Modal Analysis Of Cracked Continuous Beam Using ANSYS

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 02 | Feb -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 86
Modal Analysis Of Cracked Continuous Beam Using ANSYS
1 P. Y. Ghodke, 2 D. H. Tupe , 3 G. R. Gandhe
Department of Civil Engineering, Deogiri Institute of Engineering and Management Studies, Dr. BAMU University,
Aurangabad, Maharashtra, India.
---------------------------------------------------------------------------***----------------------------------------------------------------------
Abstract: In this present work, the important task is to
determine the effect of crack on the beam structure. The
presence of cracks in structure is changes the physical
properties and its dynamics response. The effect on
structure are analysed using ANSYS software and then it
compare with the regression analysis. In vibration
analysis the crack location and crack depth is the main
parameter to determine the natural frequencies and its
changes in mode shape. The natural frequencies is
decreases when increasing the crack depth at same
location of beam. It results the reduction of natural
frequencies and change their mode shape of crack and
without crack beam. ANSYS V15 software is used for FE
analysis of both crack and uncrack simply supported
continuous beam with two different materials one is
structural steel and another aluminium. Creo software is
used to designing of I section simply supported
continuous beam model.
Keywords:- ANSYS, Creo, Natural frequency, Crack,
Modal analysis, Simply supported continuous beam .
INTRODUCTION
Vibration analysis method is a very good approach to
crack detection in beams. All most all types of beam
operated under different kinds of loading conditions,
which may be causes damages and cracks in
overstressed zones. Cracks is also found in mechanical
foundations due to different reasons. Generally in
structural members like beam the presence of crack
causes the reduction in stiffness which is depends on
two parameters; location of crack and depth of the crack.
In now a days it is very important to know whether the
beams is crack free or any crack is present in beam and
to detect the crack position of beam for our safety
purpose. A crack or local defect is affects on the vibration
response of the structural member. It results in the
changes of natural frequencies and its mode shapes of
crack and uncrack structure. Also crack may be classified
on the basis of geometry and its orientation as cracks
parallel to shaft axis are known as longitudinal cracks,
cracks that are open and close when affected part of
material is subjected to alternative stresses are known
as breathing crack, crack which are perpendicular to the
axis of shaft are known as transverse crack, the cracks on
surface which is not visible known as sub-surface crack,
crack which appear on the surface are known as surface
crack.
What is Vibration.
The term vibration describes repetitive motion that can
be measured and observed in a structure. Unwanted
vibration can be causes fatigue or degrade the
performance of the structure. Therefore it is desirable to
reduce the effects of vibration. In other cases, vibration
is not able to be avoided or even desirable. In this case,
the goal is to understand the effect on the structure, or to
control or to modify the vibration, or isolate it from the
structure and minimize structural response.
What is Free Vibration.
Free vibration is the natural response of a structure to
some impact or displacement. The response are
complete determine by the properties of the structure,

and its vibration is be understand by examining the
structure's mechanical properties. For example, when
we pluck a string of a guitar, it vibrates at the tuned
frequency and it generates the desired sound.
LITERATURE SURVEY
P. Amit et al. [1] scrutinized the vibration analysis of
cantilever beam in different location and size of a crack.
They used ANSYS workbench software to get the natural
frequencies of cracked and un-cracked beam. Sharma
P.K. et al. [2] studied in the experiment that the presence
of crack leads to lower the natural frequencies. They
used ANSYS software for FE analysis of both cracked and
un-cracked beam by taking input file as established in
CATIA. Muhannad Al-Waily [3] conducted studies on
cracked of beam with different supports. The analytical
results is reveal the effects of a crack in a continuous
beam and the parameters calculated were the equivalent
stiffness, Youngs modulus and moment of inertia for a
rectangular beam is to involve an exponential function
with depth and location of crack effect, with the solution
of assuming equivalent stiffness of the beam (EI) by
using of Fourier series method. And, the beam materials
are studied were low carbon steel, Alloys Aluminium,
and Bronze materials with different beam length and
different depth. A comparison made between the
analytical results from theoretical solution of general
equation of motion of beam with crack effect with
numerical by ANSYS results, where the biggest error
percentage is about the (1.8 %). Ertugrul Cam et. al. [4],
was presented information about the location and depth
of cracks in cracked beams. For this purpose, vibrations
as the result of impact shocks were analyzed. The signals
are obtained in defect-free and cracked beams were
compared in the frequency domain. The results of a
study suggest to determine the location and depth of
cracks by analyzing the from vibration signals.
Experimental results and simulations obtained by the
software ANSYS are in good agreement. Yamuna and
Sambasivarao [5] concluded from their study that the
lowest natural frequency achieved at the mid span of
simply supported beam and rises from there on. Jagdale
and Chakrabarti [6] presented free vibration study of a
beam with open edge crack. They found that the natural
frequency fluctuates due to cracks at various crack
position and depth. Hai-Ping Lin [7] has studied an
analytical transfer matrix method, is used to solve direct
and the inverse problems of simply supported beams
with an open crack. The crack is modeled as the
rotational spring with sectional flexibility. The natural
frequencies of a cracked system can easily be obtained
through many of the structural testing methods. When
any two natural frequencies of a cracked simply
supported beam are obtained from measurements, the
location and a sectional flexibility of the crack can then
be determined from the identification equation and the
characteristic equation.
3. Finite Element Model Using ANSYS
In the present research the ANSYS is used as a tool to
model and simulate a beam with a crack, to observe the
variation in its vibrational characteristics. The beam
model is design in software such as creo and it is
imported to ANSYS workbench for the analysis. Now,
after importing the model file, its geometry is modify and
divide the entire structure into meshes by using FEM
and has been solved for the modes of frequencies. The
meshing size is increases so that it uniformly covers the
entire structure. After the model is properly mesh and
solve by using FEM, the various frequency values is
obtaine for a particular combination of crack location
and depth.
The above procedure is detailed as follows.
1. Double click on workbench. Import geometry
from solid works file saved in solid works as
IGES file.

2. Modify geometry, click on mesh, and increase
the meshing size and select meshing type.
3. Provide free support .
4. Apply pressure or load.
5. Click on solve.
6. Click on deformation.
A. Design of Simply supported continuous Beam
without crack
The model of simply supported continuous beam has
been design in ANSYS for frequency analysis. The length
(L),width (W) and depth (D) of the beam are considered
as 3000 mm, 140 mm and 275 mm respectively
.Aluminium alloy and mild steel is taken as the material
for the simply supported continuous beam and its
properties taken as for aluminium Young's modulus as
71 GPa, Poisson's ratio as 0.33 and density as 2700
kg/m3.For steel Young's modulus as 200 GPa, Poisson's
ratio as 0.3 and density as 7850 kg/ The simply
supported continuous beam considered for modeling in
ANSYS is shown in Fig.
B. Design of Simply supported continuous Beam with
Crack
A triangular crack is considered having original
dimension of 6mm width. The initial location of the crack
is taken at middle 1500 mm from one end of the simply
support beam. The crack depth is taken as 3mm mm and
later on the depth increases to 6mm, 9mm, 12mm and
15mm respectively. The cracked simply supported
continuous beam with the volumetric model built in
ANSYS is shown in Fig.
4. Modal Analysis of Simply supported
continuous Beam with Crack and without Crack
A triangular crack is introduced in the simply supported
continuous beam model for frequency analysis. Initially
the triangular crack is assumed to be located at middle of
beam model. The first five natural frequencies of the
simply supported continuous beam are obtained in
ANSYS. The crack depth of beam varies at middle of the
simply supported continuous beam. The Relative natural
frequency for various crack depth with respect to same
crack location of the beam respectively.
A] Analysis of structural steel beam
The modal analysis of structural steel I section simply
supported continuous beam Without crack and crack is
done to determine its natural frequency with various
mode.
Analysis of simply supported continuous beam
without crack.
Table 1 Frequencies of structural steel without crack
beam
Mode Frequency[Hz]
ANSYS
Frequency[Hz]
Reg. Analysis
1 0.087118 -4.5017
2 35.114 47.6402
3 102.48 92.4307
4 129 129.86
5 158.72 159.95

Mode1
Mode2
Analysis of simply supported continuous beam with
crack.
Table 2 Frequencies structural steel crack beam by
ANSYS
Crac
k
dept
h
3mm 6mm 9mm 12mm 15mm
mod
e
Freq.
[Hz]
Freq.
[Hz]
Freq.
[Hz]
Freq.
[Hz]
Freq.
[Hz]
1 0.06845
1
0.0684
0
0 0 0
2 19.571 19.405 0.0683
8
0.068
3
0.068
2
3 104.87 104.87 104.69 104.4
7
104.3
6
4 125.15 125.13 124.30 123.4
2
123.1
7
5 158.96 158.95 154.80 154.4
5
154.3
4
Table 3 Frequencies structural steel crack beam by
Regrassion Analysis
Crack
depth
mode Freq.
[Hz]
Freq.
[Hz]
Freq.
[Hz]
Freq.
[Hz]
Freq.
[Hz]
1 -
8.149
3
-8.1904 -13.449 -13.32 -13.29
2 41.98
7
41.923
4
35.112
4
34.937
6
34.87
3
3 86.92
43
86.860
4
80.219
9
79.843
6
79.71
4
4 126.6
6
126.62 121.87
6
121.38
8
121.2
3
5 161.1
95
161.20
4
160.08
5
159.57
2
159.4
2
Figures:-Natural frequencies at 3 mm on different mode
Mode 1
Mode 2
Mode 1
Mode 2

Mode 1
Mode 2
Mode 1
Mode 2
Mode 1
Mode 2
b] Analysis of aluminium beam
Analysis of simply supported continuous beam
without crack.
Table 4 Frequencies of aluminium beam without crack
beam
Mode Frequency[Hz]
ANSYS
Frequency[Hz]
Regression
1 0.087371 0.7538
2 43.614 49.32
3 102.93 90.83
4 113.35 123.76
5 151.31 148.119
Mode 1
Mode 2

Analysis of simply supported continuous beam with
crack.
Table 5 Frequencies of Aluminium crack beam by ANSYS
Crac
k
dept
h
mod
e
Freq.
[Hz]
Freq.
[Hz]
Freq.
[Hz]
Freq.
[Hz]
Freq.
[Hz]
1 0 0 0 0 0
2 0.0686
5
0.068
6
0.0685
9
0.0685
6
0.068
5
3 103.33 103.3
2
102.74 102.02 101.7
2
4 114.52 114.4
9
112.64 111.28 110.9
6
5 143.84 143.8
1
143.43 143.41 142.0
1
Table 6 Frequencies of Aluminium crack beam by
Regression Analysis.
Crac
k
dept
h
mod
e
Freq.
[Hz]
Freq.
[Hz]
Freq.
[Hz]
Freq.
[Hz]
Freq.
[Hz]
1 -12.86 -12.86 -12.58 -12.365 -12.37
2 34.53 34.52 34.070
8
33.770
8
33.636
4
3 77.147
3
77.13 76.251
8
75.711
8
75.302
9
4 114.96
3
114.9
4
113.95
7
113.45
7
112.61
9
5 147.98
3
147.9
6
147.18
7
147.00
7
145.58
6
Mode 1
Mode 2
Figures:-Natural frequencies at 6mm on different mode
Mode 1
Mode 2
Figures:-Natural frequencies at 9mm on different mode
Mode 1
Mode 2

Mode 1
Mode 2
Mode 1
Mode 2
RESULTS AND DISCUSSION
In this present work, FEM method has been used in
order to obtain the analytical solution for simply
supported continuous beam with crack and without
crack with two different material structural steel and
aluminium. In ANSYS, modal analysis is used to
determine its natural frequency and mode at different
crack depth. The comparision between regression
analysis and modal analysis is also done. The results of
regression analysis is quite more than modal analysis.
Graph 1 Mode vs Frequency of structural steel and
aluminium alloy without crack
Graph 2 Mode vs Frequency structural steel and
aluminium at 15 mm crack depth.
CONCLUSION
The main objective of present study is to calculate the
natural frequencies and modes of simply supported
continuous I section beam with crack and without crack
with two materials structural steel and aluminium. It is
observed that the when increase the crack depth of beam
then the natural frequencies is slightly decreases in both
modal and regression analysis. It is also observed that
the natural frequencies structural steel are slightly
higher than that of aluminum alloy for simply supported
continuous beam .
The difference between natural frequency of crack and
un cracked beam is also having minium difference.
y = -3.6757x2 + 63.169x - 63.995
R² = 0.9838
y = -4.2878x2 + 62.945x - 59.411
R² = 0.9793
-50
0
50
100
150
200
1 2 3 4 5
Frequency
Mode
St.Fr.
Al.Fr
y = -1.6627x2 + 53.155x - 64.786
R² = 0.9022
y = -2.1749x2 + 52.541x - 62.746
R² = 0.8871
-50
0
50
100
150
200
0 2 4 6
Frequency
Mode
St.Fr
Al.Fr

REFERENCES
[1] P. Amit V., M. Pathak, and P.K.Sharma,“Theoretical
and Software analysis of crack detection in structure”,
IJERT, Vol. 2, Issue-5, May 2014.
[2] P.K.Sharma, M. Pathak, and P. Amit V., “Alternative
Solution to the detection of crack location and crack
depth in structure by using software analysis method”,
IJARSE, Vol. 3, Issue-8, August 2014.
[3] Muhannad Al-Waily, Theoretical and Numerical
Vibration Study of Continuous Beam with Crack Size and
Location Effect, International Journal of Innovative
Research in Science, Engineering and Technology, Vol. 2,
Issue 9, September 2013, pp. 4166-4177.
[4] Ertugrul Cam, Sadettin Orhan, and Murat Luy ‘An
analysis of cracked beam structure using impact echo
method’ NDT&E International, Vol. 38, 2005.
[5] P.Yamuna, and K.Sambasivarao, “Vibration Analysis
of Beam with Varying crack Location”, IJERGS, Vol.2,
Issue-6, October- November, 2014.
[6] P.M. jagdale, and M.A.Chakrabarti, “Free Vibration
Analysis of Cracked Beam”, IJERA, Vol. 3, Issue 6, Nov-
Dec 2013, pp. 1172-1176.
[7] Hai-Ping Lin “Deterministic Direct and inverse
methods on free vibration analysis of simply supported
beams with a crack” Engineering Structures; 2004;
vol.26; pp.427–436.
[8] Patil D.P., Maiti S.K., Detection of multiple cracks
using frequency measurements, Engineering Fracture
Mechanics 70, (2003), pp.1553–1572.
[9] Patil D.P., Maiti S.K., Experimental verification of a
method of detection of multiple cracks in beams based
on frequency measurements, Journal of Sound and
Vibration 281,(2005),
pp.439–451.

Modal Analysis Of Cracked Continuous Beam Using ANSYS

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Modal Analysis Of Cracked Continuous Beam Using ANSYS