This document summarizes research on determining the mechanical properties of nanocomposite laminated structures using modal analysis and optimization. Experimental modal testing was performed on glass fiber-epoxy composite plates with 0%, 1%, and 2% nanoclay additions. Finite element modeling and optimization were used to determine elastic properties by minimizing differences between experimental and model natural frequencies. Results showed the tensile modulus increased with nanoclay content while shear modulus peaked at 1% nanoclay. Damping also increased in nanocomposites. Challenges included sensor effects and non-thin plate behavior limiting property determination. The inverse method was effective for analyzing new materials when direct methods cannot be used.
Multi-Objective Genetic Topological Optimization for Design of composite wall...Sardasht S. Weli
The aim of this presentation is to show the utilization of Topology Optimization to optimize a wall barrier thickness and its resistance under the extreme environment which is blast loading.
Presentation at icotom17 dresden 20140826Xiaodong Guo
ICOTOM stands for International Conference on Textures of Materials. it is the biggest conference in the field of texture and microstructure of materials in the world.
An Experimental Investigation into the Grindability Aspects of Newly Develope...IDES Editor
Ceramics are getting widely used in many engineering applications. These ceramic materials need to be ground. Unfortunately, the ground ceramic components mostly contain surface/subsurface damages. To minimize the grinding induced damages selection of appropriate grinding process parameters is very important. Ceramic composite material (AlSiTi) has been selected in the present study to investigate its grindability. This research work deals with the analysis of the process parameters such as wheel speed, table feed and infeed as influential factors, on the force components, grinding specific energy and surface roughness values based
on Taguchi’s experimental design method. Scanning electron microscopy (SEM) has been used to analyze the subsurface damages. The result provides valuable insight into the grindability aspects of the composite ceramic (AlSiTi).
Vibrational Analysis Of Cracked Rod Having Circumferential Crack IDES Editor
The frequency ratio of torsional vibration of a rod without crack and of rod with crack subjected to torque at the free end for various crack depth and varying crack location is investigated. It is found that even a cracked of small depth is
dangerous at the fixed end, also as the crack depth is increases more than 50% of diameter of rod there is a considerable drop in natural frequency of the rod .
Presentation used for Ian Nieves dissertation. It summarizes using FEA simulation to model impact mechanics and damping in a novel materials characterization device, and in biomedical materials designed to promote bone regeneration.
Multi-Objective Genetic Topological Optimization for Design of composite wall...Sardasht S. Weli
The aim of this presentation is to show the utilization of Topology Optimization to optimize a wall barrier thickness and its resistance under the extreme environment which is blast loading.
Presentation at icotom17 dresden 20140826Xiaodong Guo
ICOTOM stands for International Conference on Textures of Materials. it is the biggest conference in the field of texture and microstructure of materials in the world.
An Experimental Investigation into the Grindability Aspects of Newly Develope...IDES Editor
Ceramics are getting widely used in many engineering applications. These ceramic materials need to be ground. Unfortunately, the ground ceramic components mostly contain surface/subsurface damages. To minimize the grinding induced damages selection of appropriate grinding process parameters is very important. Ceramic composite material (AlSiTi) has been selected in the present study to investigate its grindability. This research work deals with the analysis of the process parameters such as wheel speed, table feed and infeed as influential factors, on the force components, grinding specific energy and surface roughness values based
on Taguchi’s experimental design method. Scanning electron microscopy (SEM) has been used to analyze the subsurface damages. The result provides valuable insight into the grindability aspects of the composite ceramic (AlSiTi).
Vibrational Analysis Of Cracked Rod Having Circumferential Crack IDES Editor
The frequency ratio of torsional vibration of a rod without crack and of rod with crack subjected to torque at the free end for various crack depth and varying crack location is investigated. It is found that even a cracked of small depth is
dangerous at the fixed end, also as the crack depth is increases more than 50% of diameter of rod there is a considerable drop in natural frequency of the rod .
Presentation used for Ian Nieves dissertation. It summarizes using FEA simulation to model impact mechanics and damping in a novel materials characterization device, and in biomedical materials designed to promote bone regeneration.
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temperature as well as furnace atmosphere is among the most important parameters affecting on final
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Proceedings of the American Society for Composites 2009-Twenty-Fourth Technical ConferenceWith the Canadian Association for Composite Structures and Materials (Joint Canadian-American International Conference), September 15-17, Newark, DE
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ABSTRACT: Composites have numerous applications in engineering field. In engineering design averting failure of composite material system has been a vital concern. Composite are subjected to numerous types of damage, mostly cracks and delamination. The presence of crack causes a variation in stiffness and it also affects the mechanical behavior of entire structure. Cracks are caused by fatigue under service conditions as a consequence of limited fatigue strength. Measurement of natural frequency can be taken as a tool to identify the presence of cracks which are propagated due to fluctuating stress conditions. In the present work an attempt has been made to find the natural frequencies of fiber reinforced composite cantilever beams with and without presence of a transverse surface crack. E-Glass fiber reinforced composite beams with epoxy resin having a volume fraction of 16.6% have been casted by hand lay-up method and are used for determination of natural frequencies of beams. The free vibration study is carried out by ATALON FFT analyzer, accelerometer and excitation by impact hammer. The DEWESOFT software is used to convert the responses from time domain to frequency domain and the Frequency Response Functions (FRF) are obtained. The experimental results are compared with numerical predictions using the FEM based software package ANSYS 16.2. The process of finding of natural frequencies is carried out for various crack depth ratios at various crack locations by both numerical and experimental methods. A good accord is observed between the experimental and ANSYS results.
Cocrystallization is a promising approach in improving the physicochemical properties of drugs/APIs. But to develop a suitable formulation mechanical properties should also be considered and cocrystallization technique has demonstrated improvement in the mechanical properties of poorly compressible drugs.
Determination of the equivalent elastic coefficients of the composite materia...eSAT Journals
Abstract We must first find a behaving law of a material, before using it in the structure. The establishment of this law in the case of a composite material requires the knowledge of his elastic equivalent coefficient. In this work, we will present the vibratory technic with which we can extract the equivalent elastic coefficients of some composite materials. The relationships we have obtained through this analysis permits to evaluate the equivalent elastic coefficients of composite materials as a function of their self throb. Those relationships are first validated with the determination of mechanical characteristics of conventional materials. After that, equivalent elastic coefficients of some composite materials are evaluated. Simulated results we have obtained are discussed in comparison of Voigt and Reuss boundaries.
Application of two comparator in mass calibration using subdivision methodDarmaa Unuruu
Application of two mass comparators with different resolution in one decade of subdivision method is presented here. This work done at mass lab of MASM / Mongolian Agency for Standardization of Metrology/ in 2014.
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The aim of this study is to investigate the effect of different process parameters on densification of
Samarium Cobalt 1:5 series (SmCo5) magnet by powder metallurgy technique. Different parameters for
sintering and heat treatment process such as particle size, load of press, sintering time and temperature,
furnace atmosphere and heating rate were tested in order to achieve the highest density. To analyze and
evaluate the microstructure and particle size of manufactured magnets scanning electron microscopy
(SEM) and X-ray diffraction (XRD) tests were conducted. Results of different tests showed that sintering
temperature as well as furnace atmosphere is among the most important parameters affecting on final
density of the samples. Investigations illustrated that highest density could be obtained with the sintering
of green bodies which made from initial particles with the size of 3 to 6 µm in vacuum condition at 1135˚C
for 30 min by rapid heating at the shortest time.
High-Gradient Magnetic Separation Method for Weakly Magnetic Particles: an In...Barhm Mohamad
The high-gradient magnetic separation process is a technique used in heavy industries, particularly steel mills, to extract magnetic particles from mixtures. The difficulty of separating the slightly magnetic particles from the nonmagnetic ones lies in the distribution of the magnetic field and the fineness of their class to be separated. A use of different separation matrix profile is implemented, making it possible to act on the value of the gradient of the inhomogeneous magnetic field. Different matrixes are tested and the results obtained experimentally allows to choose the most efficient matrix form in the operation of extraction which increased by 11% in magnetic fraction yield, 15% iron content and 17% of extraction degree relative to the John’s matrix. This matrix used is consistent with that cited in literatures. The separation technology used can extend its useful application to small particles from very weakly magnetic materials. Its exploitation will result in the method of reducing the degree of pollution and improvement the process of extraction of minerals that has an impact on the environment and on human health as a result a high level of extraction.
Role of αc–relaxation in high-temperature polymer deformation.
Proceedings of the American Society for Composites 2009-Twenty-Fourth Technical ConferenceWith the Canadian Association for Composite Structures and Materials (Joint Canadian-American International Conference), September 15-17, Newark, DE
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Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
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Nano comp lam method
1. 2nd
International Conference on Engineering Optimization
September 6-9, 2010, Lisbon, Portugal
Mechanical Properties of Nanocomposite Laminated Structures by Modal
Method
Horacio V. Duarte, L´azaro V. Donadon, Antˆonio F. ´Avila
Universidade Federal de Minas Gerais, Av. Antˆonio Carlos 6627, Belo Horizonte, Brasil
Abstract
The Finite Element model of the laminate plate is used to approximate the experimental modal results
by a optimization procedure. From the modal properties the tensile and shear modulus and the Poisson
coefficient of a woven orthotropic composite plate were determined by this method. The plates used
in the experiment are made of S2-glass/epoxy with 16 layers are manufactured by vacuum assisted wet
lay-up. The matrix of the nanocomposite has been obtained by adding 0%, 1%, 2% nanoclays in weight
into epoxy matrix. Remarks are made about the results, analysis methodology and its limitations. .
Keywords:Nanocomposites, Laminated Composites, optimization, Modal analysis .
1. Introduction
There is a numbers of researchers who studied the effect of nanoparticles (organically modified montmo-
rillonite - Cloisite 30B) into epoxy systems. One aspect of the nanocomposite structure is the damage
reduction due to impact loadings. Among researchers who studied the effect of nanoparticles, Yasmin et
al. [1] and Isik et al. [2] found also an increase in the elastic moduli and toughness [2].
A more comprehensive study on clay-epoxy nanocomposites was performed by Haque et al. [3], since they
evaluated both mechanical and thermal properties. Their main conclusions were that thermo-mechanical
properties mostly increase at low clay loadings ( 1-2% in weight) but decrease at higher clay loadings
( 5% in weight). In addition, the uses of nanoclays also decrease the coefficient of thermal expansion
(CTE). They also observed a degradation of properties at higher clay loadings. This phenomenon can be
due to the phase-separated structures and defects in cross-linked structures.
The objective of this paper is to study the nanoparticle influence into the plate vibration behavior and
to determine the elastic constants using the optimization procedure. To analyze only the nanoparticle
influence all manufacturing parameters are kept fixed but the nanoparticle concentration. The modal
analysis was made with the objective to determine the structural mode shape to compare the frequencies
and modal properties for different nanoclay composite plates.
A commercial code, Ansys, which offers the function of design optimization, is employed to model the
woven laminate a orthotropic model. The optimization allows to approximate the theoretical laminate
model modal results to experimental ones and by this way determining the elastic properties.
2. Testing Procedures and Results
The nanocomposite prepared for this work is a S2-glass/epoxy-clay. The epoxy formulation is based on
two parts, part A (diglycidyl ether of bisphenol A) and part B - hardener aliphatic amine- (triethylenete-
tramine). The nanoclay particles used in this study are organically modified montmorillonite in a platelet
form, while the S-2glass fiber has a plain-weave woven fabric configuration with density of 180 g/m2
from
Texiglass. The S2-glass/epoxy-nanoclay composite is a laminate plate with 16 layers and 65% fiber vol-
ume fraction. The nanocomposite synthesis followed the methodology proposed by ´Avila et al. [?] [5]. In
order to be able to investigate the nanoparticles influence into vibration analysis, samples with 0%, 1%,
2% of nanoclay with respect to the matrix mass were employed. All plates were rectangular and had the
same dimensions 136mm x 116mm x 2.4mm.
The vibration analyses were performed to determine the shape modes and its natural frequency, shape
mode amplitude and the damping coefficient. The vibration testing were performed using a Laser Doppler
Vibrometer, laser model OFV 303.8 and controller model OFV 3001 S from Politec, a Hewlett Packard
data acquisition system model 35670A, a nini-shaker, a shaker power amplifier and force transducer from
PCB. The test plates were hanged by a fine nylon wire and excited by a random signal (white noise). A
piezoelectric force transducer was used as the reference for the force bonded to the plate and linked to
the stinger/shaker exciter, which transform the amplified electrical signal in force. There was only one
force excitation point at the same position for all plates. The velocity of the plate surface was measured
1
2. using a grid of 35 points by the laser Doppler vibrometer. The data acquisition system processed the
signal response of the measurement point generating the Mobility (velocity/force) Function Response
Frequency (FRF), for each point of the plate.
A modal analysis program has done the mode shape identification from the 35 FRF for each plate.
This modal analysis program is based on polynomial interpolation and employs Chebycheff Orthogonal
Polynomials method, Arruda et al. [6].
Mode 1 180.6321 [Hz] Damping=0.0297 Mode 2 344.4358 [Hz] Damping=0.0166
Mode 3 423.6049 [Hz] Damping=0.0098 Mode 4 568.7344 [Hz] Damping=0.0112
Mode 5 692.8686 [Hz] Damping=0.0137 Mode 6 735.2092 [Hz] Damping=0.0131
Figure 1: Shape modes for epoxy resin composite plate.
There is no difference between the modal shapes of the 1% nanoclay composite and those of the resin
reference plate, so the 1% resin shape are not showed. Figure (2) plots the shape modes for the composite
plate with 2% nanoclay weight. The latest shape mode, named 7th
mode, is out of the increasing frequency
order, and this mode is similar to 4th
one.
Table (1) brings a summary of the modal properties natural frequencies, the associated damping coeffi-
cients and Mobility amplitude for each experimental mode. The 7th
mode, for the 2% nanoclay plate, is
detached and presented in the appearing sequence.
2
4. Table 1: Matrix composite content and Modal Properties.
Composite Mass Modal Shape Modes
Matrix [gr] Properties 1th 2th 3th 4th 7th∗ 5th 6th
Pure Nat. Frequency [Hz] 180.6 344.4 423.6 568.7 692.9 735.2
Epoxy 66.37 Damping Coef. 0.0297 0.0166 0.0098 0.0112 0.0137 0.0131
Resin Amplitude [m/s]/kgf 57.0 17.0 6.5 4.8 12.1 8.5
Epoxy Nat. Frequency[Hz] 184.9 347.4 424.6 550.1 683.4 728.2
Nanoclay 65.27 Damping Coef. 0.0209 0.0247 0.0088 0.0136 0.0137 0.0138
1% weight Amplitude [m/s]/kgf 79.9 14.0 24.1 2.6 17.9 9.6
Epoxy Nat. Frequency [Hz] 173.6 361.3 424.0 578.0 655.3 ∗ 716.1 783.0
Nanoclay 66.92 Damping Coef. 0.023 0.0248 0.0116 0.0173 0.0052∗ 0.0134 0.0166
2% weight Amplitude [m/s]/kgf 32.9 5.8 4.7 21.5 44.3 ∗ 15.0 8.1
3. Data Analysis
To determine the elastic properties was used the inverse method. This method is based on optimization of
a Finite Element Model and is very popular. The optimization is a zero-order approach method, offered
as a tool of the FE commercial code, and followed the Hu and Wang [8] procedure. The state variables
ξn are related to difference between FE, fF E
n , and experimental modal nth frequency fn:
ξn =
fF E
n − fn
fn
100 (1)
The cost function F is defined as:
F(Exy, Gxy, νxy) =
k
n=1
ξ2
(2)
Where the mechanical properties are Exy the Tensile Modulus, Gxy the Shear Modulus and νxy the
Poisson’s ratio.
The element used in the Finite Element Model was the shell181 element. This shell element has four
nodes and six degrees of freedom in each node. This element has been formulated to thin to moderately
thick plates. This element also accepts multi-layers shell allowing the construction of complex models of
laminates. The FE model also employed the mass21 element, to consider the effect of mass and rotary
inertia of the force transducer bonded to the plate. The structure was modeled by 320 shell elements and
by concentrated mass element.
For the reference resin plate and 1% nanocomposite plate the results are obtained by direct application
of the method. The 2% nanocomposite plate showed a singular situation. The 4t
h and 7t
h has identical
shape modes at different frequencies. This behavior was not observed in the previous cases. The finite
element simulation showed a coupling mode between the plate and the force transdutor, this result has
appeared for all plate simulations but at a low frequency, below the experimental frequency range.
There was not used a complex FE model to deal wiht the dynamical coupling between the elastic plate
the force trandutor, the elastic stinger and shaker. So the dynamical coupling appeared something like
a rigid body mode. But this model offered a answer to the similar modes, one of them were a coupling
mode between the experimental apparatus and the elastic plate. The nanocomposite mass in the matrix
changed the elastic properties of the plates and the coupling frequency mode move inside the range of
the experimental plate natural frequencies.
The problem is to determine what mode is a plate mode and what is not. The solution presented here
is to find the real mode by comparing the error between the experimental mode frequencies and the
frequencies of the optimized or minimized model.
4
5. Table 2: Frequency mode error in each iteration. Frequency for the 4th
mode 578.0 Hz
iteration 1th
mode 2th
mode 3th
mode 4th
mode 5th
mode 6th
mode
1th
0.872E-02 0 0 0 0 0 0.01
2th
0.423E-01 0.389E-01 0 0 0 0 0.08
3th
0.985 2.08 2.22 0 0 0 5.28
4th
0.984 2.10 2.20 0.789 0 0 6.08
5th
1.03 2.02 2.28 0.670 2.30 0 8.29
6th
1.02 2.03 2.27 0.692 2.28 3.92 12.21
The Tab. (2) and Tab. (3) show the frequency error for each mode in the minimization procedure. The
minimization was not done for all frequencies in a unique process. The procedure was to include one
mode frequency at time and find the elastic properties. The latest elastic propeties are used as initial
value in a new minimization process, that includes the next frequency. This procedure will be called
an iteration. The latest iteration is performed using a small tolerance for the cost function F, Eq. (2),
for all cases F < |10−2
|. The Tab. (2) presents error for each mode frequency in each iteration, in this
case, the fourth mode is supposed to be the plate mode. The Tab. (3) presents the same error evolution
considering the seventh mode (655.3 Hz) as the plate mode.
Table 3: Frequency mode error in each iteration. Frequency for the 4th
mode 655.3 Hz
iteration 1th
mode 2th
mode 3th
mode 4th
mode 5th
mode 6th
mode
1th
0.872E-02 0 0 0 0 0 0.01
2th
0.423E-01 0.389E-01 0 0 0 0 0.08
3th
0.985 2.08 2.22 0 0 0 5.28
4th
1.0087 7.5204 2.0591 2.7306 0 0 13.3
5th
1.0262 2.4241 1.5333 8.8377 1.6721 0 15.5
6th
0.98710 2.4631 2.0953 9.5305 2.1113 4.1373 21.3
The Tab. (2 shows the lowest errors for the fourth and the sum of error of each frequency mode. So it is
used to determine the elastic properties showed on Tab(4).
4. Closing Remarks
The inverse method used here minimizing a finite element model showed to be a powerful, fast and
very flexible method of analysis. Without the method it was necessary to repeat all the experimental
procedure to find the problem.
In this work the sensor mass and mainly the rotatory inertia has made a strong influence on the results,
this parameter is difficult to determine with precision. The excitation of the system is still a problem
and can introduce error in the results.
The Tensile Modulus Exy increases with nanoclay mass increase in the matrix epoxy resin. The Tensile
modulus for the 2% composite plate is 17% greater than the equivalent resin modulus. For the Shear
Modulus, Gxy, the maximum value is at 1 % nanoclay in matrix resin. The Poisson’s coefficient νxy
showed a very low value. Part of the problem is that the Shear and Tensile modulus have highest values
compared to Poisson’s coefficient value. Probably the shape modes used do not capture its influence [7].
Table 4: Elastic Properties
Composition Exy[GPa] Gxy[GPa] νxy
Resin 100% 27.3 4.2 0.10425E-07
Nanoclay 1% weight 28.3 5.1 0.10212E-03
Nanoclay 2% weight 31.9 3.8 0.75339E-03
5
6. All nanocomposite plates had a highest damping coefficient and this properties must be included as it
can change the frequencies mainly the highest ones. The plates used in this work can not be considered
thin and some shape modes are difficult to obtain, the synclastic mode for instance. The behavior of the
new materials can not be obtained by standard procedures.
Acknowledgements
This work was supported by the Funda¸c˜ao de Amparo a Pesquisa de Minas Gerais FAPEMIG, which
support the authors are grateful.
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