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133APPENDIX C. MODAL ANALYSIS OF HINGED-HINGED BE4M
APPENDIX C - MODAL ANALYSIS OF HINGED-HINGED BEAM
Number of averaged Procedures: 100
The identified natural frequencies, modal damping factors and normal modes are listed in Tables C.l and C.2.
Table C.l - Natural Frequencies and modal dampingfactors for the hinged-hinged
beam
Natural frequencies Modal damping factors x [10-4]
17.130 81.206 57.222 22.496 129.81 41.237 216.48 36.900 342.64 7.6922
Table C.2 Identified normal modes for the hinged-hinged beam
Position Mode 1 x [1001
]
Mode 2 x [1001
]
Mode 3 X [1001
]
Mode 4 X [1001
]
Mode 5
x [1001 ]
2 3 4 5 6 7 8 9 10
1.1956 2.6710 4.1645 5.3259 5.1190 4.7935 4.0780 3.0438 1.6110
-2.7045 -4.8463 -5.0361 -3.0588 -0.0773 2.8529 4.8785 4.8799 2.8048
3.9763 5.1423 1.9649
-2.7845 -5.1073 -2.9713 1.8480 4.9294 4.0255
4.7034 3.0304 -2.8866 -4.7733 -0.1078 4.7192 2.9380 -2.9332 -4.6629
-5.4634 -0.4111 5.2821 0.1926 -5.1595 0.0530 5.1217 -0.2507 -5.2576
The following figures show the measured frequency response function data corresponding to reference position 8 and the reconstructed normal mode model without the contributions ofthe residual terms.
ASSESSMENT OF FREQUENCY DOMAINFORCE IDENTIFICATION PROCEDURES
137APPENDIX D. MODAL ANALYSIS OF HINGED-HINGED BE4M
APPENDIX D - MODAL ANALYSIS OF HINGED-HINGED BEAM
Number ofaveraged Procedures: 200
The identified natural frequencies, modal damping factors and normal modes are listed in Tables D.1 and D.2.
Table D. J - Natural frequencies and modal dampingfactors for the hinged-hinged
beam with two harmonic force inputs
Natural frequencies Modal damping factors [Hz] x [10.4]
17.228 148.44 57.303 42.140 129.79 44.154 216.31 56.103 342.66 8.410 494.19 11.672 648.33 10.021
Table D.2 - Identified normal modes for the hinged-hinged beam with two harmonic
force inputs
Position Mode 1 x [10.1]
Mode 2 x [l0·1]
Mode 3 x [10.1]
Mode 4 X [l0'1]
Mode 5 X [l0·1]
2 3 4 5 6 7 8 9 10
-1.0774 -2.4214 -3.6565 -4.3895 -4.6137 -4.2844 -3.6914 -2.6569 -1.3283
-2.7529 -4.7255 -4.9741 -3.2095 -0.1007 2.9175 4.7672 4.7833 2.9776
4.0682 5.1187 2.0027 -2.7771 -4.8680 -2.8460 1.9263 5.0503 3.9585
4.7618 3.1239 -2.8965 -4.8207 -0.0438 4.7831 3.0309 -2.9069 -4.6472
-4.9274 -0.4099 4.6762 0.1359 -4.7837 0.0314 4.7526 -0.2191 -4.8786
Position Mode 6 x [10,1]
Mode 7 X [10.1]
2 -4.8896 3.7760 3 2.4546 4.2764 4 3.0719 1.4962 5 -4.5333 2.9315 6 -0.0551 4.4332 T 4.6077 2.7099 8 -2.9897 1.6478 9 -2.4897 4.2718 10 4.8393 3.5324
The following figures show the measured frequency response function data and the reconstructed normal mode model without the contributions of the residual terms.
ASSESSME1VT OF FREQUENCY DOMAIN FORCE IDE1VTIFICATION PROCEDURES
APPENDIX D. MODAL ANALYSIS OF HINGED-HINGED BEAM
102
~ 10° "'", ~ 1)
!.a
~ ~
,.:;
10"' 100
102
~ 10° ~ 2-0
~ ~
,.:;
104
100
102
~ 10° '" '" E.-o <.)
I 10-2
,.:;
104
100
102
~ 10° '" ~ 2-0 !.a
j 10"'
100
200
200
200
200
Position 2J Reference 5
300 400
Frequency [Hz]
500
Position 31 Reference 5
300 400
Frequency [Hz]
500
Position 4/ Reference 5
300 400
Frequency [Hz]
500
Position 5/ Reference 5
300 400
Frequency [Hz]
500
1- Data - Nor. model I
600 700
1- Data - Nor. model I
600 700
- Data - Nor. model I
600 700
I - Data I - Nor. model I
600 700
ASSESSMENT OF FREQUENCY DOMAIN FORCE IDENTIFICATION PROCEDURES
138
800
800
800
800
APPENDIX D. MODAL ANALYSIS OF HINGED-HINGED BEAM
102
~ 100
~ .:. <> (J
~ <> ..s
10-4 100
102
~ 100
~ .:. <> (J
J 10-4
100
102
~ 100 '"I '" = .:. <> (J
= ~ -=
10-4 100
102
~ 100 '"I ~ .:. <>
~ 2 -=
10-4 100
200
200
200
200
Position 61 Reference 5
300 400
Frequency [Hz]
500
Position 7/ Reference 5
300 400
Frequency [Hz]
500
Position 8/ Reference 5
300 400
Frequency [Hz]
500
Position 9/ Reference 5
300 400
Frequency [Hz]
500
1- Data I - Nor. model
600 700
600 700
1- Data - Nor. model
600 700
1- Data - Nor. model
600 700
ASSESSMENT OF FREQUENCY DOMAIN FORCE IDENTIFICA TION PROCEDURES
139
800
800
800
800
APPENDIX D. MODAL ANALYSIS OF HINGED-HINGED BEAM
102
~ 10° <"I ~ .:.
" Sol
~ ~
..::I
10-4 100
105
;f '" ~ 10°
~ t: ~
..::I
10-5
100
102
;f 10° '" .§. 8
I 10-2
10-4 100
104
;f 102
'" :: .:.
"
J 10°
10-2
100
200
200
200
200
Position 10/ Reference 5
300 400
Frequency [Hz]
500
Position 2J Reference 8
300 400
Frequency [Hz]
500
Position 3/ Reference 8
300 400
Frequency [Hz]
500
Position 4/ Reference 8
300 400
Frequency [Hz]
500
1- Data - Nor. model
600 700
I- Data I - Nor. model
600 700
I-Data I - Nor. model I
600 700
800
800
800
- Nor. model _
600 700 800
ASSESS}VfENT OF FREQUENCY DOMAIN FORCE IDENTIFICATION PROCEDURES
140
APPENDIX D. MODAL ANALYSIS OF HINGED-HINGED BEAM
102
~ 10° '" E-I)
~ ]
10"' 100
lOS
~ ~ 2. 10° I)
~
j lO-s
100
102
~ 10° ~ 2. I)
~ 10-2
~ :2
,.:::;
10"' 100
lOS
~ <"i '" a 10° " ~ ~
,.:::;
IO-S
100
200
200
200
200
Position 5/ Reference 8
300 400
Frequency [Hz]
500
Position 61 Reference 8
300 400
Frequency [Hz]
500
Position 7/ Reference 8
300 400
Frequency [Hz]
500
Position 81 Reference 8
300 400
Frequency [Hz]
500
1- Data - Nor. model
600 700
1- Data - Nor. model I
600 700
- Data - Nor. model
600 700
600 700
ASSESSlvfENT OF FREQUENCY DOMAIN FORCE !DENTIFICA TION PROCEDURES
141
800
800
800
800
APPENDIX D. MODAL ANALYSIS OF HINGED-HINGED BEAM
100
lOS
~ "I
." :::
10° .::. 4)
~ ]
10-5
100
200
200
Position 9/ Reference 8
300 400
Frequency [Hz]
500
Position 10/ Reference 8
300 400 500
Frequency [Hz]
1- Data I
- Nor. model I 600 700
600 700
ASSESSMENT OF FREQUENCY DOMAIN FORCE IDENTIFICATION PROCEDURES
142
800
800
