download

CIRA, The Italian Aerospace Research Center
Vibration and Acoustics Laboratory
Modal Analysis of a Benchmark Aeronautic Structure:
Modal Analysis and FE Model Updating
V. Quaranta, I. Dimino
LMS Conference March 22 & 23, 2006, Munich

Objectives
! To assess a complete reference case on which
applying the available methodologies aiming to the
dynamic characterisation of an aeronautical
structure.
! The work was accomplished by the following
steps:
" Model realisation (after GA specifications)
" Numerical analysis
" Experimental tests
" Model upgrade
" Model validation

Dynamic Characterization
of Aerospace Structures
# Finite Element Analysis;
# Ground Vibration Test (Phase(
Separation
and Phase Resonance techniques):
Pre-Test, Test and experimental model
validation;
# Computational Model Updating by using the
inverse sensitivity approach.

Ground Vibration Test

Description of Testbed
Design requirements:
# Beam assembly;
# 3 modes within 1 Hz
frequency band;
# Damping treatment;
# Very low frequency
sospension.
Garteur SM AG 19

FE Model
Eigenvalue analysis of undamped sistems
It consists of:
V1
FEM Simulation:
# 3018 DOFs; 0 – 150 Hz
# 502 elements;
# 2 lumped masses (CONM2).
-900.
-750.
-600.
-450.
-300.
-150.
0.
150.
300.
450.
600.
750.
900.
Y
-900.
-750.
-600.
-450.
-300.
-150.
Z
Y
0.
150.
300.
450.
600.
X
X
Lumped masses

Mode Description
2N wing bending
Fuselage rotation
Antisymmetric wing torsion
Symmetric wing torsion
3N wing bending
4N wing bending
Antisymmetric fore and aft
Symmetric fore and aft
5N wing bending
Tail torsion
Lateral fuselage bending
2nd tail bending
6N wing bending
7N wing bending
Natural Frequency (Hz)
5.82
16.81
31.35
31.51
38.61
46.74
53.92
57.11
65.44
67.94
105.07
131.04
136.74
151.59

Pre-Test
An integrated
experimental–analytical
analytical
procedure allows to:
# Plan testing strategy;
# Optimise the
experimental setup;
# Improve results quality;
# Reduce testing time.

Pre-Testing
# Guyan
Reduction and
its variant - the
M/K method;
# MODMAC
method;
! 27 nodes
! 32 DOF
Experimental Test Setup

Pre-Test
MAC =
r,
r'
[ ]
T
V [ ]
r
Vr
'
([ ]
T
[ ])[ ]
T
V V V [ V ]
r
r
( )
r'
2
r'

MAC : Accelerometer plan
(0 -150
Hz)
Coarse Mesh (27 dofs)
Refined mesh (32 dofs)

Phase Separation Test
# Identification of the Normal Modes
Broadband excitation (random
or impulsive or sine sweep) to global identify all
modes of the structure and modal parameters extraction (curve fitting methods)
from the measured FRFs.
Hypothesis: : LTA structural system
! Random signal
4-150
Hz

Phase Separation Test
H 1( ω)
=
H
2
( ω)
=
XPS
input(
APS)
output(
APS)
XPS
γ
2
=
H
H
1
2
( ω)
( ω)

Normal mode Test
# MIF
∑
∑
u'
i
u
MIF = 1−
2
u
i
i
# Lissajous Display
# Phase Scatter
Diagram
# On-line
visualization
of mode shapes.

Normal mode:
generalized parameters
Complex power
P
1 T
= [ f ] [ V ] P= P’ + jP’’
2
ω k
Resonance frequencies :
⎛
⎜
⎝
dP'
⎞
⎟
dω
⎠
ω
k
=
0
P' '( ω k
) =
0
P'(
ω )
k
= α
k
ω
k
γ
k
⎛
⎜
⎝
dP''
⎞
⎟
dω
⎠
ω
k
= −γ
k
= −µ
k
ω
2
k

Normal mode Test

Linearity Tests
2N 4N wing wing bending mode mode
42
5,3
41,8
natural frequenciy (Hz)
natural frequency (Hz)
41,6
41,4
41,2
5,26
5,22
5,18
5,14
41
5,1
0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5
Master Force (N)
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
Master Force (N)

Measured Normal Modes
Nr
Mode
MIF
ξ [%]
M gen
[Kg m²] m
Frequency [Hz]
Ph Separation
Frequency [Hz]
Ph Resonance
Excitation
1
2N wing bending
0.9749
1.476
3.27
5.30
5.2656
Gart 22z
2
Fuselage rotation
0.9955
1.4
4.46
14.25
13.3750
Gart 13z
3
Antisymmetric wing
torsion
0.9559
0.6
0.61
33.25
28.17
Gart 22z
Gart 19z
4
Symmetric wing
torsion
0.95
0.5
1.71
32.86
28.637
Gart 22z
Gart 19z
5
3N wing bending
0.9990
1.084
2.06
31.83
31.5
Gart 13z
6
4N wing bending
0.9998
0.510
2.8
42.81
41.4843
Gart 13z
7
Antisymmetric Fore
and aft
0.9525
2.186
7.14
41.15
40.20
Gart 3y
8
Symmetric Fore
and aft
0.9989
0.8
3.84
51.09
50.6718
Gart 7x
9
5N wing bending
0.9905
2.1
3.76
55.62
54.00
Gart 13z
10
Tail torsion
0.9980
0.2
0.48
61.90
56.5312
Gart 25z
11
Lateral fuselage
bending
0.9990
0.840
1.02
100.48
97.3437
Gart 3y
12
2° Tail bending
0.9788
1.280
3.38
120.00
117.3906
Gart 13z
13
6N wing bending
0.9960
0.963
2.17
126.66
123.3750
Gart 13z
14
7N wing bending
0.9568
1.358
1.73
134.34
132.1718
Gart 13z

Correlation of Analytical and
Test Results
T
[ Φ ] [ M ][ Φ ] [ I ]
sper num sper
=
XOR
=
MAC =
T
[ Φ ] [ M ][ Φ ]
num
num
sper
T
T
( Φ Φ )( Φ Φ )
test
Φ
T
test
test
Φ
num
num
2
num

Modal correlation
MAC
=
T
T
( Φ Φ )( Φ Φ )
test
Φ
T
test
test
Φ
num
num
2
num

FRFs correlation
FRAC( j)
=
T
2
FE
Test
{ H ( ω
i
) } { H ( ω ) }
j
i j
FE T
FE
Test T
{ H ( ω ) } { H ( ω ) }{ H ω } { H ( ω ) }
Test
( )( ( )
)
i
j
i
j
i
j
i
j

FE model updating:
sensitivity study
Design Sensitivity
Wing
Wing Fuselage junction
V Tail
H Tail
Physical and geometric
updating parameters:
# Cross section;
# Area moment of inertia Ix;
# Area moment of inertia Iy;
# Area moment of inertia Iz.

Model Updating Results
35,00%
30,00%
25,00%
20,00%
Wing
Plate
Vertical Tail
Horizzontal Tail
Density of the model
Density of the plate
Parameter changes after updating
A
Iy
Error % FE Model versus GVT
-7%
-19.81%
+2.66%
+24.54%
+28.06%
+10%
+10%
+4.86%
+23.71%
Iz
-30.36%
J
-15.49%
-10.23%
-21.20%
Updated FEM -9.86%
Initial FEM
15,00%
10,00%
5,00%
0,00%
5,27 13,38 28,17 28,64 31,5 41,48 40,2 50,67 54 56,53 97,34 117,4 123,4 132,2
Natural frequency

FE Model Validation

Conclusions
# Pre – Test Analysis allowed to optimize the
accelerometer’s number and location;
# Experimental model validation was performed
using two methods: modal and FRF analysis;
# Computational
model
updating
procedure
made use of the inverse sensitivity approach.
It drastically reduced the FE modal parameter
errors.