DAMAGE ASSESSMENT IN A WALL STRUCTURE USING RESONANT FREQUENCIES AND OPERATING DEFLECTION SHAPES

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International Journal of Mechanical Engineering and Technology (IJMET)
Volume 8, Issue 3, March 2017, pp.
Available online at http://www.iaeme.com/IJME
ISSN Print: 0976-6340 and ISSN Online: 0976
© IAEME Publication
DAMAGE ASSESSMENT IN
STRUCTURE USING
FREQUENCIES AND OPER
DEFLECTION SHAPES
Department of Mechanical Engineering
ABSTRACT
This paper describes the application of vibration modal analysis for
monitoring and locating damage inside a wooden wall structure, by evaluating
damage-sensitive parameters such as resonant frequencies
shapes (ODS). Artificial damage was created in one of the walls of a specially
constructed room. The wall was excited using an impact hammer and its frequency
response was measured with a laser vibrometer. Damage
extracted from the frequency response and utilized for assessing damage, both
qualitatively and quantitatively. Resonant frequency shifts and changes in ODS were
used for detecting and monitoring the progression of damage, qualitatively. These
methods make direct use of FRF data
will help a lot in identifying da
Key words: Resonant Frequency, Operating Deflection Shape, Structural Damage
Assessment, Experimental Modal Analysis
Cite this Article: Prakash Jadhav, Damage Assessment In A
Resonant Frequencies and Operating Deflection Shapes
Mechanical Engineering and Technology
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1. INTRODUCTION
Wooden homes are very commonly used in western countries and internal invisible damage in
the load carrying wooden members is a very common problem. This internal
mostly caused by termites or in some cases ageing or due to some shock/impact loadi
occurred during any repair work/building work happened nearby. It is very important to
assess this damage (identify and locate) in order to increase the life of homes. This paper is an
attempt to develop a simple technique to do that.
assessing damage in structures [1
structure and is not visually apparent. Other damage detection techniques such as ultrasonic
IJMET/index.asp 97 editor@iaeme.com
International Journal of Mechanical Engineering and Technology (IJMET)
2017, pp. 97–107 Article ID: IJMET_08_03_011
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6340 and ISSN Online: 0976-6359
Scopus Indexed
DAMAGE ASSESSMENT IN A WALL
STRUCTURE USING RESONANT
FREQUENCIES AND OPERATING
DEFLECTION SHAPES
Prakash Jadhav
Department of Mechanical Engineering
CMRIT, Bangalore, India
This paper describes the application of vibration modal analysis for
sensitive parameters such as resonant frequencies and operating deflection
Artificial damage was created in one of the walls of a specially
ucted room. The wall was excited using an impact hammer and its frequency
measured with a laser vibrometer. Damage-sensitive parameters were
tatively. Resonant frequency shifts and changes in ODS were
methods make direct use of FRF data and mode shapes for damage assessment, w
will help a lot in identifying damaged walls.
Resonant Frequency, Operating Deflection Shape, Structural Damage
Assessment, Experimental Modal Analysis
Prakash Jadhav, Damage Assessment In A Wall Structure Using
Resonant Frequencies and Operating Deflection Shapes. International Journal of
Mechanical Engineering and Technology, 8(3), 2017, pp. 97–107.
com/IJMET/issues.asp?JType=IJMET&VType=8&IType=3
the load carrying wooden members is a very common problem. This internal
mostly caused by termites or in some cases ageing or due to some shock/impact loadi
attempt to develop a simple technique to do that. Vibration techniques have been used for
assessing damage in structures [1-4], especially when the damage is located inside the
editor@iaeme.com
T&VType=8&IType=3
A WALL
RESONANT
ATING
This paper describes the application of vibration modal analysis for detecting,
operating deflection
Artificial damage was created in one of the walls of a specially
ucted room. The wall was excited using an impact hammer and its frequency
sensitive parameters were
tatively. Resonant frequency shifts and changes in ODS were
for damage assessment, which
Resonant Frequency, Operating Deflection Shape, Structural Damage
Wall Structure Using
International Journal of
ET&VType=8&IType=3
the load carrying wooden members is a very common problem. This internal damage is
mostly caused by termites or in some cases ageing or due to some shock/impact loading
es have been used for
4], especially when the damage is located inside the

Damage Assessment In A Wall Structure Using Resonant Frequencies and Operating Deflection
Shapes
http://www.iaeme.com/IJMET/index.asp 98 editor@iaeme.com
and x-ray scanning are believed to be cumbersome and expensive. Vibration techniques
provide an inexpensive, fast and reliable method for assessing damage and have the potential
for commercial application. Several vibration-related procedures have been suggested for
detecting the existence and monitoring the progression of damage. One simple approach
consists of comparing and monitoring resonant frequency shifts, which was also utilized in
this paper as a preliminary study. Most vibration-related methods utilize the modal data at
resonance as a parameter for damage assessment [5-7]. This requires a complete modal
analysis to be performed for each successive damage stage and is time-consuming. A faster
qualitative approach would be to compare the operating deflection shapes (ODS). In this
approach, the modal curve-fitting process is needed only for the base line case. Visual
interpretation of changes in the ODS of successive stages is used for damage detection.
The methods reported in this paper require a baseline/reference vibration response of the
test structure to be acquired experimentally first. This baseline/reference simply provides a
basis for comparison and need not be for the undamaged condition only. If successful, this
technique can be applied to any kind of wall structure including concrete ones.
2. EXPERIMENTAL SETUP
To simulate realistic conditions, an enclosed room: 2.45 m (height) × 2.1 m (width) × 1.95 m
(depth) with 2×4 wooden columns and gypsum plaster board, was used. This room was
constructed inside a laboratory in the same manner as a typical wall in buildings and houses,
where non-uniform column spacing and inconsistent usage of nails in walls are commonly
encountered. The gypsum board is 1.2 cm thick, and each wooden column is 3.8 cm thick and
8.5 cm wide. The primary focus of this experiment is not the entire room but only one of the
four walls, as shown in Fig. 1. The wall of interest, measuring approximately 2.45 m × 1.95
m, has a total of 6 vertical wooden columns (A to F). Nails were shot along the four corners
of the room using a nail-gun. For the wall of interest, nails were also used to secure the base
to the ground; one between columns B and C and the other between columns D and E.
Figure 2 shows the complete experimental setup for performing modal analysis. Data
acquisition was performed using the Model 20-42 DSPT SigLab from Spectral Dynamics
Corporation. It has good bandwidth up to 20 kHz range and a 3200-resolution line capability.
The impact hammer was used to excite the structure and its vibration response picked up
using a laser vibrometer. The force transducer used for input excitation is a PCB Piezotronic
Model #086B01 Impulse Force Hammer with a force range of 0 to 100 lbf. A metal tip is
attached to the hammer-head for exciting a wider range of frequencies. For measuring
velocity, a Polytec laser vibrometer was used. The system consists of a Model #OFV-350
optical head and a Model #OFV 2600 controller. The vibrometer was located approximately
60 cm from the target and its sensitivity set to 25 (mm/s)/V. The hammer was connected to
channel 1 of SigLab through a signal amplifier unit and the vibrometer was connected directly
to channel 4. The SigLab system was interfaced with a laptop computer via a PCMCIA card.
Data was collected using a bandwidth of 0 to 200 Hz with a resolution, ∆f of 0.5 Hz (800
blocks and 0% overlap). Force-exponential window was used to minimize leakage. Post-
processing of the data like curve-fitting, animating mode shapes and ODS of the wall
structure was performed using the ME’ scope VESTM
vibro-acoustic software. Global curve
fitting using Rational Fraction Polynomial (RFP) method was utilized for parameter
extraction.
The wall was discretized into a total of 42 equidistant grid points, as shown in Fig. 1. All
the points were located along the length of the wooden columns. Initial measurements were
obtained at several locations with the laser and compared to determine the point where most
resonant peaks appear (in the FRF). If the reference response (laser) is located at a nodal point

Prakash Jadhav
of one or several resonant modes, the transducer will pick up minimal response associated
with that particular mode. As such, the laser beam from vibrometer was targeted at point #21
(an arbitrary point where response appeared to be acceptable) on the outside of the room.
Trial runs indicated no difference in response, whether the room was impacted from inside or
outside. For convenience, the wall was impacted from the outside. The procedure for
performing modal analysis is elaborated by Avitable [8].
Figure 1 Model of the wall with simulated damage
Figure 2 Experimental setup for acquiring FRF data
3. PROCEDURE
Once all calibration was completed, the impact hammer was used to tap each of the 42 grid
points sequentially. The force and velocity responses were picked up by the hammer and
vibrometer respectively, and processed into frequency response function (FRF) curves using
the Fast Fourier Transform technique via SigLab. FRF is simply the ratio of the output

Shapes
response i.e. velocity or acceleration of a structure due to input excitation force. The FRF data
was then exported to ME’scopeVESTM
for post-processing. A baseline/reference FRF data set
was obtained for the wall before artificial damage was introduced. The coherence of all points
was checked to ensure that the quality of frequency measurement is acceptable. Coherence is
a measure of how much output is caused by the input excitation and not by noise or other
disturbances that could cause inaccuracies in the data. The coherence data also shows the
linearity between two measurements. An acceptable measurement would have a coherence
value of close to ‘1’ over the frequency range of interest. It was observed that coherence data
for points located at the boundary is poor, and therefore not used in the analysis. It is
suspected that the low values of coherence at the boundary might result from non-linearity
between the force (hammer) and velocity data.
Next, three separate progressive stages of damage were induced (holes simulating termite
infestation) in the wooden columns (Fig. 1) using a hand-drill. It should be noted that damage
simulation using hand drill causes loss in mass. The first-level damage was created along
column-D between grid points #28 to #34. Second-level damage was induced along column-B
between grid points #8 to #14. For the third-level, additional damage was created between
grid points #21 to #39, from the base of column-C up to a height of approximately 110 cm.
The level of damage created (or in other words, the amount of material removed) was
approximately quantified to be 3% for the 1st
level case, 6% cumulative damage for the 2nd
level, and 14% cumulative damage for the 3rd
level case. This percentage value is obtained by
roughly estimating the portion (length) of damaged section over the total length of all the
wooden columns inside the wall. All the 42 grid points were re-impacted for each successive
level of damage and the response was acquired with the non-contact laser vibrometer. Testing
was performed under ambient room conditions, with temperature and relative humidity
between 22-24°C and 70-72%, respectively. These conditions were assumed to be constant
throughout data acquisition process. Post analysis was performed using the ME’scopeVESTM
vibro-acoustic software [9], to extract damage-sensitive parameters for detecting and locating
the damage region. The methodology and results obtained using both the qualitative and
quantitative techniques are described in the following sections.
4. RESULTS AND DISCUSSION
4.1. Frequency Shifts
As mentioned, post processing and data extraction from the FRFs was performed using
ME’scopeVESTM
. Narrowband global curve fitting using Rational Fraction Polynomial (RFP)
method was used to obtain the dynamic properties i.e. resonant frequencies, damping and
mode shapes. The first twelve modal frequencies obtained using the laser vibrometer are
tabulated in Table 1. Resonant modal frequencies are represented by peaks in the FRF curve
as shown in Fig. 3, for the baseline case at driving point. Driving point is the point where the
impact location and reference response (laser) are coincident. Each peak represents one mode
of vibration.
As mentioned, a total of three cumulative levels of damage were induced. It is expected
that the resonant frequencies drop as damage is induced, since frequency is proportional to
stiffness, as shown by the generalized expression below [10]:
∫
∫
= L
L
n
dxxwA
dx
dx
xwd
k
0
2
0
2
2
2
))((
)
)(
(
ρ
ω
(1)

Prakash Jadhav
where ωn, k, ρ, L and A are the natural frequency, stiffness, density, dimension, and cross
section area of the structure respectively, and w(x) is the mode shape function. Fig. 4 shows a
plot of the baseline, 2nd
level and 3rd
level FRF (at driving point) superimposed together. It
was observed that the frequencies drop as successive damage was created.
Presence of damage lowers the structural stiffness, thus causing a reduction in resonant
frequencies. However, some types of damage like drilling as in this case, also cause mass
reduction. Although mass plays a role, it is expected that the effect of damage on stiffness is
generally greater than the mass effect [11]. In cases where mass is reduced significantly
without much change to stiffness, the structure’s flexural resonant frequencies may show an
increase after damage induction. This is when the mass effect is more dominant than the
stiffness effect. One example is when damage (by drilling) is formed at the neutral axis of the
2×4 wooden beam, which has been demonstrated by the author [12,13]. However, for most
cases where structural damage is significant, the presence and extent of damage may be
monitored through frequency reduction.
The results in Table 1 show that frequency reduction is dependent on two attributes;
magnitude and location of damage. Comparison of frequencies between the baseline and 1st
level damage indicates a slight drop only for some of the frequencies. An increase in
frequencies for some other modes could be attributed to mass and damping effects being more
dominant [7], provided other parameters like temperature and moisture are maintained
constant. Recall that the 1st
and 2nd
level damage (located between grid points #28 to #34 and
#8 to #14, respectively), are relatively smaller in size compared to the 3rd
level. The amount of
damage is almost identical for these two cases, and an inexperienced investigator would
expect that the percentage of decrease in frequency would be equal from 1st
case to 2nd
case,
as it is from baseline to 1st
case (with other parameters assumed unchanged). It is observed,
however, that for most of the modes the magnitude of decrease in frequencies from baseline
to 1st
level case is more than the decrease from 1st
level to 2nd
level case. This means that the
effect of the 1st
level damage on modal frequencies is greater than 2nd
level case, even though
the amount of damage created for both cases is almost identical. Hence, there is another
parameter that affects frequency shifts, besides the amount of damage itself, which would be
the location of the damage region.
Table 1 Damped Modal Frequency, ωd (Hz), for Various Levels of Damage
Mode # Baseline Data
1st
Level
Damage
2nd
Level
Damage
3rd
Level
Damage
1 17.92 16.04 16.03 15.13
2 21.63 21.47 21.67 20.83
3 28.68 28.85 27.81 26.66
4 31.14 31.53 32.03 31.47
5 39.50 39.94 39.38 36.79
6 47.09 45.94 45.88 45.34
7 55.98 54.52 54.53 53.14
8 65.94 62.38 * *
9 71.03 * 66.99 65.52
10 78.60 73.40 73.10 72.81
11 84.18 81.59 82.28 82.97
12 95.79 95.05 93.91 -
* Missing modes

Shapes
Figure 3 FRF curve for the Baseline case at driving point
Figure 4 Superimposed FRF for Baseline and Damaged Case
The dynamic response of the side wall simulates a fixed-pinned configuration and with
damage located at a region of high strain energy density i.e. at the fixed end, the effect on the
dynamic properties would be greater compared to damage located at a lower strain energy
region. 1st
level damage is located at the fixed end while the 2nd
level damage is at the upper-
pinned end having lower strain energy. The effect of location and boundary conditions on the
resonant frequencies of a complex structure (such as this wooden wall), is not as apparent as it
is for a simple 2×4 wooden beam [11, 12]. Also, the extent of damage created for the first two
cases may not be sufficient for dramatically affecting the resonant frequencies.
The modal frequencies for the 3rd
damage case show the greatest percentage reduction
(Table 1). This is because the amount of damage created between grid points #21 to #39, is
approximately three times the amount created for each of the first two damage cases. This
reinforces the concept that more damage would result in a greater reduction in resonant
frequencies. The observations made here indicates that the existence of damage does
influence the modal frequency i.e. modal frequencies decrease due to the presence of damage,
and therefore can be used as a parameter for detecting and monitoring the progression of
damage. The magnitude of this ‘influence’ or in other words, the amount of decrease in
frequencies (for similar sized damage), was also observed to be affected by the damage
location and boundary condition. The highlight of this approach is to use the relative drop in
modal frequencies to detect the presence and monitor the progression of damage. The setback
to this approach is that it is more sensitive to major structural damage, and may not be
successful at detecting minor damage. Also, it should be noted that this study is valid if
temperature and humidity is maintained constant and is assumed to have no contribution. A
study of the affect of these environmental factors is currently under investigation.

Prakash Jadhav
4.2. Comparison of ODS for damage detection
Another qualitative approach for assessing structural damage is a comparison of the operating
deflection shapes (ODS), before and after damage. This approach however, is useful for
detecting the presence of damage and monitoring its progression if the damage is sufficiently
large. ODS is the deflection or deformation of the structure at a given frequency. It should not
be confused with resonant mode shapes, which are an inherent property of the structure and
unique for each mode of vibration, whereas ODS is dependent upon the loading condition.
Mode shapes are dimensionless quantities whereas ODS can be specified in terms of
displacement, velocity and acceleration. The ODS consists of all the modes of vibration
interacting together to give the actual vibration (deformation) behaviour of the structure at a
particular frequency of interest. When the excitation frequency coincides with the natural
frequency, only one dominant mode will characterize the deformation pattern, with the effects
of other modes attenuated and the unique deformation pattern of a resonant mode will appear.
In other words, the mode shape can be considered as a special case ODS at resonance.
If a machine operating at a particular frequency is damaged, one would expect the ODS
before and after damage to be different. This is similar for structural damage. The actual
deformation at a selected frequency would change once damage is present. This is the basis
for utilizing ODS for detecting and monitoring damage, inside the wooden wall. The
advantage of this approach is that complete modal analysis, which includes the mode shape
curve-fitting process, is not required for each successive damage case. The deformation
pattern at any frequency can be used for comparison. For the purpose of this investigation, the
undamaged (baseline) resonant frequencies are taken as the reference frequency, since the
resonant frequencies have already been acquired. The deformation patterns for each
successive level of damage were obtained and compared with each of the baseline reference
frequency mode shapes.
In comparing ODS patterns, the relative change in the ODS pattern between the damaged
case and the undamaged baseline case are monitored. As more damage is introduced into the
structure, the ODS pattern will differ greater, since it will be affected by the contribution of
other modes. The degree of influence of other modes on the ODS pattern is dependent upon
the extent of damage with frequency reducing as damage increases.
The ODS patterns can easily be generated in ME’scopeVESTM
. This is done by drawing
the structure (with grid points) and then assigning the FRFs to the measurement grid points.
ME’scopeVESTM
can then animate the ODS at any frequency. Figs. 5 and 6 show the freeze-
frame ODS for baseline, 1st
level, 2nd
level and 3rd
level damage for Modes 5 and 9,
respectively. The ODS pattern changes as more damage is induced in the structure. The effect
of 3rd
level damage on Mode 9 (Fig. 6) is large enough that it changes the deformation pattern
quite a bit. It can be observed that the ODS of the 3rd
level damage is different from baseline
ODS. This mode is ideal for monitoring the progress of damage, since the change in ODS
between each successive level of damage is obvious. Not all modes, however, can be used for
monitoring, since the presence of damage does not affect all modes equally. A basis for
selecting which modes are affected by damage has been suggested by Khoo [13].
This qualitative approach can be used for detecting the presence of damage provided the
damage is significant. ODS comparisons for minute damage that has little effect on the
deformation pattern is not recommended. Another, disadvantage is that the ODS patterns can
be misinterpreted by different investigators, especially for small damage. Although utilization
of ODS may not be the best approach for damage assessment, ODS patterns are nonetheless a
valuable tool in machine diagnostic and design [14].

Shapes
Fig 5(a): Baseline mode shape @ 39.5 Hz (Mode 5) Fig 5(b): ODS @ 39.5 Hz (Mode 5) 1st
Level Damage
Fig 5(c): ODS @ 39.5 Hz (Mode 5) 2nd
Level Damage Fig 5(d): ODS @ 39.5 Hz (Mode 5) 3rd
Level Damage
Figure 5 ODS comparison of Mode 5 @ 39.5 Hz

Prakash Jadhav
Fig 6(a): Baseline mode shape @ 71 Hz (Mode 9) Fig 6(b): ODS @ 71 Hz (Mode 9) 1st
Level Damage
Fig 6(c): ODS @ 71 Hz (Mode 9) 2nd
Level Damage Fig 6(d): ODS @ 71 Hz (Mode 9) 3rd
Level Damag
Figure 6 ODS comparison of Mode 9 @ 71 Hz
5. CONCLUSIONS
Two qualitative vibration based approaches for assessing structural damage have been
described in this paper. An experimental investigation using an actual wooden wall with
plasterboard was performed to demonstrate the feasibility of these approaches. Data
acquisition was performed using the conventional ‘roving hammer - fixed transducer’ impact
vibration testing. In the qualitative approach, the presence of damage was detected and its
progress monitored by either tracking resonant frequency shifts or visually identifying
changes in the Operating Deflection Shapes (ODS). The presence of damage causes a
decrease in structural stiffness, characterized by a reduction in the resonant frequencies. The
deformation pattern of the undamaged and damaged structure will be different and therefore
can be used for detecting whether additional damage exists or progresses in the structure. For
locating the damage however, new quantitative methods need to be developed which can
précised locate the damage and easier and faster to use.

Shapes
For commercial or large-scale applications, data acquisition by impact testing is time
consuming. When dealing with complex structures, finer discretization or more data points
are needed for improved accuracy and precision in locating damage. It is believed that more
sophisticated instruments like the Scanning Laser Doppler Vibrometer (SLDV) can be
implemented for faster and finer data acquisition. A fully automated damage assessment tool
that utilizes both SLDV and the broadband FRF quantitative approaches presented in this
paper show potential for commercial or large-scale applications. Investigations are currently
ongoing for refining this technique using such sophisticated instrumentation.
ACKNOWLEDGMENT
The part of this work was done by the author in his graduate studies research at the University
of Mississippi and would like to thank Prof PR Mantena and Lay Menn Khoo for their help.
REFERENCES
[1] D.C. Zimmerman, S.W. Smith, H.M. Kim and T.J. Bartkowicz., Spacecraft Applications
for Damage Detection using Vibration Testing, Proceedings of the 14th
International
Modal Analysis Conference, Volume 1, 1996, 851-856.
[2] R. Ahmadian, and P.R. Mantena, Modal Characteristics of Structural Portal Frames Made
of Mechanically Joined Pultruded Flat Hybrid Composite Beams Composite Part B
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[3] S. Alampalli. Modal Analysis of a Fiber-reinforced Polymer Composite Highway Bridge,
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[4] S. Ventakappa, S.E. Chen, E. Aluri and A. Culkin Modal Analysis of a Miniature Model
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Prakash Jadhav
[14] P. Jadhav and P. R. Mantena Analytical and Experimental Assessment of Damage in
Wooden Beams using Vibration Response Measurements, ASME Southeastern Region XI
Technical Journal, 2002, 3.1–3.8.
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[16] H. Vold, B.J. Schwarz, and M.H. Richardson, Display Operating Deflection Shapes from
Nonstationary Data, Sound and Vibration, 2000, 34,14-18

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