Using blurred images to assess damage in bridge structures?
Dr Alessandro Palmeri
The School of Civil and Building Engineering
Loughborough University, UK Email: [email protected]
1
Structural Dynamics
Stochastic Mechanics
Seismic Analysis and Design
Wind Engineering
Train-Bridge Interaction
Random Vibration
Random Composites
Design Assisted by Testing
Performance-Based Design
Fast Dynamics (Blast Loading)
Isolators and Dampers
Structural Health Monitoring
Research Mind Map
2
Research Word Cloud (2000-date)
3
University of
Messina 2000-07
University of
Naples Federico II 2001
University of California at
Berkeley 2002
University of
Patras 2004
University of
Bradford 2008-09
Loughborough University 2010-date
Outline
• Introduction
• 1. Coupled dynamics of composite bridges (Analytical formulation, 2009-10)
• 2. How sensitive is the envelope to damage?
(Numerical study, 2012-13)
• 3. How can we measure the envelope? (Experimental investigations, 2011-14)
• Conclusions
4
Introduction
• Composite steel-concrete beams are widely used in bridge engineering
5
Introduction
• Their performances are strongly influenced by the flexibility of the shear connection
6
Introduction
Partial-interaction No Interaction (Non-composite bridge)
• Steel-concrete shear interaction allows reducing deflections and mitigating the accelerations experienced by vehicles
7
Coupled Dynamics of Composite Bridges
Analytical formulation, 2009-10
8
Coupled Dynamics of Composite Bridges
• Literature Review
• The most popular approach for the mechanics of composite steel-concrete beam is due to Newmark et al. (1951), in which top slab and bottom girder are two beams continuously connected by a linear-elastic interface
However…
• Non-rigid steel-concrete connection is ignored in the technical literature devoted to the coupled vibrations of bridges and vehicles
9
Coupled Dynamics of Composite Bridges
10
Moving force: Time-invariant equation of motion
Moving mass: Time-dependent inertia
Moving oscillator: Dynamic interaction (mass, stiffness and damping vary with time)
Coupled Dynamics of Composite Bridges
• Computational Approach
• Higher-order partial differential equations of motion for slender composite beams with partial interaction under a platoon of moving oscillators are cast in a novel state-space form with time-varying coefficients
• Time-independent modifications in inertia and rigidity due to partial interaction between concrete and steel
• Time-dependent modifications due to the dynamic interaction between composite beam and moving oscillators
Palmeri, 10th Int Conf on Rec Adv in Struct Dyn (RASD), 2010
11
Coupled Dynamics of Composite Bridges
v(1)mv(2)mvv( )nm L
v(1)kv(2)kvv( )nk
v(1)cv(2)cvv( )nc
(s)bf
bL
s s
s s
,,E
A Iρ⎧
⎨⎩
c c
c c
,,E
A Iρ⎧
⎨⎩
}i b,K dc
v
,( , ),( )
zw z tz t
b
v
,( , ),( )
yv z tv t
Figure 1. Simply-‐supported steel-‐concrete composite beam crossed by a platoon of moving oscillators.
Simply-supported steel-concrete composite beam crossed by a platoon of moving oscillators
12
Coupled Dynamics of Composite Bridges
! Cascade'equations'of'motion:'
! where:'
[ ](s)b
c c s sb
fA A Ag
ρ ρ ρ= + +
[ ]
[ ] [ ]
c c s sb(0)
2c s c sbb( ) b(0)
c c s s
EI E I E I
E E A AEI EI dE A E A∞
= +
= ++
[ ] [ ][ ]
[ ][ ]
[ ] [ ][ ]
22 i bb
b(0)b(0)
b( )
2b(0)2 2 i b
b bb( ) b(0)
b( )b( )
1
;
1
K dEI
EIEI
EI K dEI EI
EIEI
α
β α
∞
∞
∞∞
=⎛ ⎞⎜ ⎟−⎜ ⎟⎝ ⎠
= =⎛ ⎞⎜ ⎟−⎜ ⎟⎝ ⎠
Non$Composite$
Fully$Composite$
Composite$beam$transverse$deflections$
Concrete$slab$axial$displacements$
[ ] [ ]
[ ] [ ]
2 2 2 4 2b b
b b2 2 2 2 2 4 2 2b b( )b b b
2 2 42c
b i b b b b2 2 2 4b b(0)b b c c
1 ( , ) 1 ( , ) 11 1 ( , ) 1 ( , ) ,
( , ) 1 ( , ) ( , ) ( , ) ( , ) ;
v z t v z tA EI R z t f z tz t z z z
w z t f z t K d v z t A v z t EI v z tz r E A z t z
ρβ α β
ρβ
∞
⎧ ⎧ ⎫ ⎧ ⎫ ⎧ ⎫∂ ∂ ∂ ∂ ∂− + − + = −⎪ ⎨ ⎬ ⎨ ⎬ ⎨ ⎬∂ ∂ ∂ ∂ ∂⎩ ⎭ ⎩ ⎭ ⎩ ⎭⎪⎪⎨⎪ ⎛ ⎞∂ ∂ ∂ ∂⎪ = + − −⎜ ⎟⎪ ∂ ∂ ∂ ∂⎝ ⎠⎩
13 Vibration of the beam: Governing equation
Coupled Dynamics of Composite Bridges
! Transverse(loading:(
! Classical(modal(analysis:(
( )v
(s)b b b v( ) v( ) v( )
1( , ) ( ( )) ( ) ( )
n
i i ii
f z t f z t f t z z tχ δ=
= + −∑
Dynamic(loads(due(to(moving(oscillators(
Static(load(b b( ) ( ) ( )
1 , Within the beam0 , Outside the beam
z U z U z Lχ = − −
⎧= ⎨⎩
b(s) (s) T
b b b( ) b( ) b b b1
( , ) ( ) ( ) ( ) ( ) ( ) ( )n
j jj
v z t v z z q t v z z tφ=
= + = + ⋅∑ qφ
Static(contribution(
Modal(contributions(
14 Vibration of the beam: Loads and displacements
Coupled Dynamics of Composite Bridges
! Modal&equations&of&motion:& qb(t)+Ξb ⋅ qb(t)+Ωb
2 ⋅qb(t) = Jb ⋅Qb(t)
b
1
b bin
−⎡ ⎤= + Δ⎣ ⎦J I m
1 22b b b( ) bi
b b b2ζ
−
∞⎡ ⎤⎡ ⎤= ⋅ + Δ⎣ ⎦⎣ ⎦
=
J kΩ Ω
Ξ Ω
bb( ) b( ,1) b( ,2) b( , )Diag nω ω ω∞ ∞ ∞ ∞⎡ ⎤= ⎣ ⎦LΩ
[ ][ ]
2b( )
b( )b b
j
EIjL Aπω
ρ∞⎛ ⎞
= ⎜ ⎟⎝ ⎠
[ ]
6b( )
bi b2b bb
[ ]EIA L
πα ρ
∞ ⎡ ⎤Δ = ⎢ ⎥
⎣ ⎦k N
[ ]b bDiag 1 2 n=N L
2
bi b2b b
1Lπ
β⎡ ⎤
Δ = ⎢ ⎥⎣ ⎦
m N
v
b b v( ) v( ) b v( ) b v( )21 b
1( ) ( ( )) ( ) ( ( )) ( ( ))n
i i i ii
t z t f t z t z tχβ=
⎧ ⎫′′= −⎨ ⎬
⎩ ⎭∑Q φ φ
15 Vibration of the beam: Modal analysis
Coupled Dynamics of Composite Bridges
! Absolute)displacements)are)used:)!Impulsive!terms!in!the!equations!of!motion!can!be!avoided!)(Muscolino,)Palmeri)&)Sofi,)2009))
mv(i ) vv(i ) (t) = −cv(i ) vv(i ) (t) − vw(i ) (t)( )− kv(i ) vv(i ) (t) − vw(i ) (t)( ) ,
vw(i ) (t) = rv(i ) (t) + χb (zv(i ) (t))abv(i )T (t) ⋅qb (t)
vw(i ) (t) = sv(i ) (t) + χb (zv(i ) (t)) abv(i )T (t) ⋅ qb (t) + bbv(i )
T (t) ⋅qb (t)( )Static!contributions! Dynamic!contributions!
16 Vibration of the oscillator: Governing equation
Coupled Dynamics of Composite Bridges
! Equations*of*motion:*Mv ⋅ vv (t) +Cv ⋅ vv (t) +Kv ⋅vv (t) =Cv ⋅sv (t) +Kv ⋅rv (t)
+Cvb ⋅ qb (t) + Kvb (t) +Lvb (t)⎡⎣ ⎤⎦ ⋅qb (t)
Mv = Diag mv(1) mv(2) mv(nv )⎡⎣⎢
⎤⎦⎥
Cv = Diag cv(1) cv(2) cv(nv )⎡⎣⎢
⎤⎦⎥
Cvb(t) = Cv ⋅Xv (t) ⋅AbvT (t)
K v = Diag kv(1) kv(2) kv(nv )⎡⎣⎢
⎤⎦⎥
K vb(t) = K v ⋅Xv (t) ⋅AbvT (t)
Lvb(t) = Cv ⋅Xv (t) ⋅BbvT (t)
Xv (t) = Diag χb (zv(1) (t)) χb (zv(2) (t)) χb (zv(nv ) (t))⎡⎣⎢
⎤⎦⎥
Abv (t) = abv(1) (t) abv(2) (t) abv(nv ) (t)⎡⎣⎢
⎤⎦⎥
Bbv (t) = bbv(1) (t) bbv(2) (t) bbv(nv ) (t)⎡⎣⎢
⎤⎦⎥
17 Vibration of the oscillator: Matrix equations
Coupled Dynamics of Composite Bridges
! The$generic$oscillator/beam$interaction$force$is$given$by:$
$Leading$to:$
fv(i ) (t) = mv(i ) g
+cv(i ) vv(i ) (t) − sv(i ) (t) − χb (zv(i ) (t))abv(i )T ⋅ qb (t) − χb (zv(i ) (t))bbv(i )
T ⋅qb (t)( )+kv(i ) vv(i ) (t) − rv(i ) (t) − χb (zv(i ) (t))abv(i )
T ⋅qb (t)( )qb (t) + Ξb + ΔCb (t)⎡⎣ ⎤⎦ ⋅ qb (t) + Ωb
2 + ΔKb (t)⎡⎣ ⎤⎦ ⋅qb (t)
=Cbv (t) ⋅ vv (t) +Kbv (t) ⋅vv (t) + Qb (t)
ΔCb (t) = Tbv (t) ⋅Cvb (t)
ΔKb (t) = Tbv (t) ⋅ Kvb (t) +Lvb (t)⎡⎣ ⎤⎦Cbv (t) = Tbv (t) ⋅CKbv (t) = Tbv (t) ⋅Kv
Qb (t) = Tbv (t) ⋅ gMv ⋅τ v −Cv ⋅sv (t) −Kv ⋅rv (t){ }
τ v = 1 1 1{ }T
Tbv (t) = Jb ⋅ Abv (t)+ ΔAbv (t)⎡⎣ ⎤⎦ ⋅Xv (t)
ΔAbv (t) = − 1βb
2 ′′φb(zv(1) (t)) ′′φb(zv(2) (t)) ′′φb(zv(nv ) (t))⎡⎣⎢
⎤⎦⎥
18 Vibration of the oscillator: Matrix equations
Coupled Dynamics of Composite Bridges
! Matrix'equations'of'motion'can'be'obtained'for'the'platoon'of'moving'oscillators:'
qv (t) +Ξv ⋅ qv (t) +Ωv2 ⋅qv (t) = Qv + µv ⋅Cvb ⋅ qb (t) + µv ⋅ Kvb (t) +Lvb (t)⎡⎣ ⎤⎦ ⋅qb (t)
Ξv = 2Diag ζ v(1) ζ v(2) ζ v(nv )⎡⎣⎢
⎤⎦⎥⋅Ωv
Ωv = Diag ω v(1) ω v(2) ω v(nv )⎡⎣⎢
⎤⎦⎥
Qv (t) = µv ⋅ Cv ⋅sv (t) +Kv ⋅rv (t){ }
v( )v( )
v( )
v( )v( )
v( ) v( )2
ii
i
ii
i i
km
cm
ω
ζω
=
=
1 2v v
−=Mµ{ }b
Tv v(1) v(2) v( )( ) ( ) ( ) ( )nt q t q t q t=q L Dimensional*
consistency*
19 Coupled vibration
Coupled Dynamics of Composite Bridges
! Finally'the'two'matrix'equations'are'rewritten'in'an'enlarged'modal'space:'
q(t) + c0 + Δc(t)⎡⎣ ⎤⎦ ⋅ q(t) + k0 + Δk(t)⎡⎣ ⎤⎦ ⋅q(t) =Q(t)
v b
b v
v v
v
0b
v vb
bv v b
( )( )
( ) ( )
n n
n n
n n tt
t t
×
×
×
⎡ ⎤⎢ ⎥=⎢ ⎥⎣ ⎦
− ⋅⎡ ⎤Δ = ⎢ ⎥− ⋅ Δ⎢ ⎥⎣ ⎦
Oc O
O Cc
C C
Ξ
Ξ
µ
µ[ ]
v b
b v
v v
2v
20b
v vb vb
bv v b
( ) ( )( )
( ) ( )
n n
n n
n n t tt
t t
×
×
×
⎡ ⎤Ω⎢ ⎥=
Ω⎢ ⎥⎣ ⎦⎡ ⎤− ⋅ +
Δ = ⎢ ⎥− ⋅ Δ⎢ ⎥⎣ ⎦
Ok
O
O K Lk
K K
µ
µ
{ }TT Tv b( ) ( ) ( )t t t=q q q Q(t) = Qv
T (t) QbT (t){ }T
“Small”'modifications'
20 Coupled vibration: Proposed model
Coupled Dynamics of Composite Bridges
! Single'step+(unconditionally+stable)+numerical+integration:+
! Reference+transition+matrix+without+dynamic+interaction:+
! Dynamic+modification+matrix:+
[ ] [ ] [ ]{ }0 01 01 02( ) ( ) ( ) ( ) ( ) ( )t t t t t t t t+ Δ = ⋅ + ⋅ Δ ⋅ + ⋅ ⋅ + ⋅ ⋅ + Δx E D x V Q V QΘ Γ Γ Γ
v b
1
2( ) 02( ) ( )n nt t t−
+⎡ ⎤= − ⋅Δ + Δ⎣ ⎦E DΙ Γ
v b
v b
10 0 2( ) 0
101 0 0 0
102 0 2( ) 0
1
1
n n
n n
t
t
−+
−
−+
⎡ ⎤= − ⋅⎣ ⎦⎡ ⎤= − ⋅⎢ ⎥Δ⎣ ⎦⎡ ⎤= − ⋅⎢ ⎥Δ⎣ ⎦
L I D
L D
L I D
Θ
Γ Θ
Γ
[ ]0 0exp t= ΔDΘ
21 Coupled vibration: Proposed numerical scheme
Coupled Dynamics of Composite Bridges
Time histories of beam’s transverse deflection at midspan for different levels of partial interaction
22
Coupled Dynamics of Composite Bridges
Time histories of oscillator’s absolute acceleration for different levels of partial interaction
23
Part-1 Conclusions (from 2010)
• A novel method of dynamic analysis has been proposed and numerically validated for studying the dynamic interaction phenomenon in composite steel-concrete beams subjected to a platoon of single-DoF moving oscillators • Time-independent modifications arise in the composite beam because of the
partial interaction between concrete slab and steel girder • Beam-oscillators dynamic interaction is represented by a set of time-
dependent functions, playing the role of time-varying stiffness and damping coefficients
• A single-step numerical scheme of solution has been formulated, based on the observation that the dynamic modifications are small
• Further studies: • Effect of roughness in the beam-oscillators’ contact • Sensitivity of the dynamic response of the subsystems to the degree of PI in
the supporting beam
24
Part-1 Conclusions
Bending Moment M Shear Force V
Mean value µ (top) and standard deviation σ (bottom) of the internal forces M and V due to a single moving oscillator at midspan of a simply-supported solid beam with rough surface
Muscolino, Palmeri & Sofi, 10th Int Conf on Struct Safety & Reliability (ICOSSAR), 2009
25
How sensitive is the envelope to damage?
Numerical study, 2012-13
26
How sensitive is the envelope to damage?
• Literature Review
• Conventional approaches of damage detection (including ultrasonic, thermal, eddy current and X-ray testing) were termed as cumbersome and expensive
• Vibration-based damage methods have emerged, as they allow identifying meaningful changes in the dynamic characteristics of the composite beam
• Accelerometers have been extensively employed, BUT their application to large structural systems may be difficult because of long cabling, number of sensors and installation time
• Laser doppler vibrometers can be used as a viable non-contact alternative, especially when targets are difficult to access, BUT the simultaneous acquisition of vibration at multiple points would make very expensive the dynamic testing
Therefore…
• The idea of using the envelopes profile of deflections and rotations induced by a moving load has been investigated
• That’s radically different than recording and analysing multiple time histories
Kasinos, Palmeri & Lombardo, Structures, In press
27
How sensitive is the envelope to damage?
• Key Assumptions
1. Linear-elastic constitutive law 2. Finite element model built with SAP2000, using:
• Beam elements for top concrete slab and bottom steel girder • Elastic springs for the shear connectors
3. Planar motion (no twisting moment) 4. Moving force F (massless) with constant velocity V 5. Damage simulated as stiffness reduction in the shear springs
28
Application Programming Interface
How sensitive is the envelope to damage?
• Governing equations
• Dynamic response of interest (displacement or rotation)
• Envelope of the dynamic response
• Damage measure (DM)
29
How sensitive is the envelope to damage?
Dynamic amplification factors of midspan deflection δM and right support rotation φR for different levels of concrete-steel partial interaction
= θ due to gravitational loads
= θ when the moving force is applied statically
Amplification factors:
30
How sensitive is the envelope to damage?
Normalised envelope of midspan deflection δM and right support rotation φR for different levels of concrete-steel partial interaction
31
How sensitive is the envelope to damage?
Damage sensitivities fi,j for the natural frequencies associated with the first six flexural modes of vibration in case of medium (left) and stiff (right) partial interaction
32
How sensitive is the envelope to damage?
Damage sensitivities di,j for the displacements’ envelope Eδi in case of medium (left) and stiff (right) partial interaction
V= 250 km/h
V= 300 km/h
33
0.6
How sensitive is the envelope to damage?
Damage sensitivities ri,j for the rotations’ envelope Eφi in case of medium (left) and stiff (right) partial interaction
V= 250 km/h
V= 300 km/h
34
0.6
How sensitive is the envelope to damage?
Different damage sensitive features (f= modal frequency; d= displacement’s envelope; r = rotation’s envelope; q= curvature’s envelope) in case of medium (left) and stiff (right) partial interaction
V= 250 km/h
V= 300 km/h
35
Part-2 Conclusions
• The envelope of deflections and rotations induced by moving loads has been suggested as damage sensitive feature for composite steel-concrete bridges
• The envelope of the dynamic response tends to increase when damage occurs in the shear connectors
• The envelope enjoys:
• High sensitivity to the damage (higher than frequency shifts, at least for the first few modes of vibration)
• The sensitivity tends to increase closer to the ends of the bridge, where damage in the shear connectors is more likely to happen
• Ordered sets of results, that can potentially enhance the predictiveness of damage-detection algorithms
36
How can we measure the envelope?
Experimental investigations, 2011-14
37
How can we measure the envelope?
• Literature Review
• Advantages of photogrammetric monitoring techniques includes:
• Simultaneous measurement of many points
• Non-contact • Small and inexpensive
targets • Relatively less expensive • Scalable
Ronnholm et al., The Photogrammetric Record, 2009
Albert et al., 2nd Symposium on Geodesy for Geotechnical and Structural Engineering, 2002 38
How can we measure the envelope?
Control points
Monitoring points
39
Displacement
Image number
How can we measure the envelope?
• Some studies have used the same approach for monitoring vibration, by increasing the rate at which images are taken (temporal resolution) to many per second.
Displacement
Image number
40
How can we measure the envelope?
• Current sensor hardware requires a compromise between image resolution and temporal resolution (rate at which images are taken).
• Real-time monitoring only possible at reduced image resolution
Image resolu?on
Tempo
ral resolu?
on
Consumer)DSLR)
16#MP#
<5#fps#
££#
Consumer)Camcorder)
2"MP"(1080p)"
30/60"fps"
££"
Specialist*Sensors*
15+$MP$ 0.5$MP$
30$fps$ 1000$fps$
£££££$41
How can we measure the envelope?
• Literature Review Vehicle speed
detection
Lin, Li, & Chang, Image and Vision Computing, 2008
Measuring vibration of computer circuits
Wang et al., Pattern Recognition Letters, 2007
Measuring motion of sports balls
Caglioti & Giusti, Computer Vision and Image Understanding, 2009
Blurred images for…
42
Spacecraft guidance systems
Xiaojuan & Xinlong, Acta Astronautica, 2011
How can we measure the envelope?
High speed imaging
Proposed: Long-exposure image, deliberately blurred
• Advantages • Allows measuring the
envelope of the dynamic response
• Higher image resolutions • No temporal resolution
limitation • Less image data • Frequency independent 43
How can we measure the envelope?
0
50
100
150
200
250
0
255
35
80
30
35
40
45
50
55
60
65
70
75
80
0
50
100
150
200
250
0
255
diameter = d vibra?on < d vibra?on > d
How does a blurred target look like?
44
How can we measure the envelope?
Accuracy ≅ 1 pixel Sub-pixel accuracy
45
How can we measure the envelope?
model structure
shake table
control points
measurement points accelerometer
signal amplifier
input/output device
laser displacement gauge
46
How can we measure the envelope?
• 50 points/image • horizontal scale x15
5 Hz
1st Mode: 5 Hz 2nd Mode: 8 Hz 3rd Mode: 12 Hz
47
How can we measure the envelope?
110 120 130 140 150 160 170
-20
-15
-10
-5
0
5
10
15
20
25
Dis
plac
emen
t (m
m)
Time (s)
• Full-scale case study • Wilford bridge, Nottingham • ~70m span suspension footbridge
Laser Doppler vibrometer (courtesy of Polytec Ltd)
Proposed image processing
48
How can we measure the envelope?
0.20.4
0.6
0.2
0.4
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
xy
z
0.20.4
0.6
0.20.4
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
xy
z
0.20.4
0.6
0.2
0.4
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
xy
z
1st mode (5 Hz) 2nd mode (8 Hz) 3rd mode (12 Hz)
Unm
odifi
ed st
ruct
ure
(a)
Mod
ifica
tion
1 (b
) M
odifi
catio
n 2
(c)
0.5 0.6 0.7 0.80
0.10.2
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
xy
z
0.5 0.6 0.7 0.80
0.10.2
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
xy
z
0.5 0.6 0.7 0.800.1
0.2
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
xy
z
0.5 0.6 0.7 0.800.1
0.2
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
xyz
0.5 0.6 0.7 0.80
0.10.2
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
xy
z
0.5 0.6 0.7 0.800.1
0.2
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
xy
z
• 3D effects of structural modifications
Added mass
Standard member
Reduced stiffness member (back of model)
Unmodified Modification 1 Modification 2
49
Part-3 Conclusions
• Novel approach to identifying vibration patterns in civil engineering structures using long-exposure images
• Targets appear blurred because of the motion of the structure
• The vibration envelope is recorded, not the instantaneous deformed shapes • Sensors with higher image resolutions can be used
• High-quantity measurements achieved in both laboratory and field tests
• The approach can also be used to detect structural changes
• The proposed frequency-independent approach expands the capabilities of existing sensors
• Otherwise restricted by their imaging frequency
McCarthy, Chandler & Palmeri, Photogrammetric Record, Under review
50
Final Remarks
• Part-1: Concrete-steel partial interaction and vehicle-bridge dynamic interaction can be represented efficiently with the proposed analytical formulation for the dynamics of composite bridges
• Part-2: A numerical study has shown a promising level of sensitivity to damage for the envelope of the dynamic response of composite bridges subjected to moving loads
• Part 3: Experimental investigations have confirmed that long-exposure digital images can be used to measure the envelope of 2D and 3D structural vibrations with good accuracy (sub-pixel)
51
Acknowledgments
52
Stavros Kasinos Loughborough University
Dr Mariateresa Lombardo Loughborough University
David McCarthy Loughborough University
Prof Jim Chandler Loughborough University
References
• J Albert, HG. Maas, A Schade & W Schwarz, Pilot studies on photogrammetric bridge deformation measurement, 2nd Symp on Geodesy for Geotechnical and Structural Engineering, Berlin, May 2002
• L Frýba, Vibration of Solids and Structures Under Moving Loads, 3rd Ed., Thomas Telford,1999 • S Kasinos, A Palmeri & M Lombardo, Using the vibration envelope as damage-sensitive feature in
composite beam structures, Structures, In press • DMJ McCarthy, JH Chandler & A Palmeri, Monitoring dynamic structural tests using image deblurring
techniques, 10th Int Conf on Damage Assessment of Structures, Dublin, July 2013 • DMJ McCarthy, JH Chandler & A Palmeri, Monitoring 3D vibrations in structures using high resolution
blurred imagery, The Photogrammetric Record, Under review • G Muscolino, A Palmeri & A Sofi, Absolute versus relative formulations of the moving oscillator problem,
Int Journal of Solids and Structures 46: 1085-1094, 2009 • G Muscolino, A Palmeri & A Sofi, Random fluctuation of internal forces in rough beams under moving
oscillators, 10th Int Conf on Structural Safety and Reliability, Osaka, September 2009 • NM Newmark, CP Siess & IM Viest, Test and analysis of composite beams with incomplete interaction.
Proc of the Society of Experimental Stress Analysis 9: 75-92, 1951 • A Palmeri, Vibration of slender composite beams with flexible shear connection under moving oscillators,
10th Int Conf on Recent Advances in Structural Dynamics, Southampton, July 2010 • P Rönnholm, Comparison of measurement techniques and static theory applied to concrete beam
deformation, The Photogrammetric Record, 24: 351-371
53