Monitoring Structural Damage in Complex Connections Using a Wave Vibration Approach

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Monitoring Structural Damage in Complex
Connections Using a Wave Vibration Approach C.
Mei  Department of Mechanical Engineering Univers
ity of Michigan-Dearborn 4901 Evergreen Road,
Dearborn, MI 48128, USA cmei_at_umich.edu
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• Non-Destructive Structural Health Monitoring

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Vibration Waves
Vibrational waves propagate along a waveguide and
are reflected and transmitted at a
discontinuity.
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Wave Vibration Description

• Bending waves
• containing propagating and decaying components
• Longitudinal waves
• containing propagating components only
• Torsional waves
• containing propagating components only.

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Bending Waves in Euler-Bernoulli Beams
Assuming time harmonic motion and using
separation of variables, one has
is the transverse wavenumber.
where
The responses consist of four wave components
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Propagation, Reflection, and Transmission of
Bending Waves
Propagation
Discontinuity
Boundary
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Longitudinal/Torsional Waves in Beams
Again assuming time harmonic motion and using
separation of variables, one has
where
are the longitudinal
and
and torsional wavenumbers respectively.
Both responses consist of two wave components
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Propagation, Reflection, and Transmission of
Longitudinal/Torsional Waves
Propagation
Discontinuity
Boundary
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• A structural damage, either along a structural
  element or at a structural joint, forms a
  discontinuity to an incoming vibration wave

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Wave Reflection and Transmission at a Structural
Damage
The transmitted and reflected waves are related
to the incident wave by the transmission and
reflection matrices t and r
t and r can found through the continuity and
equilibrium conditions at the crack damage.
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Numerical Examples

• A 1020 cold-rolled steel beam element was chosen
  as an example structure. The width and the depth
  of the beam are 1.0 inch (2.54 cm) and 0.5 inch
  (1.27 cm) respectively. The length of the beam is
  approximately 6.0 feet (182.88 cm). The material
  properties are Youngs Modulus 206 GN/m2, mass
  density 7800 mg/m3, shear modulus 77.5 GN/m2,
  Poissons ratio 0.29, and shear coefficient

The crack was modeled using the approach
described by Chondros T. G., Dimarogonas A.
D., and Yao J., A Continuous Cracked Beam
Vibration Theory, Journal of Sound and
Vibration, 215(1), pp. 17-34. 1998.
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Transmission Coefficients of a Cracked Structural
Element
Green 0 Blue 10 Red 20 Cyan 30
Yellow 40 Magenta 50 Black 60 (Solid
lines Timoshenko model Dotted lines
Euler-Bernoulli model)
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Reflection Coefficients of a Cracked Structural
Element
Green 0 Blue 10 Red 20 Cyan 30
Yellow 40 Magenta 50 Black 60 (Solid
lines Timoshenko model Dotted lines
Euler-Bernoulli model)
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Experimental Setup for Testing a Damaged
Structural Element
(The crack damage is created using saw cuts.)
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Wave Reflection Characteristics at a Damaged
Structural Element
With free-free boundaries
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Wave Reflection Characteristics at a Damaged
Structural Element
With both boundaries inserted into sand boxes
The responses show that the reflection
coefficients increase with the increase of crack
sizes. This indicates that the occurrence and
severity of a crack along a structural element
can be detected by monitoring the vibration wave
reflection characteristics.
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Wave Transmission Characteristics at a Damaged
Structural Element
With both boundaries inserted into sand boxes
The responses show that the transmission
coefficients decrease with the increase of crack
sizes. This indicates that the occurrence and
severity of a crack along a structural element
can be detected by monitoring the vibration wave
transmission characteristics.
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Experimental Setup for Testing a Damaged
Structural Joint
To study a damaged structural joint, an L-shaped
beam was formed by welding two beam elements
together. A saw cut was then created on the
angled joint.
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Wave Reflection Characteristics at a Damaged
Structural Joint
With both boundaries inserted into sand boxes
The responses show that the reflection
coefficients increase with the increase of crack
sizes. This indicates that the occurrence and
severity of a crack along a structural element
can be detected by monitoring the vibration wave
reflection characteristics.
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Wave Transmission Characteristics at a Damaged
Structural Joint
With both boundaries inserted into sand boxes
The responses show that the transmission
coefficients decrease with the increase of crack
sizes. This indicates that the occurrence and
severity of a crack along a structural element
can be detected by monitoring the vibration wave
transmission characteristics.
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Concluding Remarks
In this research, a vibration-based monitoring
process is proposed that adopts a different
viewpoint than modal-based methods currently
practiced. A structural health monitoring
strategy from a wave vibration standpoint for
complex structures containing localized damage is
examined both analytically and experimentally.
The study finds that such a local vibration wave
reflection and transmission based approach can
detect cracks in the millimeter range, regardless
whether the crack is along a structural element
or at a structural joint. The proposed research
lays the foundation for developing a
cost-effective, convenient, and practical
approach in health monitoring of complex built-up
structures.
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• This material is based upon work supported by
  the National Science Foundation under Grant No.
  0539187. Any opinions, findings, and conclusions
  or recommendations expressed in this material are
  those
• of the author and do not necessarily reflect the
  views of the National Science Foundation.)