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________________
Corresponding author: T.Sunil Kumar
E-mail address: [email protected]
Doi:http://dx.doi.org/10.11127/ijammc.2013.02.087
Copyright@GRIET Publications. All rights reserved.
Advanced Materials Manufacturing & Characterization Vol 3
Issue 1 (2013)
Advanced Materials Manufacturing & Characterization
journal home page: www.ijammc-griet.com
Free Vibration Analysis of a Cracked Composite Beam
T.Sunil Kumar1, K.Durga Rao2, M.M.M.Sarcar3, B.S.K.S.Rao4
1&2Vignan University, Vadlamudi, Guntur, Andhra pradesh –
522 213 3&4A.U. College of Engineering, Andhra University,
Visakhapatnam, A. P.
A R T I C L E I N F O Article history: Received 12Nov 2012
Accepted 26 Dec 2012 Keywords: Freevibration, timedomain, frequency
domain,
crack.
Introduction
A B S T R A C T The issue of crack detection and diagnosis has
gained wide spread industrial interest. Identification of crack
depths and their location from reference point are the standard
methods in performance monitoring of the composite beam. The
present work introduces an attempt to study the variations in the
Eigen-nature of cracked composite beam at different crack depths
and locations. The composite beam with edge crack is considered in
the paper. The presence of crack changes the physical
characteristics of a structure which in turn alter its dynamic
response characteristics. The frequency, amplitude and acceleration
of cracked and uncracked beam response was determined
experimentally. Analysis is carried out in both time and frequency
domains, which is aimed to identify the dynamic response associated
with the existence of crack
Surface cracks and edge crack are the frequently occurring
phenomena in the structures of engineering applications. The effect
of these cracks on the performance of the structure is more severe
and complex when the structure is made of composite material.
Identification of various parameters pertaining to cracks like
depth, distance form reference point are part of the standard
methods in performance monitoring of the structure [1]. Currently
available non-destructive testing (NDT) methods, such as acoustic
or ultrasonic methods, magnetic field methods, radiographs,
eddy-current methods and thermal field methods are time consuming
when compared to induced vibration techniques [2]. Many procedures
are proposed in this line and developed for isotropic materials.
But for composite materials very limited data is available in
identification and analysis of cracks.The presence of crack in a
structural member introduces a local flexibility that affects its
vibration response [3]In this case the system is non linear
moreover the presence of crack introduces new harmonics in the
spectrum. The papers [4-6] on this method were published in the
recent years. Some information on analytical, numerical and
experimental investigations now exits. Finite element analysis
techniques [7-10], together with experimental results are used to
detect
damage. They locate and estimate damage events by comparing
dynamic responses between damaged and undamaged structures.
According to the dynamic response parameters analyzed, these
methods can be subdivided into modal analysis, frequency domain,
time domain and impedance domain. Model-dependent methods are able
to provide global and local damage information [11]. They are
cost-effective and are relatively easy to operate. However, there
are still many challenges and obstacles before these methods can be
implemented in practice Preparation of composite material A manual
fabrication process is involves building up layers of chopped glass
mat impregnated with catalyzed resin around a suitable mold. The
reinforcement is then rolled for better wet-out and removing
trapped air. The crack will be made by using a saw cut and the
specimen will be mounted for cantilever configuration.
Material Properties and Dimensions
The test specimen is a laminated of composite beam dimensions
200 mm X 24.5 mm and thickness 8.5 mm. The total numbers of layers
are 9 and Ply angles are 0/0/0/0/0/0/0/0/0/0. The material
properties are as follows: Elastic modulus of fiber =18.66 GPa,
Elastic modulus of matrix =3 GPa, Density of fiber = 1.7 gm/cm3,
Density of matrix = 1.1 gm/cm3,density of the composite material =
1.4 gm/cm3, Volume
mailto:[email protected]://dx.doi.org/10.11127/ijammc.2013.02.087
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fraction fiber = 0.50%, Volume fraction matrix=0.50%, Poisson’s
ratio of fiber = 0.2, Poisson’s ratio of matrix= 0.3
Experimental Setup
The experimental apparatus is shown in Fig.1and 2. The specimen
was mounted on clamping and excited by 5800b Dynapulsetm impact
hammer, with a force transducer built into the tip to register the
force input. The vibrations are induced by impulse force hammer
will be used to induce impact loads. The beam response is being
sensed by SAA-1150-1000 Single axis piezoelectric accelerometer and
the captured signal will be processed by an FFT analyzer. A
personal computer outfitted with NI 9234 integrated hardware and
software (smart office) functions as data acquisition system and
multi channel fast Fourier transform signal analyzer. The analog
signals from each piezoelectric sensor will be converted from time
domain to frequency domain by fast Fourier transform. Different
frequency spectra will be obtained from different successive
mechanical impulses and will be electronically averaged to form a
single spectrum, so that the random variation inherent to the
method could be evaluated. The variation in the output signal
parameters will be analyzed for different crack locations and
depths.
Fig.1. Experimental setup formed for free vibration testing
Fig.2. Schematic layout of experimental setup
Result and discussion
The time domain and Frequency response function of laminated
composite beams have been measured and analyzed for different crack
locations and depths. The three crack location and different crack
depths for a single edge of the specimen are considered. The
experiment is carried crack location at 50mm, 100mm, 150mm from
fixed end position, and different crack depths. The data
acquisition time is 0.4 sec and band width is 1000 Hz. The
experimental natural frequencies are measurements against the
different states of crack.
Time Domain
The time domain shows time Vs magnitude (acceleration) graphs.
The input force is in the range of 0.2N to0.3N for all cases.
Appreciable variation in sinusoidal wave decay is observed for
uncracked and state of crack as shown in Figs from 3to 12.
Fig.3.Without Crack Distance of the crack from fixed end = 50
mm
-3 0
-2 0
-1 0
0
1 0
2 0
3 0
4 0
0 0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5
Am
pli
tud
e (
g)
T im e (s e c )
5 0 m m le n g th 2 m m d e p th
Fig.4. Depth of the crack = 2mm
-3 0
-2 0
-1 0
0
1 0
2 0
3 0
4 0
0 0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5
Am
pli
tud
e (
g)
T im e (s e c )
5 0 m m le n g t h 3 m m d e p th
Piezo Electric Accelerometer
DAQ Computer
(Smart Office)
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461
Fig.5. Depth of the crack = 3mm
-3 0
-2 0
-1 0
0
1 0
2 0
3 0
4 0
0 0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5
5 0 m m le n g h t 4 m m d e p th
Am
pli
tud
e (
g)
T im e (s e c )
Fig.6. Depth of the crack = 4mm
Distance of the crack from fixed end = 100 mm
Fig.7. Depth of the crack = 2mm
Fig.8. Depth of the crack = 3mm
-4 0
-3 0
-2 0
-1 0
0
1 0
2 0
3 0
0 0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5 0 .3 0 .3 5 0 .4
1 0 0 m m le n g th 4 m m d e p th
Am
pli
tud
e (
g)
T im e (s e c )
Fig.9. Depth of the crack = 4mm
Distance of the crack from fixed end = 150 mm
-3 0
-2 0
-1 0
0
1 0
2 0
0 0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5 0 .3 0 .3 5 0 .4
Am
pli
tud
e (
g)
T im e (s e c )
1 5 0 m m le n g th 2 m m d e p th
Fig.10. Depth of the crack = 2mm
-3 0
-2 0
-1 0
0
1 0
2 0
0 0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5 0 .3 0 .3 5 0 .4
1 5 0 m m le n g th 3 m m d e p th
Am
pli
tud
e (
g)
T im e (s e c )
Fig.11. Depth of the crack = 3mm
-3 0
-2 0
-1 0
0
1 0
2 0
0 0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5 0 .3 0 .3 5 0 .4
1 5 0 m m le n g th 4 m m d e p thA
mp
litu
de
(g
)
T im e (s e c )
Fig.12. Depth of the crack = 4mm
Frequency response function (FRF)
Frequency response is the quantitative measure of the output
spectrum of a system or device in response to a stimulus, and is
used to characterize the dynamics of the system. The frequency
response shows frequency Vs magnitude graphs as shown in Figs from
14 to22.
Fig.13. Without crack Distance of the crack from fixed end = 50
mm
http://en.wikipedia.org/wiki/Frequency_spectrum
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Fig.14. Depth of the crack = 2mm
Fig.15. Depth of the crack = 3mm
Fig.16. Depth of the crack = 4mm
Distance of the crack from fixed end = 100 mm
Fig.17. Depth of the crack = 2mm
Fig.18. Depth of the crack = 3mm
Fig.19. Depth of the crack = 4mm
Distance of the crack from fixed end = 150 mm
Fig.20. Depth of the crack = 2mm
Fig.21. Depth of the crack = 3mm
Fig.22. Depth of the crack = 4mm
The highest natural frequencies in above graphs are tabulated in
table 1
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463
Table 1: Natural frequency for state of crack
Crack location (mm) from fixed end
Crack depth(mm) Frequency(Hz)
50
2 465
3 464
4 463
100
2 450
3 449
4 449
150
2 448
3 447
4 446
From the Fig.13, it is observed the natural frequency of
uncracked is 450Hz. The various states of cracks in beam changes
its Eigen nature of beam as shown in Table 1. The trend follow of
results satisfies the literature.
Conclusion
In the present work, an investigation into the Eigen-nature of a
cracked composite beam is investigated experimentally. The natural
frequency for transverse vibration of cracked and uncracked beams
are compared. The results obtained from the experiments are
presented in graphical form. From the experiments presented in this
paper, the following conclusions are obtained.
1. Results show that there is an appreciable variation between
natural frequency of uncracked and state of crake in cantilever
composite beam.
2. The crack depth increase the natural frequency is
decreases.
3. The crack location is increases from fixed end, the natural
frequencies are decreased.
The present study provides an efficient nondestructive technique
for the detection and prediction of the current state of the crack
for any composite structure system.
References
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