Vibrations and fatigue- vibration interactions of laminated composites.

Study of Vibration Characteristics and
Interaction of Cyclic Fatigue Loading on Vibration
Responses of Thin Walled Woven Fabric Glass-Carbon
Epoxy Composites for Structural Applications
R. Murugan (Reg.No. 2714299703/PhD/AR7)
Research Scholar, Department of Mechanical Engineering,
Sri Venkateswara College of Engineering, Sriperumbudur
Supervisor
Dr. K. PADMANABHAN
Professor and Assistant Director
Centre for Excellence in Nano Composites
School of Mechanical & Building Sciences
VIT University, Vellore
Joint Supervisor
Dr. R. RAMESH
Professor
Department of Mechanical Engineering
Sri Venkateswara College of Engineering
Sriperumbudur – 602117

Introduction
 Woven fabric reinforced polymer
composites are the most widely used
forms of textile composites
 In woven fabric composite, fiber
strands are interlaced in two mutually
orthogonal directions to one another,
which promote
 Excellent integrity and conformability
 More balanced properties within the
fabric plane
2
warp
weft

3
Woven fabric composites are more
popular in structural applications such as
Automotive structures
Aircraft structures
Marine structure etc.
Composite structures used in such
applications experiencing vibration and
considerable cyclic loading in operations,
are inevitable in dynamic conditions
In all dynamic service conditions, to
perform well, these composite structures
should possess good vibration damping
along with high stiffness
Introduction

Literature Review - Summary
 Many researchers have contributed towards evaluation of Vibration
performance of fiber reinforced polymer matrix composites but in
the form of unidirectional and cross ply laminates
 There are many investigations on damping performance/behaviour
of various types of fundamental fibers as reinforcement under both
analytical and experimental approach
 The evaluation by controlling the geometric parameters like fibre
orientation and laminate configuration was extensively studied with
free end conditions and as well offering other boundary conditions
 Limited experimental work/attention on vibration performance of
woven fabric/hybrid fabric composite laminates
 Increase in material damping along with stiffness of woven fabric
polymeric composite by hybridization approach is much important
for structural applications
 There is little work on interaction of cyclic fatigue loading and
Vibration characteristics of woven fabric hybrid composite beams
4
Detailed Literature survey reports that,

Objective of Research work
5
The main objective of the research work is
 To understand and investigate the vibration
characteristics, interaction of cyclic fatigue loading on
vibration responses of thin walled woven fabric Glass-
Carbon/Epoxy composites
 To characterize the hybrid composites for automotive
and aircraft structural applications

The objective includes :
 Understanding the Mechanical Properties of Dedicated Glass/Carbon and its
Hybrid composite laminates
 Evaluation of vibration characteristics of Hybrid composite plates made of
Glass/Carbon fabrics with different aerial density under free vibrating
condition
 Experimental investigation on modal analysis of thin walled composite beams
for structural application
 Study of Influence of the stacking sequence on vibration characteristics of
beams of Glass/Carbon layered arrangement
 Influence of size effect of hybrid composite beams on vibration
characteristics using Finite Element Analysis for higher operating frequency
range
 Design and development of displacement controlled cyclic test rig to apply
completely reversed cyclic bending stress on composite specimen
 Influence of cyclic fatigue loading on vibration characteristics of composite
beams
 Modal response study of hybrid composite beams after cyclic loading.
6

7
Fabrication of Glass/Carbon
Hybrid Composite Laminates
with Different Fiber Aerial
Densities using Epoxy as
matrix

Fibers and Matrix material considered
 Fiber:
Plain woven fabric Type
E-Glass
T300 Carbon
 Aerial Density
200 gsm, 400 gsm , 600 gsm
gsm – gram per square metre
 Matrix:
Epoxy - LY556
Hardener - HY951
8
E-Glass Fabric
T300 Carbon fabric
Warp
Weft
Warp
Weft
Epoxy and Hardner

9
Specimen prepared by
Hand Layup technique
Cured for 24 hours with nominal
pressure of 2.5 MPa in
Compression Moulding Machine
at room temperature
Volume fraction of laminate
Vf - 0.5
Processing by Hand Lay up technique
Curing by Compression Moulding Machine
Method of Fabrication

January 13, 2016 10
Symbol
Aerial
Density
Specimen description Layer sequence
H1200
200 gsm
4 layered Hybrid laminate
Outer – Glass & Inner – Carbon
GCCG
H2200
Outer – Carbon & Inner – Glass
CGGC
H1400
400 gsm
GCCG
H2400 4 layered Hybrid laminate
CGGC
H1600
600 gsm
GCCG
H2600 4 layered Hybrid laminate
CGGC
4G Dedicated 4 layered Glass laminate GGGG
4C Dedicated 4 layered Glass laminate CCCC
The layer arrangement of hybrid beam was selected in concerned towards
the balanced modulus property
both in longitudinal and transverse direction w. r. t neutral axis of the beam
Types of Composite laminates fabricated

11
Fabricated Composite Plates
H1600 H1400 H1200
H2600
H2400 H2200
Symbol
Dimensions
(l*w*t)
mm
H1200 250*250*1.0
H2200 250*250*1.0
H1400 250*250*1.8
H2400 250*250*1.8
H1600 250*250*2.4
H2600 250*250*2.4
Hybrid samples with different Aerial Density fabricated
using Hand layup technique

Confirmation of Fiber Weight fraction
through Burnout Test
 ASTM STD: D3171-09
 Sample Size: 25 x 25 mm
 The specimens were placed in an electric furnace for
6 hrs at a temperature of 500oC
 Before and after the burn out test, the specimens
were weighed using a sensitive electronic balance
 The fiber volume fractions of all the laminates were
accurately estimated and the variation was found to
be  2.5%
12
Electronic Balance
Electric Furnace
Mi = Initial mass of specimen (g) Mf = Final mass of specimen (g)
For 600 gsm
Specimen
Mi
(g)
Mf
(g)
Vol%
4G 2.454 1.501 48.28
4C 2.450 1.516 52.47
H1 2.347 1.447 47.41
H2 2.370 1.464 47.53

Understanding the Mechanical
Properties of Dedicated
Glass/Carbon and their Hybrid
Composite Laminates
13

Evaluation of Tensile Strength
 Make: SHIMAD2U
 Feed Rate: 5 mm/min
 Standard: ASTM 3039
14
190
250
End Tab length = 30
All Dimensions are in mm
25

Evaluation of Flexural Strength
 Make: INSTRON 3382
 Feed rate: 1.2 mm/min
 Standard: ASTM D790
 Span : Thick = 16:1
15
W
48
63
12.5

16
Dynamic Mechanical Analysis Test
Standard : ASTM D4065
Instrument : TA Q800
Frequency : 1 Hz
Temperature Range : 30oC and 140oC
Heating Rate : 5oC/min
Amplitude : 15m
Specimen Size : 63  13  t mm3
63
13

17
Mechanical Properties of Hybrid
Composite Laminates of Three Different
Aerial Densities
* * Reported values are the average values obtained from four trials
Specimen
Tensile Strength
(MPa)
Flexural Strength
(MPa)
200
gsm
400
gsm
600
gsm
200
gsm
400
gsm
600
gsm
H1 286.41 342.57 413.62 314.38 392.97 491.21
H2 275.48 338.02 410.41 324.63 405.79 507.24
 Irrespective of fibre aerial density, there is small variation in
tensile and flexural strength among hybrid laminates

18
Static Mechanical Properties of Dedicated
and Hybrid Composite Laminates
* * Reported values are the average values obtained from four trials
Specimen
Tensile strength
[MPa]
Flexural Strength
[MPa]
4G 365.79 378.40
4C 462.08 573.27
H1 413.62 491.21
H2 403.41 507.24
Source: Murugan R, Padmanabhan K, Ramesh R, “Vibration Characteristics of Thin Walled Hybrid Carbon Composite
Beams under Fixed Free Boundary Condition” in 3rd Asian Conference on Mechanics of Functional Materials and
Structures (ACMFMS 2012) held on 5th -8th December 2012 at Indian Institute of Technology, New Delhi
Fibre Aerial Density 600 g/m2

19
Maximum stress is found for dedicated
carbon laminate arrangement, 4C
Considerable tensile strength variation
between dedicated 4G glass beam and
dedicated 4C carbon laminate
This is due to high resistance offered by
high modulus carbon fibre against tensile
loading
0
100
200
300
400
500
600
0 0.02 0.04 0.06 0.08 0.1
TensileStress(MPa)
Tensile Strain
4G 4C
Tensile behaviour of Composite Laminates
0
100
200
300
400
500
600
0 0.02 0.04 0.06 0.08 0.1
TensileStress(MPa)
Tensile Strain
H1 H2
 Among hybrids, there is small variation in
tensile strength irrespective of fiber aerial
density
Tensile strength of H1 is greater than H2
 Though the four layers of hybrid laminate
are equally loaded during tensile testing
condition, the variation in axial strain between
glass and carbon layers caused the marginal
difference in tensile strength
Dedicated Glass, Carbon Laminates Glass, Carbon Hybrid Laminates

20
Flexural strength of composite laminate is
majorly controlled by the strength of outer
layer which is in direct contact to bending load
There is a considerable flexural strength
variation between dedicated 4G glass laminate
and dedicated 4C carbon laminate
0
100
200
300
400
500
600
700
0 2 4 6
Load(N)
Deflection (mm)
4G 4C
Flexural behaviour of Composite Laminates
0
50
100
150
200
250
300
350
400
450
0 1 2 3 4 5 6
Load(N)
Deflection (mm)
H1 H2
 Among hybrid samples, H2 arrangement
has higher flexural strength than H1
arrangement in all types of laminates
 This is because the laminate in which
high modulus carbon fibre is plied as outer
layer offers more resistance to flexural loading
than low modulus glass fibre plied as inner
layer
Dedicated Glass, Carbon Laminates Glass, Carbon Hybrid Laminates

21
 Epoxy based woven fabric composites are viscoelastic in nature which exhibit a
combination of both elastic and viscous behaviour
 Complex modulus notation (E*) is used to define the viscoelastic material as
shown in the following Equation
E* = E’ + E” = E’[1 + i (tan)]
where E’ = the elastic storage modulus, a measure of stored energy,
E” = the loss modulus, a measure of dissipation of energy as heat,
tan = the loss factor or damping factor
 Characterization of composite material should include
both the static mechanical properties like tensile, flexural strength, etc.
and the dynamic mechanical properties such as storage modulus, loss
modulus and loss factor
Need for DMA study

22
Variation of Storage Modulus
Storage modulus E’ values increased with the increase of carbon fibre content
High modulus carbon fibre of dedicated carbon laminate caused the large
storage modulus than dedicated glass laminate
Storage modulus of hybrid laminate H2 is higher than other laminates including
dedicated carbon laminate due to Synergy and positive hybrid effect
There is significant fall in the storage modulus between the temperatures 80oC
and 100oC
Increasing the temperature beyond the glass transition temperature Tg causes
the change in state of composite laminates from solid to rubbery
Variation of Storage Modulus of
Dedicated Glass, Carbon and its
Hybrid Laminates made of
600 gsm Fibre Aerial Density
Storage modulus (E’) is the
measure of stores energy per cycle
in a viscoelastic material under
dynamic condition
0
2
4
6
8
10
12
14
16
18
20
22
24
20 30 40 50 60 70 80 90 100 110 120 130 140 150
StorageModulus(GPa)
Temperature (oC)
4G
H1
H2
4C

23
The glass transition temperature Tg of the resin is measured from the peak of the loss
modulus curve as per ASTM D4065
The transition peak occurs at 85oC for the dedicated glass laminate and for the dedicated
carbon laminate, it is 95oC
The increase in Tg, from 85oC to 90oC, with respect to 4G, is due to the immobilization of the
polymer molecules near the surface of the carbon fibre
Loss modulus of hybrid laminate H2 is much higher than the other laminate H1 and raises to
a larger extent than dedicated glass laminate, 4G
Increased energy absorption due to the layering sequence, CGGC, caused the large increase
(89%) in loss modulus peak in hybrid H2
Variation of Loss Modulus
Variation of Loss Modulus of
Dedicated Glass, Carbon and its
Hybrid Laminates made of
600 gsm Fiber Aerial Density
Loss modulus (E”) is the measure
of dissipated heat energy per cycle
in a viscoelastic material under
dynamic condition0
0.5
1
1.5
2
2.5
3
3.5
20 30 40 50 60 70 80 90 100 110 120 130 140 150
LossModulus(GPa)
Temperature (oC)
4G
H1
H2
4C

24
90
95
95
100
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
20 30 40 50 60 70 80 90 100110120130140150
Tan
Temperature (oC)
4G
H1
H2
4C
Variation of Loss Factor
Variation of Loss Factor of
Dedicated Laminates made of
600 gsm Fiber Aerial Density
Loss factor (Tan), the ratio of the
loss modulus to the storage
modulus (E”/E’), gives balance
between the elastic and viscous
phase in a polymeric material
Below Tg, the chain segments present in the resin are in frozen state causes low
Tan values in all laminates
 In the transition region resin molecules attain high mobility which causes high
Tan values
The Tan value is high for hybrid laminate, H2, than dedicated carbon and
dedicated glass laminate
Among hybrids, transition peak values, Tg are same as 95oC however the Tan
value at the Tg is 17% higher for H2 arrangement than H1 arrangement

25
1
1.5
2
2.5
3
3.5
4
3 3.5 4 4.5
LogE"
Log E'
4G
H1
H2
4C
 Imperfect semi-circular curve of dedicated and hybrid composite
laminates indicates the heterogeneity of the laminates with a good matrix
and fibre bonding
Cole-Cole Plot
 Measure viscoelastic
properties of FRP materials
 Perfect semi-circle for pure
polymeric material

26
Specimen
Storage Modulus
(E’max)
[GPa]
Loss Modulus
(E”max)
[GPa]
Tg from E”max
[oC]
4G 12.684 1.665 85
4C 18.849 1.250 95
H1 13.033 1.771 90
H2 21.601 3.150 90
Dynamic Mechanical Properties of Dedicated
and Hybrid Composite Laminates - Summary

27
Summary
Static Mechanical Properties
Investigations on variation of mechanical properties of woven fabric composite
laminates for varying stacking sequence with different fiber aerial density were carried
out
Dedicated carbon laminate has higher mechanical strengths than dedicated glass
laminate
Laminate with glass as envelope layer, H1 (GCCG), has marginally higher tensile
strength than the other arrangement H2 (CGGC)
Carbon enveloped hybrid laminate, H2 (CGGC), has higher flexural strength
Dynamic Mechanical Properties
Storage modulus, loss modulus and loss factor of hybrid laminate H2 is greater than
H1 hybrid laminate and dedicated carbon laminate
The glass transition temperature, Tg of H2 laminate was shifted through 5o C from
dedicated glass laminate which facilitates the higher operating temperature
Hybrid laminate with carbon fibre as enveloping layer, H2, performs better than other
hybrid arrangement, H1

28
Evaluation of vibration
characteristics of Hybrid composite
plates made of Glass/Carbon fabrics
with different aerial density under
free vibrating condition

Quasi Static Table with Impulse
Excitation Testing facility
29
 Impulse excitation technique
 Free-free boundary condition
 Impulse hammer (DYTRAN®) is
used to induce the excitation
 Flexural vibrations of the hybrid
composite plates were tapped by
a dynamic analyser (LDS
DACTRON Photon+®) supported
with RT Pro® software
 Frequency response functions
(FRF) of all specimens were
recorded
(1) Quasi-static Table
(2) Composite Specimen
(3) Impact Hammer (B&K Type 5800B4)
(4) Uniaxial Accelerometer (B&K Type 3055B2)
(5) Data Acquisition Card (B&K Type Photon+)
(6) PC with RT Pro Software showing FRF
6
5
1
2
3
4

30
FRF response of Plates - 400 gsm FAD
Screen shot of RT Pro® showing FRF of 400 gsm AD Plates
H1400 Plate
H2400 Plate

31
Comparison of FRF plots among Hybrid
Plates
 Free vibration response of hybrid
Plate H1 shows modified amplitude
over the other hybrid arrangement,
H2
 The difference in natural frequency
of carbon and glass fabric layers
interplied in hybrid beams together
promotes the increased amplitude
under free vibration
0
10
20
30
40
50
60
70
0 200 400 600 800 1000
Amplitude(gn/N)
Frequency (Hz)
H1 H2
0
10
20
30
40
50
0 200 400 600 800 1000
Amplitude(gn/N)
Frequency (Hz)
H1 H2
0
10
20
30
40
50
60
0 200 400 600 800 1000
Amplitude(gn/N)
Frequency (Hz)
H1 H2

32
Mode
200 gsm 400 gsm 600 gsm
H1 H2 H1 H2 H1 H2
1 64 72 124 162 162 202
2 284 338 334 454 440 576
3 538 696 582 776 784 960
Comparison of Modal frequency of Plates
with different Fiber Aerial Densities
 Increase in Aerial Densities of fiber in epoxy matrix increases the
modal frequency values indicating an increase in the dynamic
stability for a thickness range of 1-2.5 mm for the four layered beams

33
Comparison of Loss Factor of Plates with
different Fiber Aerial Densities
Mode
200 gsm 400 gsm 600 gsm
H1 H2 H1 H2 H1 H2
1 0.089 0.087 0.047 0.033 0.031 0.030
2 0.028 0.027 0.025 0.019 0.017 0.010
3 0.014 0.018 0.012 0.012 0.012 0.013
 There is consistency in material damping under the control of
stacking sequence over each plate made of different aerial density of
fiber in epoxy matrix

34
Variation in resonant frequency level in successive
transverse modes of hybrid composite plates made of
three different fibre aerial densities
0
100
200
300
400
500
600
700
800
1 2 3
FrequencyinHz
Mode No.
H1
H2
0
100
200
300
400
500
600
700
800
900
1 2 3
FrequencyinHz
Mode No.
H1
H2
0
200
400
600
800
1000
1200
1 2 3
FrequencyinHz
Mode No.
H1
H2
200 g/m2
400 g/m2
600 g/m2
Hybrid plate with H2 layer arrangement
exhibited higher resonant frequencies
than the other layer arrangement, H1 in
all modes of vibration

35
0
50
100
150
200
250
ModalFrequency(Hz)
Fiber Areial Density (g/m2)
H1 H2
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
LossFActor
Fiber Aerial Density (g/m2)
H1 H2
Variation of Modal frequency for first
mode due to different Fiber Aerial
Density
Effect of Fiber Aerial Densities on Modal
frequency and Loss factors
Variation of Loss factor for first mode
due to different Fiber Aerial Density
200 gsm
400 gsm
600 gsm
600 gsm
400 gsm
200 gsm
First Mode values alone considered
First Mode values alone considered

36
Summary
The aerial density of woven fabric affects the vibration
characteristics significantly
Increased Resonant frequency was attained with increase in
fibre aerial densities
Magnitude of material damping value is more or less consistent
in terms of all fibre aerial densities
Loss factor is lesser in higher aerial densities

37
Experimental Investigation on
Modal analysis of Thin walled
Glass/Carbon Composite beams
for Structural applications

Beam Specimen
4G
H2
H1
4C
600 g/m2 Aerial Density - Dedicated and Hybrid
samples fabricated using Hand layup Technique
38

Dimensions and Mass properties of
Composite Beams
39
** l – length of the beam; w – width of the beam; t – thickness of the beam
Laminates Dimension (l*w*t) mm
Density
() Kg/m3
4G 250*250*2.1 1881
H1 250*250*2.4 1640
H2 250*250*2.4 1627
4C 250*250*2.5 1446

Experimental Test Conditions
 Impulse excitation technique
 Fixed-free boundary condition
 Impulse hammer (DYTRAN®) is
used to induce the excitation
 Flexural vibrations of the beam
were tapped by a dynamic
analyser (LDS DACTRON
Photon+®) supported with RT
Pro® software
 Frequency response functions
(FRF) of all specimens were
recorded
40
Experimental Setup
(2) Impact Hammer (B&K Type 5800B4)
(3) Uniaxial Accelerometer (B&K Type 3055B2)
(4) Data Acquisition Card (B&K Type Photon+)
(5) PC with RT Pro Software showing FRF

FRF of Dedicated Beam –
4G Arrangement (GGGG)
Screen shot of RT Pro® showing FRF of 4G600 Beam
January 13, 2016 41

FRF of Hybrid Beam –
H2 Arrangement (CGGC)
Screen shot of RT Pro® showing FRF of H2600 Beam
January 13, 2016 42

43
0
0.2
0.4
0.6
0.8
1
0 15 30 45 60
Amplitude(gn/N)
Frequency (Hz)
4G H1
H2 4C
(a)
0
5
10
15
20
25
60 80 100 120 140 160 180 200 220 240 260 280 300
Amplitude(gn/N)
Frequency (Hz)
4G H1
H2 4C
(b)
Comparison of FRF of Dedicated and
Hybrid Beams Tested
FRF curves of various
specimen obtained from
RT Pro® software
Mode I
Mode II

44
 Among all samples tested, the spectrum of glass fabric beams, 4G,
showing relatively less amplitude at all successive resonance levels
 This attribute indicates increased damping performance of glass
fabric beam
 Vibration response of hybrid beam H1 shows modified amplitude
over the other hybrid beam arrangement H2
 The difference in natural frequency of carbon and glass layers
interplied in hybrid beams together promotes the increased amplitude
 Carbon beam which keeps relatively high strength and stiffness as
compared to other test specimens showed higher amplitude frequency
spectrum
 The uniform rate of deformation and retrieval with higher modulus
attribute caused less damping performance
Comparison of FRF of Dedicated and
Hybrid Beams Tested – Contd…

Modal Analysis
 Roving Hammer method
 FRF results were given as input to ME SCOPE VES®
software for evaluating mode shape and modal frequency
 All Dedicated and Hybrid beams were tested
45
Schematic diagram showing the various points of
measurement
All Dimensions in mm

46
Collective FRF Signals as Input for
attaining Mode shapes of Beams
Collective FRF curves obtained by exerting disturbing force at
various target region of H2 specimen

Transverse Mode Shapes of 4G Beam (GGGG)
represented by three axial components
47
First Mode at 13 Hz Second Mode at 108 Hz
Third Mode at 301 Hz

Transverse Mode Shapes of H1 Beam (GCCG)
48
Second Mode at 145 HzFirst Mode at 18 Hz

Transverse Mode Shapes of H2 Beam (CGGC)
49

Transverse Mode Shapes of 4C Beam (CCCC)
50

Influence of Stacking sequence on Modal
frequencies of Dedicated and Hybrid Beams
Sample
Mode I
Hz
Mode II
Hz
Mode III
Hz
4G 13 108 301
H1 18 145 401
H2 21 201 540
4C 29 280 766
 Modal frequencies of high
modulus carbon beam are
higher than that of
dedicated glass fabric beam
 Modal frequencies of hybrid
beams are lying in between
the dedicated glass and
carbon beams
 Among the two hybrid
beams H2(CGGC) has higher
frequency values than GCCG
51

Sample Mode I Mode
II
Mode
III
4G 0.468 0.065 0.035
H1 0.241 0.024 0.019
H2 0.248 0.031 0.020
4C 0.125 0.050 0.033
 Hybrid beams indicate improved
damping and dynamic stability
against the dedicative glass beam
 Among the hybrid beams, the
carbon layers preferred as
envelope in the fabric sequence,
H2 (CGGC), resulted in minimal
variation in damping and
increased frequency resonance
set
 Improved flexural strength of this
stacking sequence promotes this
modified performance 52
Influence of Stacking sequence on Loss
Factor of Dedicated and Hybrid Beams

53
0
50
100
150
200
250
300
350
400
450
500
1 2 3
FrequencyVariation(Hz)
Mode No.
H1 H2 4C
Variation in successive resonance
frequency sets of hybrid and carbon beams
compared with dedicated glass beam
Carbon fabric beam showed
relatively very high resonance
frequency level and H2 stacking
sequence exhibited nearly 50%
performance of dedicated carbon
fabric beam
Nearly 50% of performance
exhibited for hybrid beam, H2, as
compared to carbon fabric beam
indicates its effective hybridization
achieved by interplying
arrangement of carbon/glass
layers

Evaluation of Effective Modulus
 Effective modulus values for all samples were calculated by
using the frequency equation based on Euler-Bernoulli’s
beam theory
54
Euler-Bernoulli’s Frequency equation
Source: ASTM Standard E756-05, Standard Test Method for Measuring Vibration
Damping Properties of Materials, ASTM International, West Conshohocken, PA, 2003
Eeff
where
 = Density of the beam in kg/m3
n = Mode number
Cn = Coefficient for nth mode,
(for first transverse mode, C1 = 0.55959)
l = length in m
H = thickness of beam
fn = the resonance frequency of nth mode in Hz and
Eeff = the effective modulus in Pa

Combined Stiffness and Damping Performance
of Dedicated and Hybrid Beams
 Eeff  - a figure of merit for
combined stiffness damping
performance of viscoelastic
polymeric composite materials
 Stacking sequence is
influencing the combined
stiffness-damping values
 Among hybrid form, H2 (CGGC)
has higher value of Eeff 
 H2 arrangement is most
preferable to use where
strength and damping are
important parameters
Specimen
Eeff
(GPa)

Eeff
(GPa)
4G 7.02 0.468 3.29
H1 8.35 0.241 2.01
H2 11.37 0.248 2.82
4C 12.8 0.125 1.60
55
Eeff – Effective
Modulus
 - Loss Factor

56
Summary
 Vibration characteristics of thin walled woven fabric composite
beams were experimentally investigated
 There is appreciable raise in damping performance and
structural stability by modifying the glass laminates with
carbon plies by interply method
 Modal analysis of hybrid structure exhibits increased
frequency range for resonance set
 The hybrid samples fabricated under varying stacking
sequence showed very minimal variation in damping
performance, but influencing greatly on combined stiffness-
damping values

57
Influence of Size effect of hybrid
composite beams on
vibration characteristics using
Finite Element Analysis for
higher operating frequency range

Theoretical Evaluation of Elastic
Constants
Elastic constants of woven fabric glass and carbon composite
laminate were evaluated from the constituent material
properties using the standard rule-of-mixture equations
58
Physical properties Carbon fiber Glass fiber Epoxy
Elastic modulus (GPa) 230 74 4.3
Shear modulus (GPa) 96 30 1.5
Poisson’s ratio 0.20 0.25 0.35
Mechanical properties of constituent materials
Source: Mallick. P. K. (2008). Fibre reinforced composites, materials and manufacturing and Design.
CRC Press, Taylor & Francis Group

Evaluation of Elastic Constants for
Unidirectional Lamina
59
Properties Carbon Glass
Elastic modulus E1 (GPa) 94.58 32.18
Elastic modulus E2 (GPa) 9.691 9.055
Shear modulus G12 (GPa) 2.474 2.419
Poisson ratio 12 0.29 0.31
Poisson ratio 23 0.396 0.41
Source: Mallick. P. K. (2008). Fibre reinforced composites, materials and manufacturing and Design

Properties Carbon Glass
Elastic modulus E1=E2(GPa) 52.665 21.387
Elastic modulus E3(GPa) 11.285 10.427
Shear modulus G13(GPa) 2.889 2.76
Poisson ratio u12 0.054 0.136
60
Evaluation of Elastic Constants for
Woven Fabric Lamina
Source: Mohammed F. Aly., Goda. I.G.M., Galal A. Hassan. (2010). Experimental investigation of the dynamic characteristics of
laminated composite beam. International Journal of Mechanical & Mechatronics IJMME-IJENS 10(03): 59-58

Selection of Finite Element for Woven fabric
Composite Beam
61
 ANSYS v12.0
SHELL 99 - layered element
8 node element
6 DOF at each node
 Beam Dimension
220 mm length and
25 mm width
 Four layer arrangement was
selected in defining the thickness
of beam
 Actual specimen thickness was
equally divided for four layers
SHELL 99
FE model of composite beam

Finite Element Modeling of Dedicated and
Hybrid Composite Beam
62
 Material Properties
The elastic constants of glass and
carbon fabric lamina evaluated
using rule of mixture were
assigned as input according to
required stacking sequence
 Actual density evaluated from
fabricated samples was given for
the model for imposing mass
properties of beam
 Each woven fabric lamina was
modeled as a layer of 0o fiber
orientation
Lay plot with 0o orientation of CGGC
woven fabric beam [02/01/01/02]

Linear Regression analysis for evaluating
Effective Elastic Constants
63
First 10 transverse mode frequency values
are considered which is much higher than
the number of elastic constants to be
evaluated
Error function
* =  [(fi – fi
*)/ fi
*]2 i = 1 to 10
where fi
* is the experimental resonant
frequency and fi is numerical modal
frequency
Error function is minimized by simple
regression analysis
The degree of deviation obtained from
regression analysis is used for finding the
effective elastic constants of hybrid
composite beams
Yes NoEffective Elastic
constants
Error Function
Computation (*)
If *is
min
Elastic constants derived
through Rule of Mixture
Equations
Finite Element Modelling and
Analysis of unit plied
composite beam
Regression
Analysis
Experimental
modal frequency
values (fi
*)
Theoretical modal frequency
values (fi)
Flow chart for identification
of effective elastic constants
January 13, 2016

Effective elastic constants of woven
fabric lamina evaluated using Regression
analysis
January 13, 2016 64
Material
Effective elastic constants of glass/carbon woven
fabric lamina
E11=E22
[GPa]
E33
[GPa]
G12
(GPa)
G13= G23
(GPa)
12 13=23
Glass 14.8 7.21 1.66 1.94 0.094 0.277
Carbon 29.4 6.3 1.39 1.62 0.030 0.216
Experimental frequency obtained from unit plied dedicated composite
beams were helpful in establishing effective elastic constants of fibre
reinforced polymer composite material with specified volume fraction

Influence of size on hybrid beam under
higher operating frequency
65
 Size of the unit plied composite beam was amplified by
repeating three times (3T)
 Modal analysis was carried out for all the four types of
composite beams with fixed-free boundary condition using FE
method
 The frequency range set for the analysis was 1-10000 Hz
 The basic mode shapes such as
•Transverse mode,
•Twisting mode and
•Shear mode were tapped and
corresponding resonant frequency values were recorded
January 13, 2016

Modal frequencies of various modes of
composite specimen with unit plied and
increased thickness beams
66
Mode
No.
Modal frequency of various modes (Hz)
Transverse Mode Twisting Mode Shear Mode
H1 H2 H1 H2 H1 H2
1T 3T 1T 3T 1T 3T 1T 3T 1T 3T 1T 3T
1 25 75 32 97 220 611 211 587 291 291 291 291
2 157 465 202 593 675 1864 658 1816 1494 1494 1494 1494
3 439 1275 564 1605 1173 3205 1177 3188 3434 3434 3434 3434
4 857 2427 1098 3005 1739 4672 1801 4751 5551 5551 5551 5551
5 1411 3872 1802 4711 2390 6283 2552 6508 7743 7743 7743 7743
6 2096 5556 2667 6639 3137 8036 3441 8435 9936 9936 9936 9936
January 13, 2016
The layer arrangement of H2 exhibited higher transverse and twisting resonant
frequencies than H1 arrangement both in unit plied beam and enlarged size beam
There is no frequency variation in shear mode for both hybrid samples tested.
The identical inter laminar shear strength of hybrid beams facilitates negligible
effect in shear mode

Various mode shapes of enlarged size H2 beam
67
5th Transverse mode at 4711 Hz
5th Twisting mode at 6508 Hz
5th Shear mode at 7743 Hz
6th Transverse mode at 6639
6th Shear mode at 9936 Hz
6th Twisting mode at 8435 Hz
January 13, 2016
It is evident from the mode shape plots that in higher operating frequency
level both the hybrid beams are subjected to transverse mode, twisting mode
and shear mode with more number of node points

Size effect on Modal frequency of Hybrid
Beams in transverse mode
68
Stacking sequence of hybrid beam influences the vibration
characteristics even at higher vibrating frequency level
Frequency values of hybrid beam manifolds as the number of unit
plied arrangement used for fabricating composite laminate
0
1
2
3
4
5
6
7
1 2 3 4 5 6
NaturalFrequencyinkHz
Successive Transverse Mode in Number
H1 (1T) H1 (3T)
H2 (1T) H2 (3T)
January 13, 2016

Mean shift in frequency at various modes
among unit plied and enlarged size beams
69
In all successive transverse and twisting modes, carbon plies maintained
as envelope and glass plies as core stock, H2, showed relatively increased
resonant frequency and confirms its improved dynamic performance
January 13, 2016
0
500
1000
1500
2000
2500
3000
Transverse mode Twisting Mode
MeanshiftinFrequency
(Hz)
H1 H2

70
Summary
 Finite element modal analysis was carried out for finding
out the vibration characteristics of hybrid carbon composite
beam with fixed-free boundary condition under higher
operating frequency range
 The stacking sequence maintained for increased size of
beam affects the modal response even at higher vibrating
frequency level
 Finite element results obtained using effective elastic
constants shows that carbon fabric plied as envelope offered
enhanced vibration stability than the envelope replaced by low
modulus glass fabric

71
Influence of Cyclic Fatigue loading
on Vibration Characteristics of thin
walled Glass-Carbon Epoxy Hybrid
Composite Beams

Fully Reversed Bending Stress
Beam element subjected to a repeated and alternating
tensile and compressive stresses
72

Applying alternating fluctuating load on the composite
specimen to subject reversed bending stress
Total deflection D = 2 times of d
Fixing the specimen
dd
Functional Requirements

 Driving mode is the DC electric motor
 Rotary motion  reciprocating
motion
 Eccentric crank mechanism is used to
bring in this conversion
 Total Displacement (D) = twice of
eccentricity (e)
ee
D
Selection of Mechanism
Stress Ratio R = -1
R = σmin / σmax
Completely Reversed cycle
Eccentric crank
Displacement
Angle of Rotation
D/4 D/4 D/4 D/4
D/2 D/2
D
0
180
360

Reciprocating Mechanism
SPECIMEN HOLDER
lINEAR MOTION
BEARING
ROD END BEARING
YOKE AND DOWEL
PIN ASSEMBLY
HEIGHT ADJUSTER
ROD
ECCENTRIC DISC
NEEDLE BEARING
BLOCK
ECCENTRICITY
ADJUSTING PLATE
A
SPECIMEN HOLDER
ON TABLE
A
VIEW AA
75

Parts of Test Rig
1) DC Motor of the calculated power rating and
corresponding DC drive.
2) Gear Box Assembly
3) Eccentric disc assembly
4) Rotating Rod Eye and Dowel pin setup
5) Exciter rod
6) Linear movement bearing to arrest the sway and
guide the vertical to-and-fro motion of the exciter
rod
7) Clamp designed to hold the test specimen
8) Table enclosing the whole setup
9) R.P.M Counter and Revolution Counter
76

Machine Layout
10
50100
=125=
40
140
20 20
A
VIEW - AA
145
280
1
2
12
13
14
15
16
17
18
1920
21
50D
D
C
C
330
B
B
VIEW - BB
= 44 =
= 28 =
1010
1
SECTION - CC SECTION - DD
M6 HSHC BOLTS
4 NOS M6 HSHC BOLTS
4 NOS
180
60
90
A
9
10
11
BILL OF MATERIAL
PART NO
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1 MOTOR - 1
2 LOVE JAW COUPLING - 1
SL.NO DESCRIPTION MATL QTY
3 GEAR BOX - 1
4 FLYWHEEL EN24 1
5 VIBRATION PAD - 2
LEVELING PAD - 4
DRIVING SHAFT EN24 1
DRIVEN SHAFT 1
ECCENTRIC DISC 1
ADJUSTER PLATE
NEEDLE BEARING BLOCK 1
ADJUSTING ROD-1 1
ROD END BEARING - 1
DOWEL PIN - 1
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
YOKE MS 1
LINEAR BEARING - 1
EXCITER ROD MS 1
SPECIMEN HOLDER-1 MS 1
SPECIMEN HOLDER-2 MS 1
FRAME MS 1
16
17
18
19
20
21
EN24
EN24
1EN24
EN24
MS
1MSADJUSTING ROD-2
ALL DIMENSIONS ARE IN mm
FATIGUE TEST RIG: ASSEMBLY DRAWING
ASSY 01
DRAWING NAME
DRN BY
CHK BY
DATE
DRAWING NO.
ORGANISATION SRI VENKATESWARA COLLEGE OF ENGG.
Mr. R. MURUGAN
Dr.RAMESH
10/11/2011
6
3
4
5
TEST SPECIMEN
5
8
7
160 70
77

78
(1) DC Motor (2) Eccentric Crank (3) Linkage
(4) DC Control unit (5) Speed Indicator
(6) Total number of cycles counter
Experimental Set-up for completely
reversed bending test
(1) Fixed end
(3) Free End
Work holding devices
for fixed and free end
of the specimen

Evaluation of Optimum span length
for two different Hybrid specimens
-0.5
0
0.5
1
1.5
2
2.5
3
0 50 100 150 200 250
Beam length
Deflection
CGGC
GCCG
Linear (CGGC)
Linear (GCCG)
79
136
25

80
Evaluation of Equivalent beam deflection
for two different hybrid beams
• Stress controlled fatigue test
• 20% of flexural strength of hybrid beams, i.e. 100 MPa, as limiting stress
• Equivalent load for the limiting bending stress for the hybrid beams H1
and H2 are arrived by using the bending equation, b = M/Z
• Based on the dimensions of the hybrid beams the equivalent load P was
evaluated and it was found as 19.15 N
F=19.15 N
136mm
Equivalent deflection of the beam is
calculated by using standard beam
deflection equation, max = Pl3/3EI
The equivalent deflection of the hybrid
beams with different flexural modulus of
10.55 MPa and 17.41 MPa respectively
are evaluated as 17 mm and 12 mm
respectively

81
Test specimen type : H1 & H2
Free length, L : 136 mm
Test frequency, f :10Hz
Induced deflection, d :
±17 mm - H1 &
±12 mm - H2
Equivalent load, F : 19.15 N
Induced stress, σb : ± 100
MPa
Stress Ratio, R = σmax/σmin : -1
Experiment test conditions
(1) DC Motor (2) Eccentric Crank (3) Linkage (4) DC Control
unit (5) Speed Indicator (6) Total number of cycles counter (7)
Composite Specimen (8) Impact Hammer (B&K Type 5800B4)
(9) Accelerometer (B&K Type 3055B2) (10) Data Acquisition
Card (B&K Type Photon+) (11) PC with RT Pro Software
showing FRF
Experimental Setup for measuring vibration
characteristics of hybrid composite beam after
completely reversed bending cyclic loading

82
0
2
4
6
8
10
12
14
16
18
20
0 200 400 600 800 1000
Amplitude(gn/N)
Frequency (Hz)
0 cycle
1 Lakh cycles
2 Lakh cycles
Comparison of FRF plots of Hybrid beams
after cyclic loading
0
5
10
15
20
25
0 200 400 600 800
Amplitude(gn/N)
Frequency (Hz)
0 cycle
1 Lakh
cycles
There is reduction in modal frequency values at successive modes of hybrid
beams, H1 and H2 due to cyclic loading, accordingly peaks in FRF plot were
shifted in opposite direction

83
No. of
Cycles
(x 105)
Mode 1 Mode 2 Mode 3
Frequency
(Hz)
% of
Damping
Frequency
(Hz)
% of
Damping
Frequency
(Hz)
% of
Damping
0.0 33.75 6.52 302.50 2.62 757.50 1.34
0.5 23.75 15.60 265.00 3.78 632.50 3.05
1.0 22.50 17.69 266.25 3.48 647.50 2.74
1.5 22.50 18.89 255.00 6.71 620.00 2.89
2.0 20.00 23.20 247.50 6.71 697.50 2.48
Variation of Modal frequency and Damping values
at successive Resonance set of H1 hybrid beam
subjected to cyclic loading
Resonance frequency set values at successive modes decreasing trend
Vibration damping shows increasing trend with respect to number of cycles

84
No. of
Cycles
(x 105)
Frequency
(Hz)
% of
Damping
Frequency
(Hz)
% of
Damping
Frequency
(Hz)
% of
Damping
0.0 46.88 6.06 386.72 1.14 962.40 1.79
0.5 45.41 6.18 373.54 2.23 887.70 2.31
1.0 43.12 8.76 366.21 2.94 823.24 2.24
1.5 38.09 12.04 342.77 4.39 805.66 2.55
2.0 36.62 12.14 339.84 5.72 783.84 3.46
Variation of Modal frequency and Damping values
at successive Resonance set of H2 hybrid beam
Due to cyclic loading
Resonance frequency set values at successive modes decreasing trend
Vibration damping shows increasing trend with respect to number of cycles

85
No. of
Cycles
( 105)
Modal Stiffness (kN/m)
H1 H2 H1 H2 H1 H2
0.0 0.59 1.14 47.64 77.85 298.72 482.18
0.5 0.29 1.07 36.56 72.64 208.26 410.22
1.0 0.26 0.97 36.90 69.82 218.26 352.82
1.5 0.26 0.76 31.89 61.17 200.11 337.91
2.0 0.24 0.70 31.89 60.12 200.11 319.85
Variation in Modal Stiffness of Hybrid beams
due to cyclic loading
Modal Stiffness values are evaluated based on experimental modal frequency
values of H1 and H2 hybrid beams

86
Mode 1
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.5 1.0 1.5 2.0
NormalisedModalStiffness
No. of Cycles (x105)
H2
Influence of cyclic loading on Modal stiffness
H1
Rate of loss of stiffness in H1
beam is larger than the other
arrangement H2 due to cyclic
loading at all successive modes
Mode 2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.5 1.0 1.5 2.0
H1
H2
Mode 3
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.5 1.0 1.5 2.0
H1
H2

87
Mode shapes of hybrid beam H1 before and
after Cyclic loading
Mode I
303 Hz
758 Hz
20 Hz
248 Hz
698 Hz
34 Hz
Mode II
Mode III
Before After

88
Mode shapes of Hybrid beam H2 before and after
Cyclic loading
46 Hz
386 Hz
963 Hz
Mode I
Mode II
Mode III
36 Hz
339 Hz
783 Hz
Before After

89
Severe breakages of fibre roving in H1 (GCCG) as fundamental arrangement
Morphology of H1 Beam
H1 Beam after 2x105 cycles
of Reversed bending load

90
Severe delamination of the epoxy resin reveals
longitudinal and lateral fibres. Longitudinal fibre
breakage near the fixed end appears to be predominant
In addition to the delamination of the surface
resin revealing the longitudinal glass fibres
below, transverse matrix fatigue striations are
also found. Fibre breakage is also seen.
Figure reveals transverse matrix cracking
in agreement with the fatigue cycling.
Notice the total debonding and peel off of
the longitudinal fibres in vibration
Scanning Electron Microscopy

91
Morphology of H2 Beam
Limited breakages of fibre roving in H2 (CGGC) as fundamental arrangement
and crack propagation predominantly through Epoxy matrix
H2 Beam after 2x105 cycles
of Reversed bending load

92
Longitudinal carbon fibres exhibiting
breakage. However, the fibre damage in
H2 is lesser than what is exhibited by H1.
Longitudinal carbon fibre damage associated
with matrix striations in fatigue transverse to
the interface.
Scanning Electron Microscopy

Conclusion
 A displacement controlled fully reversed bending cyclic test
rig for testing the cantilever type hybrid composite laminates
was designed and developed
 Experiments were conducted to determine the effects of
cyclic loading on vibration characteristics like natural frequency,
percentage of damping and the modal stiffness of the
glass/carbon hybrid composite laminate specimen under fully
reversed bending cyclic loading
 Resonance frequency set at successive modes show
decreasing trend and the vibration damping shows increasing
trend with respect to number of cycles
 Rate of loss of stiffness in H1 beam is larger than the other
arrangement H2 during cyclic loading at all successive modes
 Macrographs and SEM fractography of damaged hybrid
sample H1 (GCCG) showed severe breakages in fibre roving
whereas in H2 (CGGC) sample there are only limited breakages
of fibre roving and crack propagation is predominantly through
Epoxy matrix

International Journal
95
1. R. Murugan, R. Ramesh, K. Padmanabhan, “Investigation on Vibration Behaviour of
Cantilever Type Glass/Carbon Hybrid Composite Beams at Higher Frequency Range using
Finite Element Method” in Advanced Materials Research, Vols. 984-985 (2014) pp 257-
265, Trans Tech Publications, Switzerland DOI:10.4028/www.scientific.net/AMR.984-
985.257
2. R. Murugan, R. Ramesh, K. Padmanabhan, “Experimental Investigation on the Different
Aerial Density of Woven Fabric Glass, Carbon and its Hybrid Composite Beam Subjected to
Free Vibrating Condition” International Journal of Earth Sciences and Engineering
(Accepted for publication)
3. R. Murugan, R. Ramesh, K. Padmanabhan, “Investigation on Static and Dynamic
Mechanical Properties of Epoxy Based Woven Fabric Glass/Carbon Hybrid Composite
Laminates” Procedia Engineering, Elsevier Publications (Accepted for publication)
4. R. Murugan, R. Ramesh, K. Padmanabhan, “Vibration Characteristics of Thin Walled
Glass/Carbon Hybrid Composite Beams subjected to Fixed Free Boundary Condition”
International Journal of Mechanics of Advanced Materials and Structures, Taylor & Francis
Publications. (Communicated)
5. R. Murugan, R. Ramesh, K. Padmanabhan, “Investigation of Fibre Aerial Density effects on
Mechanical Properties and Vibration Characteristics of Epoxy based Glass/Carbon Hybrid
composite Plates made of Two fundamental Stacking Sequences” Proceedings of the
Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications,
SAGE Publications (Communicated)

International Conference
96
1. Murugan R, Padmanabhan K, Ramesh R, Rajesh M, “Hybrid effect on damping behavior of epoxy
based woven fabric composite beams” in the International conference on Advancements in
Polymeric materials during March 25-27, 2011 at CIPET, Chennai
2. Murugan R, Padmanabhan K, Ramesh R, “Vibration Characteristics of Thin Walled Hybrid Carbon
Composite Beams under Fixed Free Boundary Condition” in 3rd Asian Conference on Mechanics of
Functional Materials and Structures (ACMFMS 2012) held on December 5-8, 2012 at Indian
Institute of Technology, New Delhi
3. R. Murugan, K. Padmanabhan, R. Ramesh, M. Arulkumar, “An Investigation on Static Mechanical
Properties of Epoxy based Glass/Carbon Woven Fabric Hybrid Composites” on 2013 International
Conference on Energy Efficient Technologies for Sustainability at St. Xaviers College of
Engineering, Kanyakumari
4. R. Murugan, R. Ramesh, K. Padmanabhan, “Investigation on Vibration Behaviour of Cantilever
Type Glass/Carbon Hybrid Composite Beams at Higher Frequency Range using Finite Element
Method” in International Conference on Recent Advances in Mechanical Engineering and
Interdisciplinary Developments - ICRAMID 2014 held on 7-8 March 2014 at Ponjesly College of
Engineering, Nagercoil
5. R. Murugan, R. Ramesh, K. Padmanabhan, “Experimental Investigation on the Different Aerial
Density of Woven Fabric Glass, Carbon and its Hybrid Composite Beam Subjected to Free Vibrating
Condition” in International Conference on Modelling Optimization and Computing (ICMOC 2012),
held at Noorul Islam University, Kumaracoil, during 10-11 April 2014.
6. R. Murugan, R. Ramesh, K. Padmanabhan, “Investigation on Static and Dynamic Mechanical
Properties of Epoxy Based Woven Fabric Glass/Carbon Hybrid Composite Laminates” in 12th
Global Congress on Manufacturing and Management, GCMM 2014, held at VIT University, Vellore,
during 8-10 December 2014

National Conference
97
1. Murugan R, Padmanabhan K, Ramesh R, Anandakannan P, “Design and
Development of Fatigue Testing Facility” in the National conference on Recent
Trends in Mechanical Engineering (NCRTIME’12) held on 22nd March 2012 at
Saveetha School of Engineering, Saveetha University, Chennai-602105.
(Received First Prize)

References – Mechanical Properties
1) P. K. Malik, “Fibre reinforced composites, materials and manufacturing and Design”, Second Edition,
CRC Press, Taylor & Francis Group
2) W.T. Thomson, M. D. Dahleh, “Theory of vibration with applications”, First Edition, 2003, Pearson
Education, Inc.
3) ASTM D3171-09, Standard test methods for Constituent content of composite materials, Annual book
of ASTM standards, Philadelphia, 2005
4) ASTM D3039, Standard test method for tensile properties of polymer matrix composite materials,
Annual book of ASTM standards, Philadelphia, 2005
5) ASTM D790-03, Standard test method for flexural properties of unreinforced and electrical Insulating
Materials, Annual book of ASTM standards, Philadelphia, 2005
6) ASTM D256-05, Standard test method for Determining the Izod Pendulum Impact Resistance of
Plastics, Annual book of ASTM standards, Philadelphia, 2005
7) G. Kretsis, “A review of the tensile, compressive, flexural and shear properties of hybrid fiber
reinforced plastics”, Composites, Vol. 18(1), p. 13-23, 1987
8) Huang Gu, “Tensile behaviour of woven fabric and laminates”, Materials and Design Vol.28, p. 704–
707, 2007
9) K. Padmanabhan, E. Naveen & Nirup Philip, “The Design, Fabrication and Mechanical Characterization
of Glass and Carbon Fabric/Epoxy Matrix Hybrid Composites”, International Journal of Mechanical
Engineering and Materials Science, Vol. 3(2), p. 97-103, 2010
10) Kedar S. Pandya, Ch. Veerraju, N.K. Naik, “Hybrid composite made of carbon and glass woven fabric
under quasi-static loading”, Materials and Design, Vol. 32, p. 4094–4099, 2011
11) Bunsell.A.R, and Harris.B. (1974). Hybrid carbon and glass fibre composites. Composites: 157-164.
98

99
1) Gibson. R. F. (1992). Damping Characteristics of Composite Materials and Structures. Journal of
Materials Engineering and Performance 1(1): 11-20.
2) Gibson. R. F. (2000). Modal vibration response measurements for characterization of composite
materials and structures. Composites Science and Technology (60): 2769-2780.
3) Hajime Kishi, Manabu Kuwata, Satoshi Matsuda, Toshihiko Asami, Atsushi Murakami. (2004). Damping
properties of thermoplastic-elastomer interleaved carbon fiber-reinforced epoxy composites.
Composite and Technology (64): 2517-2523.
4) Jean-Marie Berthelot, Youssef Sefrani. (2004). Damping analysis of unidirectional glass and Kevlar
fiber composites. Composite and Technology (64): 1261-1278.
5) Botelhoa. E.C., Campos. A.N., E. de Barros., Pardini. L.C., Rezende. M.C. (2006). Damping behavior of
continuous fiber/metal composite materials by the free vibration method. Composites: Part B (37):
255–263.
6) Sanchez-Saez. S, Barbero. E, Navarro. C (2007). Analysis of the dynamic flexural behaviour of
composite beams at low temperature. Composite and Technology (67): 2616-2632
7) Abderrahim El Mahi., Mustapha Assarar., Youssef Sefrani., Jean-Marie Berthelot. (2008). Damping
analysis of orthotropic composite materials and laminates. Composites: Part B (39): 1069–1076.
8) Kyriazoglou.C, Guild. F.J. (2006). Finite element prediction of composite GFRP and CFRP laminates – a
hybrid formulation – vibration damping experiments and Rayleigh damping. Composite and
Technology (66): 487-498.
9) Mohammed F. Aly., Goda. I.G.M., Galal A. Hassan. (2010). Experimental investigation of the dynamic
characteristics of laminated composite beam. International Journal of Mechanical & Mechatronics
IJMME-IJENS 10(03): 59-58.
References – Vibration Characteristics

100
[1] Raif Sakin , _Irfan Ay, Ramazan Yaman (2008), “An investigation of bending fatigue behavior for glass-
fiberreinforced polyester composite materials”, Materials and design, vol. 29, pp 212-217.
[2] Nikola Jaksic, Chee-Hoe Foong , Marian Wiercigroch , Miha Boltezar (2008) “Parameter identification of
the fatigue-testing rig”, International Journal of Mechanical Sciences , vol.50, pp1142-1152.
[3] Dr. Muhannad Z. Khelifa, Hayder Moasa Al-Shukri (2008) “Fatigue Study of E-Glass Fiber Reinforced
Polyester Composite under Fully Reversed Loading and Spectrum Loading” Engineering and technology,
vol.26.
[4] G. Belingardi, M.P. Cavatorta , C. Frasca (2006) “Bending fatigue behavior of glass–carbon/epoxy hybrid
composites”,” Composites Science and Technology” vol.66, pp 222-232.
[5] G. Belingardi, M.P. Cavatorta (2006) “Bending fatigue stiffness and strength degradation in carbon–
glass/epoxy hybrid laminates: Cross-ply vs. angle-ply specimens”, International Journal of Fatigue,vol. 28,
pp 815–825.
[6] V.M. Harik , J.R. Klingerc, T.A. Bogetti (2002) “Low-cycle fatigue of unidirectional composites:Bi-linear
S–N curves”, International Journal of Fatigue,vol. 24, pp 455–462.
[7] W.Van Paepegem and J. Degrieck (2001) ”Experimental setup for and numerical modeling of bending
fatigue experiments on plain woven glass/epoxy composites” vol 51, pp 1-8.
[8] Rebecca A_ Abeles Couillard & Peter Schwartz (1997) “Bending fatigue of carbon-fiber-reinforced epoxy
composite strands” Composites Science and Technology ,vol.57, pp 229-235.
[9] Bryan Harris “fatigue in composites” CRC press, Tayler & Francis Group, Boca raton, London, New York.
[12] Design Data book, PSG College of Technology, Coimbatore.
[13] J.E.Shingley, ”Standard Handbook of Machine Design” Third edition,The McGraw Hill.
References – Fatigue Characteristics

Vibrations and fatigue- vibration interactions of laminated composites.

Recomendados

Recomendados

Más contenido relacionado

La actualidad más candente

La actualidad más candente (20)

Destacado

Destacado (20)

Similar a Vibrations and fatigue- vibration interactions of laminated composites.

Similar a Vibrations and fatigue- vibration interactions of laminated composites. (20)

Más de Padmanabhan Krishnan

Más de Padmanabhan Krishnan (20)

Último

Último (20)

Vibrations and fatigue- vibration interactions of laminated composites.