Discs are important structural elements in engineering application such as pressure vessel,missiles and liquid container. The turbine, brake disc and diaphragm clutch spring are the wellknown examples for the industrial application of the annular plate with radial slots. The natural frequencies of component are of great interest in the analysis for response of structures to various excitations. Annular discs are fundamental structural elements studied in ocean engineering applications from offshore platforms to under water acoustic transducers.

1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 2, February (2015), pp. 106-115© IAEME
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EXPERIMENTAL ANALYSIS OF CIRCULAR DISC WITH
DIAMETRAL SLOTS
Prof. L. B. Raut. Guide & (M.E Co-ordinator) 1
, Ramsagar A. Kalyankar 2
1,2
SEVRI’s college of Engg, Pandharpur
ABSTRACT
Discs are important structural elements in engineering application such as pressure vessel,
missiles and liquid container. The turbine, brake disc and diaphragm clutch spring are the well-
known examples for the industrial application of the annular plate with radial slots. The natural
frequencies of component are of great interest in the analysis for response of structures to various
excitations. Annular discs are fundamental structural elements studied in ocean engineering
applications from offshore platforms to under water acoustic transducers. In various papers, study of
annular discs with outer radial slot is done with the help of classical plate theory and most of the
experimental work is carried out with help of optical electronic speckle pattern interferometer
method. It is found that discs are often subjected to transverse vibrations and these vibrations
decrease the mechanism’s capabilities. Thus dynamic analysis of an annular disc with radial slots,
fixed at inner edge and free at outer edge is required.
In this dissertation work finite element method tool is implemented for modal analysis of
annular disc. Natural frequency and mode shapes of the annular disc are found out by FFT analyzer
for numbers of slots. Mode shapes obtained by numerical method are compared with experimental
method. It shows that natural frequency increases with increase in mode diameter and decreases with
increase in length of slots.
Keywords: Noise, Vibration, Accidental Failure, Vibration Characteristics.
I. INTRODUCTION
The knowledge of natural frequencies of component is of great interest in the analysis of
response of structures to various excitations. The study of the dynamic behavior of annular plates
with radial slots is important, as several machine components, such as flywheels, clutch plates,
circular saw plates etc. can be considered as annular plates with radial slots for the purpose of
analysis. This study is fundamental for high-risk plants. Unwanted noise and vibration associated
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with the disc elements has become an important economic and technological problem in the industry.
Study of the effect of vibration analysis is important for annular plates for same ratios of inner to
outer radius. Analysis is done to check the effect of variable numbers and variable lengths of radial
slots with same boundary condition. This is made for determining different parameters like natural
frequency, mode shapes, as it is important to reduce noise level and vibration damages of many
machines having disc elements. Depending on the frequency range of interest, the hydraulic system,
body panels, steering column, and other vehicle components can also become active. In an aggregate
sense, the disk brakes of only a few percent of new vehicles exhibit sufficient noise and vibration to
generate significant customer complaints, but the volume and expense of remediation efforts, in
addition to the perception of reduced product-line quality, place pressure on brake noise and
vibration. Hence experimental work is necessary to conduct.
1.1 Outline of the dissertation work
1.1.1 Scope of work
To analyze the vibration characteristics of annular plates with radial slots with same ratio of
inner to outer radius. But these plates are having variable numbers and variable lengths of radial
slots. Experimental set up of disk is done for inner edge clamped and outer edge free boundary
condition.
I.1.2 Experimental work
There are two methods of vibration analysis used in this experimental work.
1. In First method, using FFT analyzer, natural frequencies are detected by hitting the plate with
impact hammer and the response at a point of a plate is measured by using an accelerometer.
FFT analyzer analyzed the output of accelerometer.
2. In second method, the clamped disk was mounted on exciter and different resonance’s was
detected by varying the exciting frequency. Mode shapes are snapped in photo camera to
compare with FEM mode shapes of same test specimens.
I.2 Objectives
1. To find natural frequency of specimens by FFT (Impact hammer test).
To do the experimental work, Structure excitations and instrumentation of vibration analysis.
Experimentation with set up to excite a rotor structure with radial slot.
2. To find natural frequency & mode shape’s by FEM.
To visualize the dynamic properties using the FEM analysis software (ANSYS) and discussion
of mode shapes.
3. To compare the results by FFT & FEM.
To evaluate results and a comparison between FEM (ANSYS) software analysis, and
experimental (FFT and modal analysis) results.
II. EXPERIMENTAL ANALYSIS
In analysis, annular disc structure is used for investigating the disc's bending modes. The
structure is axi-symmetric and formed of an isotropic homogeneous elastic material. Three
dimensional parameters represent the disc's inner radius (b), outer radius (a) and thickness (h)
respectively.
2.1 Test Specimens
Total five annular disc specimen of M.S. are chosen with same b/a ratio i.e. aspect ratio
(Inner to outer radius ratio). These specimens prepared were taken one by one for experimental

3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
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modal analysis. Specimen dimensions tabulated in table 1 shows the range of same ratio of inner to
outer radius but variable numbers and variable lengths of radial slots for inner edge clamped and
outer edge free boundary condition. Following are the material properties for the specimen plates as
shown below.
➢Young’s modulus (E) = 2.1 X 10 11
N/m2,
➢Poisson’s ratio (γ) = 0.3,
➢Density of material (ρ) = 7850 N/m3.
➢Inner diameter =20 mm
➢Outer diameter = 200 mm;
➢Thickness =1.5 mm
Table 1: Test specimen dimensions
Specimen
Aspect ratio
b/a
Inner diameter
in mm
Outer diameter
in mm
Number of
slots
Length of
slots
1st
Disc
0.1
20200345
2nd
Disc20200645
3rd
Disc20200945
4th
Disc20200360
5th
Disc20200660
Fig: 1 Disc of 3 slot 45mm length Fig: 2 Disc of 6 slot 45mm length
Fig: 3 Disc of 9 slot 45mm length Fig: 4 Disc of 3 slot 60mm length

4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
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Fig: 5
2.2 Test Fixture
1. In vibration test annular disc is fixed in a fixture. Clamping was obtained by using two 20mm
diameter nuts and one bolt with two washers is fastened above and below the disc as shown in Fig 1,
for impact hammer test. Bolt is used to restrict the movement at inner edge of annular plate in x and
y and z direction. The fixture was hold in vice, which is rigidly fixed on concrete
Fig: 6. Test specimen and fixture in vice for impact hammer FFT test
2. Annular plate assembly was mounted on exciter pressed by a set of nut and clamping bolts
and also in diagram as shown below in the fig 2. Sufficient care is exe
5 kg-m constant torque provided by torque range spanner, uniformly to achieve the fixed end
condition.
Fig: 7. Showing Experimental Set Up
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
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Fig: 5 Disc of 6 slot 60mm length
In vibration test annular disc is fixed in a fixture. Clamping was obtained by using two 20mm
h two washers is fastened above and below the disc as shown in Fig 1,
for impact hammer test. Bolt is used to restrict the movement at inner edge of annular plate in x and
y and z direction. The fixture was hold in vice, which is rigidly fixed on concrete
Test specimen and fixture in vice for impact hammer FFT test
Annular plate assembly was mounted on exciter pressed by a set of nut and clamping bolts
and also in diagram as shown below in the fig 2. Sufficient care is exercised to tighten the bolts with
m constant torque provided by torque range spanner, uniformly to achieve the fixed end
Showing Experimental Set Up with Exciter
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
© IAEME
In vibration test annular disc is fixed in a fixture. Clamping was obtained by using two 20mm
h two washers is fastened above and below the disc as shown in Fig 1,
for impact hammer test. Bolt is used to restrict the movement at inner edge of annular plate in x and
y and z direction. The fixture was hold in vice, which is rigidly fixed on concrete foundation.
Test specimen and fixture in vice for impact hammer FFT test
Annular plate assembly was mounted on exciter pressed by a set of nut and clamping bolts
rcised to tighten the bolts with
m constant torque provided by torque range spanner, uniformly to achieve the fixed end

5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
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III EXPERIMENTATION
1. To find natural frequency of specimens by FFT (Impact hammer test)
Specimens prepared were rigidly fixed in fixture to obtain correct boundary conditions.
Analysis is done experimentally with the help of FFT analyzer, accelerometer, impact hammer and
exciter. Natural frequencies are detected by hitting with hammer; the response of a plate is measured
by using an accelerometer. FFT analyzer analyzed the output of accelerometer. This output is
tabulated ahead in table 2 showing FFT test results.
Table 2: Showing FFT test results
Test
specimen
Number of
slots
Slot length
in mm
Natural frequency in Hz
1st
345146187253490-
2nd
645109146212440490
3rd
945131156221450-
4th
360128153221437-
5th
660118146221462559
2. To find natural frequency by FEM (ANSYS software)
Vibration analysis of annular plate is done by FEM (ANSYS) software to get natural
frequencies and mode shapes of annular disk with same aspect ratio but variable (numbers and
lengths) of radial slots for inner edge clamped and outer edge free boundary condition. Results
obtained from analysis are shown in table 3.
Table 3: Natural frequencies of discs with radial slots by FEM (ANSYS)
Sr.
No.
Mode
shape
(d, c)
Frequency [Hz]Frequency [Hz]
3 Slots of
45mm
6 Slots of
45mm
9 Slots of
45mm
3 Slots of
60mm
6 Slots of
60mm
1(1,0)159.1149.81143.04156.71147.06
2(1,0)159.63150.04143.09158.15147.37
3(0,1)171.53158.95149.66166.61150.35
4(2,0)226.36222.57219.29225.5221.1
5(2,0)226.51222.84219.4225.63221.69
6(3,0)453.94448.43447.07443.3426.3
7(3,0)457.29455.45447.1456.58453.32
8(4,0)796.29793.25786.73786.24771.65
9(4,0)796.64793.61787.18786.92772.28
10(0,2)1124.41107.1086.61121.31100.4

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3. To compare the results by FFT & FEM
Table 4: Showing comparison of experimental and theoretical results
Natural frequency by
FEM analysis.
Percentage
error
1598.2
1718.6
22610.7
1502.7
2224.7
4481.8
1439.1
2190.9
4470.6
1668.4
2251.8
4431.3
1502.7
2210.00
4531.9
We shall now attempt to compare the predicted and measured results for individual modes or
pairs of modes. As these are the modes with a low number of diameter, which are most readily
identified to concentrate our interest on those with 2, 3 or 4 nodal diameters. Comparisons on the
results, concern the natural frequencies and the mode shapes is done here. A comparison between
theoretical and experimental results shows an average error of 5%, which is quite acceptable.
Graph: 1. Modal diameter v/s Frequency (3 slots of 45mm)
Graph: 2. Modal diameter v/s Frequency (6 slots of 45mm)
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To compare the results by FFT & FEM
Showing comparison of experimental and theoretical results
Modes
(d, c)
Mode
shape
Natural frequency by
impact hammer
Natural frequency by
FEM analysis.
1,0146
Second0,2187
Third2,0253
1,0146
Second2,0212
Third3,0440
1,0131
Second2,0221
Third3,0450
0,2153
Second2,0221
Third3,0437
0,1146
Second2,0221
Third3,1462
We shall now attempt to compare the predicted and measured results for individual modes or
e modes with a low number of diameter, which are most readily
identified to concentrate our interest on those with 2, 3 or 4 nodal diameters. Comparisons on the
results, concern the natural frequencies and the mode shapes is done here. A comparison between
theoretical and experimental results shows an average error of 5%, which is quite acceptable.
Graph: 1. Modal diameter v/s Frequency (3 slots of 45mm)
Graph: 2. Modal diameter v/s Frequency (6 slots of 45mm)
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
© IAEME
Showing comparison of experimental and theoretical results
Test
specimen
Modes
(d, c)
3 slots of
45 mm
First
Second
Third
6 slots of
45 mm
First
Second
Third
9 slots of
45 mm
First
Second
Third
3 slots of
60 mm
First
Second
Third
6 slots of
60 mm
First
Second
Third
We shall now attempt to compare the predicted and measured results for individual modes or
e modes with a low number of diameter, which are most readily
identified to concentrate our interest on those with 2, 3 or 4 nodal diameters. Comparisons on the
results, concern the natural frequencies and the mode shapes is done here. A comparison between
theoretical and experimental results shows an average error of 5%, which is quite acceptable.
Graph: 1. Modal diameter v/s Frequency (3 slots of 45mm)
Graph: 2. Modal diameter v/s Frequency (6 slots of 45mm)

7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
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Graph: 3. Mod
Experimental results shows that values of natural frequencies determined experimentally are
less than those obtained by FEM analysis due to certain parameters as Boundary condition,
Damping, Rotary inertia, Impact hammer double hit.
4. To find modes by exciter
Comparison of mode shapes of annular disk with 3 radial slots of 45mm and aspect ratio 0.1
through exciter results and FEM (ANSYS) results showing similarity are given below:
Fig: 8 (Plate) Practical mode shape (1, 0)
Fig: 10 (Plate) Practical mode shape (0, 1) Fig: 11 ANSYS mode shape (0, 1)
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
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Graph: 3. Modal diameter v/s Frequency (9 slots of 45mm)
Experimental results shows that values of natural frequencies determined experimentally are
less than those obtained by FEM analysis due to certain parameters as Boundary condition,
ct hammer double hit.
To find modes by exciter
Comparison of mode shapes of annular disk with 3 radial slots of 45mm and aspect ratio 0.1
through exciter results and FEM (ANSYS) results showing similarity are given below:
e) Practical mode shape (1, 0) Fig: 9 ANSYS mode shape (1, 0)
Fig: 10 (Plate) Practical mode shape (0, 1) Fig: 11 ANSYS mode shape (0, 1)
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
© IAEME
al diameter v/s Frequency (9 slots of 45mm)
Experimental results shows that values of natural frequencies determined experimentally are
less than those obtained by FEM analysis due to certain parameters as Boundary condition,
Comparison of mode shapes of annular disk with 3 radial slots of 45mm and aspect ratio 0.1
through exciter results and FEM (ANSYS) results showing similarity are given below:
Fig: 9 ANSYS mode shape (1, 0)
Fig: 10 (Plate) Practical mode shape (0, 1) Fig: 11 ANSYS mode shape (0, 1)

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Fig: 12 (Plate) Practical mode shape (3, 0) Fig: 13 ANSYS mode shape (3, 0)
Fig: 14 (Plate) Practical mode shape (3, 0) Fig: 15 ANSYS mode shape (3, 0)
Fig: 16 (Plate) Practical mode shape (0, 2) Fig: 17 ANSYS mode shape (0, 2)

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IV CONCLUSION
1. Vibration analysis of annular disc without slot and with slots for aspect ratio 0.1 is conducted
by analytical and compare with finite element method and both results are matched to
average of 4% error which is acceptable.
2. It found that Natural frequency increases with increase in nodal diameters for annular disc
without slots.
3. For annular disc with increasing number of radial slots natural frequency increases with
increase in nodal diameter and it decreases with increase in number of slots for same slot
length.
4. Natural Frequency Increases with increase in nodal diameters and it decreases with increase
in length slots for same no. of slots.
5. Comparison of Mode shapes is done for annular disc through exciter results and finite
element method results which show similar mode shapes.
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