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Mostafa S. Abd ElwahabMaster of Science in Mechanical Engineering
Teaching and Research AssistantDepartment of Mathematical Science
German University in Cairo (GUC)
Outline Definition of vibration.
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x
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x
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t
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structure
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structure
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4
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∂∂+
x
txwIEEIj
x
txwIEEI
t
txwAA
ddd
dddd
ηη
ρρ
*= "
/1
Merits: loss factor is not function in mode of vibration.
Limitations: Low loss factor ( 0.8*0.5) in best designs
dd
ddds IEEI
IE+
=ηη
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Constraining layer
Structure
Damping layerNote the shear strain
h1h
2
h3
Undeformed Deformed
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dsigYg
gY
ηηη
++++=
0),(),(),(
)1(),(
2
2
22
4
4
4
6
6=
∂∂−
∂∂∂+
∂∂+−
∂∂
t
txwDmg
tx
txwDm
x
txwYg
x
txw
tt
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Merits: Better loss factor
Limitations: Mode dependency
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Vs
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Viscoelastic layer
Piezoelectric sensor
Base beam
γc
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Piezoelectric sensor
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γ
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=B"7
0),(),(),(
)1(),(
2
2
22
4
4
4
6
6=
∂∂−
∂∂∂+
∂∂+−
∂∂
t
txwDmg
tx
txwDm
x
txwYg
x
txw
tt
This equation is identical to the equation of the Beam/PCLD system
So, what is new in the technique of ACLD??
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0<dtEd n
Total Energy of the Beam/ACLD system
ttxu
k agp ∂
∂−= ),(ε
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2
2
22
4
4
4
6
6=
∂∂−
∂∂∂+
∂∂+−
∂∂
t
txwDmg
tx
txwDm
x
txwYg
x
txw
tt
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0)(
)()(
)()()(
2
22
2 3
3
4
4
5
5
=
−+Ω−−+
Ω
ΩΩΩ
xW
dxxdW
YjQdx
xWdj
dx
xWd
dx
xWd
tDm
gtDm
gYQ
g
Qj
21hK
gYtDgKQ =
The proportional
Control gain2
312
hhhh
++=
Mode shape
Geometrical Parameter
tDKKhKK
Y)( 31
231
+=111 hEK =
333 hEK =
Shear Parameter
312
31 )(KKh
KKGg d +=
Exciting frequency
=B"7
=
=B
=B
=7
6'=
New Approach for Vibration Control in Elastic Structures
y
x
x
L
dx
w(x,t)
p(x,t)
F(x,t)=F0
F(x,t)=F0
&%% $9$71&+2/"#$"%&'+2/% %!
Damping Material
Damping Material
BeamBase
Technique used for generating axial uniform damping force
New Approach for Vibration Control in Elastic Structures
Damping Material
Damping Material
BeamBase
Technique used for generating axial uniform damping force
New Approach for Vibration Control in Elastic Structures
Damping Material
Damping Material
BeamBase
Technique used for generating axial uniform damping force
New Approach for Vibration Control in Elastic Structures
Damping Material
Damping Material
BeamBase
0),( FtxF =
0),( FtxF =
Technique used for generating axial uniform damping force
New Approach for Vibration Control in Elastic Structures
This technique is called Pre-Tensioned Layer Damping
(PTLD)
7
New Approach for Vibration Control in Elastic Structures
6 %
=
EIt
txw(
),() 2
2+
∂∂
0),(
) 4
4=
∂∂
x
txwAρ(
*= "
/1
ηEIj(+4
4 ),()
x
txw
∂∂
7
New Approach for Vibration Control in Elastic Structures
6 A %$ %
0),(
2 2
2
0 =∂
∂+x
txwFEI
t
txw(
),() 2
2+
∂∂
4
4 ),()
x
txw
∂∂Aρ(
*= "
/1
ηEIj(+4
4 ),()
x
txw
∂∂
6 %
7
New Approach for Vibration Control in Elastic Structures
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0),(
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4
4
4
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2=
∂∂++
∂∂++
∂∂+
x
txwIEEIj
x
txwIEEI
t
txwAA ddddddd ηηρρ
*= "
/1
6 %
7
New Approach for Vibration Control in Elastic Structures
6 %
0),(
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4
4
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2=
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∂∂++
∂∂+
x
txwIEEIj
x
txwIEEI
t
txwAA ddddddd ηηρρ
*= "
/1 :2
2
0),(
2x
txwF
∂∂+
00 εdd AEF =
)1( dd jE η+
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9A
7
New Approach for Vibration Control in Elastic Structures
6 %
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0),(
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4
2
2=
∂∂++
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x
txwIEEIj
x
txwIEEI
t
txwAA ddddddd ηηρρ
*= "
/1 :2
2
02
2
0),(
2),(
2x
txwAEj
x
txwAE ddddd ∂
∂+∂
∂ ηεε
9A
-7
New Approach for Vibration Control in Elastic Structures
-/-1
[ ]∞
=
++Ω−++=Ω
1222222
)()(
),(n
nfddfdn
n
xWj
mLP
xωωηωωω
α
mLCAE ndd
f02 2 εω =
Main Effect
Secondary Effect
-7
New Approach for Vibration Control in Elastic Structures
-/-1%4
[ ]∞
=
++Ω−++=Ω
1222222
)()(
),(n
nfddfdn
n
xWj
mLP
xωωηωωω
α
mLCAE ndd
f02 2 εω =
7
New Approach for Vibration Control in Elastic Structures
ndnd
d
ndnd
d
s
CALIEE
I
CALI
04
04
2)2(
2)2(
εβ
εβηη
++
+=
-7
New Approach for Vibration Control in Elastic Structures
-/-1%6
FFT Analyser
CH 1CH 2Source
Disk drive hp ploter
Power Amp.
Shaker
Moving Base
AccelerometerInductive Pickup
Fixed Base
Charge Amp.
Voltage Amp.
Beam
HPIB CableHPIB Cable
y(t)b
by(t)..
by(t)
y
y
y
(Dual channel)
Harmonic signal generator
plotter
Experimental Implementation of the PTLD Technique
• Schematic drawing of test set-up and instrumentation
• Experimental set-up
Experimental Implementation of the PTLD Technique
Experimental Implementation of the PTLD Technique
002.00 =ε
Experimental Implementation of the PTLD Technique
008.00 =ε
Experimental Implementation of the PTLD Technique
016.00 =ε
Effectiveness of the New Technique
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