100
Dam
pin
g,
s-1
Velocity, m/s
Tailboom SYM. B (in plane)Tailboom - ASYM. B (out of plane)H.T Torsion
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Figure 29. Root-locus as a function of velocity for cruise altitude for the second structure (D2).
Unstable H.T
Torsion
40
60
80
100
120
140
160
180
-40 -30 -20 -10 0 10 20
Imag
inar
y p
art
Real part
30 m/s40 m/s50 m/s60 m/s70 m/s80 m/s77 m/s100 m/s
Tailboom SYM. B (OP)
Unstable
250
270
290
310
330
350
370
390
-10 -8 -6 -4 -2 0 2
Imag
inar
y p
art
Real part
30 m/s
40 m/s
50 m/s
60 m/s
70 m/s
80 m/s
90 m/s
100 m/sWing ASYM. B (IP)
Figure 30. Damping as a function of velocity for cruise altitude for the second structure (D2).
-25
-20
-15
-10
-5
0
5
0 10 20 30 40 50 60 70 80 90 100 110
Dam
pin
g,
s-1
Velocity, m/s
Tailboom SYM. B (in plane)Tailboom ASYM. B (out of plane)H.T Torsion
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Figure 31. Root-locus as a function of velocity at service ceiling level for the second structure (D2).
Unstable H.T
Torsion
40
60
80
100
120
140
160
180
-40 -30 -20 -10 0 10 20
Imag
inar
y p
art
Real part
47 m/s
57 m/s
67 m/s
77 m/s
87 m/s
97 m/s
107 m/s
Tailboom SYM. B (OP)
Unstable
250
270
290
310
330
350
370
390
-20 -15 -10 -5 0 5
Imag
inar
y p
art
Real part
47 m/s
57 m/s
67 m/s
77 m/s
87 m/s
97 m/s
107 m/s
Wing ASYM. B (IP)
Figure 32. Damping as a function of velocity at service ceiling level for the second structure (D2).
-18-16-14-12-10
-8-6-4-2024
40 50 60 70 80 90 100 110
Dam
pin
g,
s-1
Velocity, m/s
Tailboom SYM. B (in plane)Tailboom ASYM. B (out of plane)H.T Torsion
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stiffness for the horizontal
stabilizer. The flutter velocity
remains outside the flight
envelope, and the flutter velocity
is 0.26% higher to 1.2VD for
cruise altitude.
The wing torsional divergence
velocity is calculated by an
analytical approach1 at different
altitudes. Table 7 shows that the
resultant torsional divergence
velocities are higher than the
maximum aircraft velocity at
each specific flight condition.
However, the divergence velocity
exhibits a significant reduction for the second structure, which could be explained due to the torsional stiffness
distribution presented in Table 1. Table 7 summarizes the torsional divergence and flutter velocities for both structures.
VI. Conclusions
A general methodology is presented to account for flight dynamic response and aeroelastic phenomena
characteristics on the initial structural design of the ANCE X-3d main components using low-detail reduced aero-
structural models. This procedure proved to be useful in obtaining an overall evaluation of the aircraft flight dynamic
sensitivity to the structural flexibility affected by earlier modifications in the design process. The aeroelastic analysis
allowed obtaining valuable insight into the nature of the unstable aeroelastic modes and the stiffness properties linked
with the appearance of structural instabilities.
The simplified structural design of the ANCE X-3d proved to be a useful approximation to obtain an initial
structural definition of the airframe, significantly reducing computational modelling time by neglecting secondary
components that do not perform a structural function. The low computational cost of the reduced order beam-like
model also represents an important advantage due to the possibility of evaluating the physical response of the structure
for different geometric configurations, without the need to take special care of the airframe details that have a
negligible impact on the final structural properties.
The results have shown that structural flexibility does not have a significant influence on the aerodynamic and
stability characteristics of the ANCE X-3d. The aerodynamic performance has a moderate sensitivity to the wing
torsional stiffness in the section located between the fuselage and the wing-tail boom joint, but do not present an
important variation regarding the rigid body model. The ANCE X-3d flight dynamic modes are stable in the flight
envelope and they do not show a drastic modification as a consequence of aircraft flexibility, which satisfies the design
criteria.
The initial aeroelastic analyses suggest that the ANCE X-3d can operate in any condition located inside the flight
envelope with enough margin against aeroelastic phenomena. The results of the structural sensitivity analysis show
that flutter appearance is closely related to the wing first section torsional stiffness.
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Table 7. Torsional divergence and flutter velocities for both structural
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24
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