DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC LAYERS

DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC LAYERS
DYNAMIC BEHAVIOR OF SANDWICH BEAM
WITH PIEZOELECTRIC LAYERS
A THESIS SUBMITTED IN PARTIAL REQUIREMENTS FOR THE
DEGREE OF
Bachelor of Technology in Mechanical Engineering
By
SURYAKANT SAHOO (107ME041)
SHUBHAM GARG (107ME059)
DEVADASI VICKEY AVINASH (107ME006)
Under The Guidance Of
Prof. TARAPADA ROY
Prof. HARAPRASAD ROY
Department of Mechanical Engineering
National Institute of Technology, Rourkela
MAY, 2011
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
ACKNOWLEDGEMENT
It gives me immense pleasure to express my deep sense of gratitude to my
supervisor Prof. Tarapada Roy and Prof. Haraprasad Roy for their invaluable
guidance, motivation, constant inspiration and above all their ever co-operating
attitude enabled me in bringing up this thesis in present elegant form.
I am extremely thankful to Prof. R. K. Sahoo, Head, Department of Mechanical
Engineering and the faculty member of Mechanical Engineering Department for
providing all kinds of possible help and advice during the course of this work.
It is a great pleasure for me to acknowledge and express my gratitude to my
parents for their understanding, unstinted support and endless encouragement
during my study.
I am greatly thankful to all the staff members of the department and all my well
wishers, class mates and friends for their inspiration and help.
Lastly I sincerely thank to all those who have directly or indirectly helped for the
work reported herein.
SURYAKANT SAHOO (107ME041)
SHUBHAM GARG (107ME059)
DEVADASI VICKEY AVINASH (107ME006)
Department of Mechanical Engineering
National Institute of Technology, Rourkela
Page | 1
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
Contents
Serial No.
Description
1
1. Abstract
2
2. Introduction
Page No.
3-6
7
2.1 Sandwich Beam.
7-8
2.2 Behavior Of Sandwich Beam.
8-9
2.3 Advantages Of Sandwich Beam.
9-10
2.4 Critical Elements In A structure.
10
3
3. Motivation Of The Present Work
11
4
4. Literature Review
12-16
5
5. Analytical Work
17-28
6
6. Calculations
29
7
7. Conclusion
30
8
8. Scope For Future Work
30
9
9. References
31-34
Page | 2
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
ABSTRACT
Sandwich beams with composite face sheets and foam core are widely employed as lightweight
components in many of the industries that extend from automotive, marine to aerospace
applications due to its high bending stiffness and strength combined with low weight factor.
Therefore, it is important for us to gain insight about their flexural or bending behaviour under
static as well as dynamic loads. Extensive research has been carried out on the flexural behaviour
of composite laminates. The flexural and bending behaviour of sandwich structures is quite and
obviously different. Several works treating the dynamic flexural behaviour of sandwich beams
have also confirmed the marked susceptibility of sandwich structures to damage caused by the
impact of low velocity foreign objects. Impacts can certainly damage the face sheets, the core
material, and the core face interface. The type of damage found in the faces is similar to that
observed after impacts on monolithic composites. However, the damage initiation thresholds and
damage area depend on the properties of the core material and the relationship between the
properties of the core and those of the face sheets.
Thus we need the FEM simulations of sandwich beams and accurate descriptions of the damage
induced by the contact area, and finally we require the modelling of both the face sheets as well
as the core.
The researches for new vibration control systems are all about hybrid active–passive control
strategies. These were mainly based on simultaneous application of piezoelectric and viscoelastic
materials in the same damping treatment. In particular, it was found that, for the last 6 years,
these researches have focused on configurations that increase the damping ability of the
conventional passive constrained layer damping treatments. Depending on the position of the
piezoelectric actuator, the passive and active actions can operate either on their own or
simultaneously. In the former configuration, the passive constrained layer and piezoelectric
patches are placed away from each other, so that each of them uses independently its own
damping mechanism.
The piezoelectric actuator employs the conventional active control mechanism, based on induced
in-plane piezoelectric actuation strains; whereas, the passive constrained layer employs its
conventional passive damping mechanism, based on vibratory energy dissipation that happens
through the transverse shear strains induced in the viscoelastic material by relative in-plane
displacements of the constraining layer and base structure.
A sandwich beam was made of laminate faces, with elastic and piezoelectric sub layers, and
viscoelastic core. Faces was modeled using the classical laminate theory and the whole beam
was modeled using classical sandwich theory. Euler–Bernoulli assumptions were considered for
Page | 3
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
the laminate faces, whereas those of Timoshenko were retained for the viscoelastic core. The
piezoelectric layers were supposed transversely poled and subject to transverse electrical fields.
Elastic and viscoelastic layers are assumed to be insulated. All layers are assumed perfectly
bonded and in plane stress state.
An electromechanically coupled finite element model was used to handle the active–passive
damped multilayer sandwich beams. Classical laminate theory was used to model the multilayer
piezoelectric faces, whereas classical sandwich theory was considered for the laminate
piezoelectric face, viscoelastic core, laminate piezoelectric face beam, leading to three-layer
kinematic description and layer wise material constitutive equations. This has resulted in
additional membrane bending coupling terms in electromechanical internal and external forces
and translation to rotation coupling terms in inertial forces.
A hybrid active-passive damping mechanism, replacing the elastic constraining layer of a
conventional Passive Constrained Layer Damping treatment by a piezoelectric actuator, was used
to increase the shear deformation in the viscoelastic material and, thus, the energy dissipation.
The electric field was applied perpendicular to the poling direction of the piezoelectric actuators
to cause transverse shear deformation of the sandwich beam. Active vibration suppression is
achieved using either positive position feedback or strain rate feedback. The control system is
implemented in real-time using Matlab/Simulink and a dSPACE digital controller. First, the
frequency response of the adaptive beam is investigated by using one shear actuator to excite the
beam and the other to control its vibration. Parametric studies are conducted to assess the
influence of controller parameters on the frequency response of the system.
Using a proof-mass actuator that was attached to the tip of the cantilever beam in the time
domain the effectiveness of the active vibration suppression system was analyzed using a proofmass actuator which was attached to the tip of the cantilever beam to provide an input of
repeatable vibration. Piezoelectric actuators that are used in adaptive structures are thin wafers,
which are poled in the thickness direction and bonded to the surfaces of the host structure. An
electric field applied in the thickness direction causes the lateral dimensions of the actuators to
increase or decrease, thereby forcing the host structure to deform.
A piece of viscoelastic damping material sandwiched between an active piezoelectric layer and
the host structure constitutes Active constrained layer (ACL) damping. An Active Constrained
configuration will raise the viscoelastic layer damping ability by increasing its shear angle during
operation. That is the ACL will enhance the system damping when compared to a structure with
traditional passive constrained layers.
Page | 4
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
Experimental results are presented for an adaptive sandwich cantilever beam that consists of
aluminum facings and a core made of two piezoelectric shear actuators and foam. The electric
field is applied perpendicular to the poling direction of the piezoelectric actuators to cause
transverse shear deformation of the sandwich beam. Active vibration suppression is achieved
using positive position feedback. Piezoelectric actuators employed in adaptive structures are
usually thin wafers which are poled in the thickness direction and bonded to the surfaces of the
host structure.
The application of an electric field in the thickness direction causes the lateral dimensions of the
actuators to increase or decrease, thereby forcing the host structure to deform. The actuators are
usually placed at the extreme thickness positions of a plate-like structure to achieve the most
effective actuation. This subjects them to high longitudinal stresses and may lead to failure,
especially when they are made of brittle piezo-ceramics. To alleviate these problems several
researchers have investigated adaptive sandwich structures consisting of axially-poled
piezoelectric actuators.
The work to do is modeling of sandwich beam for active vibration control analysis on working
software Ansys. The inputs for the sandwich beam are varied materials with different properties
in different directions. The beam is isotropic in nature. The properties of materials include
Young‟s modulus, Poisson Ratio, and Density of material. The excitation is given in intervals
with varying frequency values within permissible limit. The material type used are coupled field,
Solid , Visco-solid. the inputs are given in Material Models in Preprocessor and Material
Properties.
The modeling is done for sandwich beam with create volume option with dimensions known in
the software. Meshing is done for the whole volume for nodal points of force application. Force
has to be applied in the nodal point which has maximum displacement. The vibration given at
that nodal point is to be suppressed with active vibration control mechanism. Solution after load
application is solved in Ansys with FloatRun option for viewing analytical solution regarding
control mechanism.
Page | 5
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
Fig 1(a). Schematic Diagram Of A Sandwich Beam
Fig 1(b). Schematic Diagram Of A Meshed Sandwich Beam
Page | 6
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
2. INTRODUCTION
2.1 SANDWICH BEAM
Sandwich beam is nothing but a composite beam in which a viscoelastic layer is sandwiched
between two elastic layers.
According to the sandwich theory, it describes the behavior of a beam which consists of three
layers - two face sheets and one core that is used in between the two face sheets. The most
commonly sandwich theory that is applied is a linear and is an extension of first order beam
theory. Linear sandwich theory is of utmost importance for the design and analysis of sandwich
panels, which are of use in building construction, vehicle construction, airplane construction and
refrigeration engineering.
The sandwich panels are a special class of composite materials that is fabricated by attaching two
thin but stiff skins to a lightweight but thick core. The core material is of a low strength material,
but higher the thickness higher will be the bending stiffness with overall low density.
Fig 2. Assembled Composite Sandwich
Diagram of an assembled composite sandwich (A), and its constituent face sheets or skins (B)
and honeycomb core (C).
Open and closed cell structured foam, polystyrene, balsa wood and honeycomb are commonly
employed as core materials. Glass or carbon fiber reinforced laminates are widely as skin
materials. Sheet metal is also employed as skin materials.
Page | 7
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
Metal composite material (MCM) is a type of sandwich structure formed by the application of
two thin skins of metal bonded to a plastic core in a continuous process under controlled
pressure, heat, and tension.
Recycled paper is also now being employed over a closed-cell recycled kraft honeycomb core,
which helps in creating a lightweight, strong and fully repulpable composite board. This material
is being employed for applications including point-of-purchase displays, recyclable office
furniture, exhibition stands and wall dividers.
To fix different panels, among other solutions, are normally use a transition zone, which is a
gradual reduction of the core height, until the two fiber skins are in touch. In this place, the
fixation can be made by means of bolts, rivets, adhesive or can be selected from different kinds
of material available.
The strength of the composite material is largely dependent on two factors:
1. The outer skins:
If the sandwich is given support on both sides, and is then stressed by means of a force in the
middle of the beam, then the shear forces from the bending moment will be introduced within the
material. The shear forces results in the bottom skin being in tension and the top skin being in
compression. The core material spaces those two skins apart. The thicker the core material, then
stronger is the composite. This principle works for an I-beam too.
2. The interface between the core and the skin:
As the shear stresses in the composite material changes rapidly between the core and the skin,
the adhesive layer also sees some degree of shear force. If the adhesive bond between the two
layers is too weak, the most probable result will be de lamination in those sheets.
2.2 Behavior of Sandwich Beam:
The behavior of a beam with sandwich cross-section under a load will differ from a beam with a
constant elastic cross section. If the radius of curvature during bending is found to be small
compared to the thickness of a sandwich beam and the strains in the component materials are
small, the deformation of a sandwich composite beam can be separated into two parts :
1. Deformations that occurs due to bending moments or bending deformation, and
2. Deformations that occurs due to transverse forces, also called shear deformation.
Page | 8
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
For sandwich beam, plate, and shell theories the reference stress state is one of zero stress. But,
during curing, there is a difference of temperature between the face-sheets because of the thermal
separation by the core material.
The face-sheets with different linear expansions are coupled. Due to temperature difference it
can lead to the bending of the sandwich beam having the warmer face-sheet compared to the
other face sheet. Residual stresses can develop during the manufacturing process if the bending
is constrained.
The superposition of a reference stress state on the solutions provided by sandwich theory is
possible when the problem is linear. However, when large elastic deformations and rotations are
expected, the initial stress state has to be incorporated directly into the sandwich theory.
2.3 Advantages of Sandwich Beam:
1. Sandwich cross sections are usually composite. They consist of a low to moderate stiffness
core which is then connected with two firm exterior face-sheets. The composite has considerable
higher shear stiffness to weight ratio compared to an equivalent beam made of only the core
material or the face-sheet material. The composite also has a very high tensile strength to weight
ratio.
2. High bending stiffness to weight ratio for the composite is achieved because of the high
stiffness of the face-sheet.
2.3.1 Piezoelectric materials:
1. Piezoelectric materials have the ability to generate electric potential in response to applied
mechanical stress.
2. This property is exhibited by certain materials like ceramics & some crystals.
3. The piezoelectric effects can be seen as transfer between electrical and mechanical energy.
4. Such transfers can only occur if the material is composed of charged particles and can be
polarized.
5. For a material to exhibit an anisotropic property such as piezoelectricity, its crystal structure
must have no centre of symmetry.
2.3.2 Piezoelectric Layered Sandwich Beams:
Active control of smart structures depends on the magnitude of electric potential difference for a
given mechanical stress. This subsequently depends on the piezoelectric stress/strain constants.
Page | 9
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
The existing monolithic piezoelectric materials being used in beams posses low
control
authority as their piezoelectric stress/strain constants are of small magnitude. Because,
tailoring of these properties may improve the damping characteristics of the smart
st ruct ures. These beams show improved mechanical
performance, electromechanical
coupling characteristics, and acoustic impedance matching with the surrounding medium over
the piezoelectric material alone.
2.4 Critical Elements in a structure:
There are two important components in a structure:
1. Actuators
2. Sensors
2.4.1 Actuators:
Actuator is generally the reverse of sensor. It converts electrical inputs to physical (thermal,
mechanical, etc) outputs. The ideal mechanical actuator would directly convert electrical
input into strain or displacement in the host structure. The principal actuating mechanism of
actuators is referred to as actuation strain.
2.4.2 Sensors:
Sensors are mechatronics devices that can convert analogue physical values into electrical
impulses thus informing of their magnitude. The ideal sensor for structures converts strain or
displacement directly into electrical output. The primary functional requirement of such
sensors is their sensitivity to strain and displacement.
Page | 10
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
3. Motivation Of The Present Work
Sandwich beams which are the answer to many structural problems demanding self control and
flexible characteristics involving mechanical and thermal stresses. The technological
implications of this class of beams are immense, as they are especially useful in remote
operations, expensive space operations subjected to extreme thermo-mechanical loadings,
aerospace skins, protective shields, components in reactor vessels, machine tools, and medical
applications, to name only a few. As the advent of steel changed the last century, similarly these
beams which will revolutionize the 21st century.
The beams have characteristics such as thermo-electro-mechanical coupling, functionality,
intelligence, and gradation at micro and nano scales. The reliability and integrity of these
systems are the main challenges before us. They can be customized to operate under varying
conditions covering the
whole spectrum of electro-thermo-mechanical conditions. The
conditions can vary across a wide range of temperature, magnetic & electric fields, pressure and
mechanical load, and/or a combination of two or many. Experimental investigations of both
these systems & beams although possible, are prohibitively expensive, and therefore must be
complemented with simulations and theoretical analyses.
Page | 11
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
4. LITERATURE REVIEW
A.Benjeddou in „Advances In Piezoelectric Finite Element Modeling Of Adaptive Structural
Elements‟ proposed that earlier piezoelectric materials were of great interest for finite element
modeling, but interests have been shifted to smart structures and modeling of the same for
advanced applications .These smart structure includes composite plates, sandwich beams, shells.
The trends and advances in these structures are determined by the electrical properties and
elemental characteristics such as shape, independent variables and degree of freedom. For finite
element formulation, the basic equation governing the electrostatic behavior of the piezoelectric
element is assumed. Modeling of intelligent structures is done for finite analysis followed by
conventional actuation method is applied. The important feature of the piezoelectric material to
finite element modeling is its electromechanical coupling and electric charge is distributed on
both top and bottom sides of the piezoelectric patches. The electromechanical coupling and
surface characteristics can be handled through three-dimensional finite element modeling with
modified degree of freedoms. Shear actuator mechanism is used for thin plates and sandwich
beams, which makes it high efficient and better performance consideration. Finite element
development took place with three-dimensional elements with electric as well as mechanical
degree of freedoms for formulating electromechanical coupling and surface characteristics of the
sample. Two-dimensional elements were formulated for thin sheets and composite plates with
electric DOF.
Brian.P.Baillargeon in „Active Vibration Suppression of Sandwich Beams Using Piezoelectric
Shear Actuators‟ proposed that piezoelectric material has a capacity of producing self-actuated
voltage, when stress is being applied on it. When load is applied on the cantilever beam,
sandwiched with piezoelectric and core material, it causes transverse shear deformation. Active
vibration suppression is achieved either through strain rate feedback or positive position
feedback. Actuators basically serve for two types of purposes. It helps in excitation of the beam
and controlling of the vibrations. Piezoelectric actuators are actually bonded to hot structures and
electric field applied to the bonded sheet causes change in lateral dimensions and hence
deformation in host structure. The actuators used in this case for deformation in piezoelectric
material with the help of application of electric field are called piezoelectric extension actuators.
These types of actuators are much efficient and brittle, which increases its failure rate. To
overcome this problem, adaptive sandwich structures consisting of the axially poled piezoelectric
actuators have been proposed. The axially poled piezoelectric actuator when sandwiched
between viscoelastic layers is of optimum strength to overcome transverse deflection within
permissible limits.
Page | 12
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
Jingjun Zhang in „Active Vibration Control of Flexible Structures Using Piezoelectric Materials‟
Proposed that Piezoelectric ceramics can be used in wide variety of applications like from active
vibration control to nano-positioning technology. Piezoelectric ceramics are of greater concern
because of its mechanical simplicity, light weight, low volume, conversion between electrical
energy to mechanical energy etc. These days, we can see undesirable vibrations are produced
during an operation, which causes failure of the system. These can be reduced with the help of
feedback control mechanism. There are two types of feedback mechanisms to damp the
undesired vibrations. Positive position feedback is applied by providing structural position
coordinate directly to compensator. Strain rate feedback mechanism is used for active damping
of flexible structures where lateral deformation occurs with load application. Here steel acts as a
core material and piezoelectric patches acts as sensor as well as actuators. Actuators actuates the
flexible structure with varied frequency and sensor senses the vibration, control system sends
signals to sensor with equal and opposing voltage to damp the vibrations.
Fig 3. An assembled sandwich beam with actuators and sensors on board.
Anna Markidou in „Soft-materials elastic and shear module measurement using piezoelectric
cantilevers‟ has proposed a method for finding shear and elastic properties of the soft materials.
Sensors made up of soft material elastic modulus and shear modulus, are used in piezoelectric
cantilever for actuation and damping purpose. Applying electric field in the direction of
thickness causes deformation generating axial displacement or force. Elastic modulus depends on
axial displacement and axial displacement can be measured with proper geometry of the
cantilever beam. The elastic and shear modulus of soft tissues like rubber material and gelatin
can be measured with the help of piezoelectric cantilever beam of lower dimensions. The main
purpose of this paper is to develop a sensor which can measure elastic and shear properties of the
soft materials with sensor operating in few micron levels. With experiments, we can calculate
Page | 13
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
spring constant K, by placing different weights at cantilever tip. Shear tests and compression
tests were carried out to find elastic and shear properties of the sample.
W.H.Liao in „on the analysis of viscoelastic materials for active constrained layer damping
treatments, 1997‟ proposed that viscoelastic material influence the functioning of active as well
as passive damping. The beam used here is viscoelastic layer sandwiched between active
piezoelectric layer and host structure. During the experimentation, it has been found out that
active piezoelectric action in Active Constrained Layer configuration will enhance the
viscoelastic layer damping by increasing its shear angle. It is desirable that viscoelastic material
has high loss factor to obtain good passive damping abilities and active passive hybrid actions.
One should select viscoelastic material with high shear modulus high active gains for lowered
rate of vibrations. Based on the experiment results, it will be desirable if one can develop means
to reduce the viscoelastic effect on active vibration control, while retaining the passive damping
ability in the Active Constrained Layer. This could increase the design space for viscoelastic
selections and enhance the ACL overall.
Raja in „Modelling, Simulation and Validation for Active Vibration Control of Smart Sandwich
Beam with Piezoelectric Actuation, 2002‟ proposed a theory on modelling and active vibration
control of smart structures with piezoelectric actuation. The sandwich beam is a composite of
piezoelectric and piezoceramic materials for intelligent behaviour response. For correct
simulation, finite element procedures have to be applied in modelling of sandwich beams with
distributed actuated and sensing capabilities. For actuation, an elastic core is sandwiched
between two transversely polarised piezoelectric layers, whereas for shear actuation, an axially
polarised piezoelectric core is sandwiched between two composite faces.
Zeki kiral in „Active control of residual vibration of a cantilever smart beam, 2007‟has proposed
a theory paper to control the residual vibrations of clamped-free beam subjected to a load.
Vibrations are considered as undesirable output due to waste of energy, precision loss, noise etc.,
and should be kept under control. Two laser displacement sensors are used to figure out the
dynamic response of the beam during load application. Dynamic response of the beam is
calculated by finite element modelling for designing a control mechanism. In this experimental
study, piezoelectric actuators are used for active vibration control and displacement feedback
mechanism is employed. Modelling is done by finite element procedures and simulation results
are done in analysis software ANSYS. Author has concluded that residual vibrations of the smart
beam are suppressed to greater extent through active vibration control and displacement
Page | 14
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
feedback. The design of active vibration control of more complex structures can be achieved
with the finite element packages, which enable us to use active elements.
D. A. van den Ende in „Piezoelectric and mechanical properties of novel composites of PZT and
a liquid crystalline thermosetting resin, 2007‟ has proposed a theory based on piezoelectric and
mechanical properties of PZT and liquid crystalline resin (LCR) for actuation purpose. The
piezoelectric properties of polymer are greatly influenced by temperature. The polymers show
excellent process ability in high temperatures. Good chemical and thermal resistance of polymer,
makes it better material for sensor applications at high temperatures. Author concluded that PZTLCR composite have high piezoelectric voltage, which is a better quality for sensor applications.
Dielectric and piezoelectric behavior of thermosetting resin have been described. These sensors
can be used in automobile and aerospace applications, where elevated temperatures are
employed. A maximum operating temperature was observed at which, piezoelectric attributes are
found to be deteriorated.
Chih-Liang Chu in „Active vibration control of flexible beam mounted on elastic base, 2006‟
investigated the active vibration control of flexible beam which is analyzed through finite
element modeling. Shearing deformation and inertia is included in experiment calculation. The
controller system in the process works on the principle of suppression of excessive vibration
during base excitation, thereby improving dynamic characteristics of system. In industries, the
heavy machines during operation are subjected to undesirable vibrations which should be cutoff
for high precision outputs. These vibrations are suppressed which control strategy employed.
Piezoelectric vibrations and optical sensors were used to perform active vibration control to
improve measurement accuracy. Independent modal space control (IMSC) mechanism was
employed because this method has a capability to reduce vibration to each and every mode and
feedback is applied to every mode, which suppresses vibrations to greater extent. The basic
principle of modal space control method is to transform the coupled system dynamic equations
into the decoupled modal space, and thereafter apply a process of feedback control to each
decoupled mode. Optimum independent modal space control is found and numerical simulation
is done during experiments. Author has concluded that Timoshenko theory has been used to
develop beam, which is good agreement with results in ANSYS finite element software. In
conclusion, the application ensures a superior dynamic performance of a flexible beam mounted
on an elastic base.
C.Mei in „Hybrid wave/mode active control of bending vibrations in beams based on advanced
Timoshenko theory,2008‟ studied active vibration control in beams based on Timoshenko
theory. Both mode and wave theory have been combined to improve the performance of the
Page | 15
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
vibration control. In the proposed hybrid control, wave control is first at one or more points in
the structure which absorb vibration energy especially during high frequencies. Modal control is
applied for accuracy and robustness of the system. In modal active vibration control, the
objective is to control the characteristics of damping factors, natural frequencies or mode shapes.
At high frequencies, rotary inertia and shear distortion are taken into consideration. In proposed
hybrid approach, two control strategies are employed, one is to absorb vibration energy and
another control system is to provide damping to the system. Author has concluded that hybrid
approach, which includes both wave as well as modal theory, has an advantage of absorbing
vibrations at higher frequency and damping is provided with higher accuracy. The hybrid
approach exhibits better active vibration control performance than the cases with either modal or
wave control individually.
C.M.A.Vasques in „active vibration control of smart piezoelectric beams‟ proposed a theory on
vibration control through smart beams. A one-dimensional finite element of a three-layered
smart beam with two piezoelectric surface layers and metallic core is made composite. The two
piezoelectric layers acts as sensor for sensing the amount of displacement and actuator for
actuating vibrations with low frequency. A partial layer wise theory and electro-mechanical
theory is considered for control mechanism. The main aim of the paper is to reduce vibration of
mechanical system by systems structural response. The ability of piezoelectric to produce
electric charge (actuating voltage) proportional to the external force applied, is the main
characteristics for most of the sensors manufacturing with PZT material. Author studied analysis
of active vibration control of a cantilever aluminum beam with piezoelectric patches acting as
sensor and actuator. Smart structures have excellent characteristics for damping purpose with
low weight applications.
Page | 16
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
4. ANALYTICAL WORK
After designing of Cantilever Beam in Ansys design software, with specific material properties,
analysis is done by applying varying loads (-10N, -50N, -100N,-1000N & -3000N ) on the
meshed node of the beam to study the stress-strain distribution along the cantilever beam. After
analysis procedure, Results are found out in the form of Stress-Strain graphs are plotted for
different loads.
Stress Analysis of Cantilever Beam with 10N Force applied in Negative Z direction:
Total No of Nodes: 2936
Load Applied: Node 2585
Maximum Stress: Node 243
Minimum Stress: Node 1502
Maximum Strain: Node 243
Minimum Strain: Node 1287
Page | 17
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
Stress-Strain relationship for 10 N Load applied in the negative Z direction.
The stress-strain curve is a relation between stress, which is measured with load applied on the
beam and strain, derived from measuring the deflection in the beam. Hook‟s Law relates these
parameters within elastic limit.
Maximum Stress: 24.715 N/mm2
Minimum Stress: 0.2768 N/mm2
Maximum Strain: 0.825E-06
Minimum Strain: 0.1361E-07
STRESS-STRAIN GRAPH
0.0000009
0.0000008
0.0000007
0.0000006
strain
0.0000005
0.0000004
0.0000003
0.0000002
0.0000001
0
0
5
10
15
20
25
30
Stress
Page | 18
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
Stress Analysis of Cantilever Beam with 50N Force along Negative Z axis direction
Total No of Nodes:2936
Load Applied: Node 2585
Maximum Stress: Node 243
Minimum Stress: Node 1502
Maximum Strain: Node 243
Minimum Strain: Node 1290
Page | 19
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
Stress Analysis of Cantilever Beam with 100N Force in Negative Z direction.
Total No of Nodes: 2936
Load Applied: Node 2585
Maximum Stress: Node 243
Minimum Stress: Node 1502
Maximum Stress: 247.15 N/mm2
Maximum Strain: 3.25E-05
Maximum Strain: Node 243
Minimum Strain: Node 1290
Minimum Stress: 2.7683 N/mm2
Minimum Strain: 1.36E-07
Page | 20
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
Strain Analysis of Cantilever Beam with 100N Force in Negative Z direction.
1) Scatter diagram for stress-strain curve for -100N load
3.50E-05
3.00E-05
2.50E-05
strain
2.00E-05
1.50E-05
strain
1.00E-05
5.00E-06
0.00E+00
0
50
100
150
200
250
300
stress
Page | 21
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
2) Stress-strain curve for 100N load applied in Negative Z direction
7.00E-06
6.00E-06
5.00E-06
4.00E-06
strain
3.00E-06
2.00E-06
strain
1.00E-06
0.00E+00
0
50
100
150
200
stress
Stress Analysis of Cantilever Beam with 1000N Force in Negative Z direction.
Total No of Nodes: 2936
Load Applied: Node 2585
Maximum Stress: Node 243
Minimum Stress: Node 1502
Maximum Stress: 2471.5 N/mm2
Maximum Strain: Node 243
Minimum Strain: Node 1290
Maximum Strain: 8.25E-05
Page | 22
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
Minimum Stress: 27.683 N/mm2
Minimum Strain: 1.36E-06
Strain Analysis of Cantilever Beam with 1000N Force in Negative Z direction.
The intensity of stain distributed along the beam is shown in figure with different colors showing
variation of strain. With red color being the maximum strain produced area and navy blue
indicating minimum strain affected area. Strain is derived from measuring the change in
deformation of the sample. Below figure shows the deformation before and after load
application.
Page | 23
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
Page | 24
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
Stress-Strain relationship for 1000 N Load applied in the negative Z direction.
1) Scatter diagram for stress-strain curve for -1000N load
9.00E-05
8.00E-05
7.00E-05
6.00E-05
STRAIN
5.00E-05
4.00E-05
3.00E-05
2.00E-05
1.00E-05
0.00E+00
0
500
1000
1500
STRESS
2000
2500
3000
2) Stress-strain curve for 1000N load applied in Negative Z direction
9.00E-05
8.00E-05
7.00E-05
6.00E-05
STRAIN
5.00E-05
4.00E-05
3.00E-05
2.00E-05
1.00E-05
0.00E+00
0
500
1000
1500
2000
2500
3000
STRESS
Page | 25
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
Stress Analysis of Cantilever Beam with 3000N Force in Negative Z direction.
Total No of Nodes: 2936
Load Applied: Node 2585
Maximum Stress: Node 243
Minimum Stress: Node 1502
Maximum Stress: 7414.5 N/mm2
Maximum Strain: Node 243
Minimum Strain: Node 1290
Minimum Stress: 83.048
Page | 26
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
Strain Analysis of Cantilever Beam with 3000N Force in Negative Z direction.
Maximum Strain Node: 243
Maximum Strain: 2.48E-04
Minimum Strain Node: 1290
Minimum Strain: 4.10E-06
As displacement and strain are directly proportional, maximum displacement occurs at the point
of maximum strain. When higher load is applied, high displacement and hence high strain
produced at the specific area of the beam.
Page | 27
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
Stress-Strain relationship for 3000 N Load applied in the negative Z direction.
1. Scatter diagram for stress-strain curve for -3000N load
3.00E-04
2.50E-04
2.00E-04
STRAIN
1.50E-04
1.00E-04
5.00E-05
0.00E+00
0
2000
4000
6000
8000
STRESS
2. Stress-strain curve for -3000N load
3.00E-04
2.50E-04
2.00E-04
STRAI
1.50E-04
1.00E-04
5.00E-05
0.00E+00
0
1000
2000
3000
4000
5000
6000
7000
8000
STRESS
Page | 28
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
Calculations:
As we know the Young‟s modulus is calculated as the ratio of stress to strain.
So as per the definition we have Y = Stress / Strain
For load 1 i.e. -10 N, from the stress v/s strain graph, we have,
Y = 31.25 TPa
For load 2 i.e. -100N, from the stress v/s strain graph, we have
Y = 30.5 TPa
For load 3 i.e. -1000N, from the stress v/s strain graph, we have
Y = 31.5 TPa
For load 4 i.e. -3000N, from the stress v/s strain graph, we have
Y = 31.25 TPa
So, taking average value from all the values for Young‟s modulus we have,
Y(avg) for this sandwich beam is 31.125 TPa.
Page | 29
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
Conclusion:
Sandwich cross sections are composite and consist of a low to moderate stiffness core which is
connected with two stiff exterior face-sheets and it has a considerably higher shear stiffness to
weight ratio compared to an equivalent beam made of only the core material or the face sheet
material. The face sheets that were used for this analysis were of PZT-5 material having a
young‟s modulus of 63 GPa and the core material was of Aluminium which has a young‟s
modulus of 69 GPa. When we analyzed a sandwich beam with core as aluminium and face sheet
as PZT-5 material the young‟s modulus for the sandwich beam composite was found to be
31.125 TPa (taking an average value from all the loads applied on a particular node). The value
is acceptable as it is proved from early researches that the young‟s modulus for a sandwich beam
is supposed to yield much better results compared to an equivalent beam made out from
individual materials that are used as core or face sheets.
Scope for future work:
For the simplification purpose a three layered sandwich beam was selected and the core material
for this purpose selected was aluminium and the face-sheets as PZT-5. There are few works that
have been carried out in this direction where instead of 3 layers, more layers are being used and
instead of simple layer like arrangements honeycomb like structures are used. Instead of core as
aluminium and face-sheets as PZT-5 other materials showing considerable young‟s modulus
value too can be used.
Page | 30
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
REFERENCES
1.Plantema, F, J., 1966, Sandwich Construction: The Bending and Buckling of Sandwich Beams,
Plates, and Shells, Jon Wiley and Sons, New York.
2. Zenkert, D., 1995, An Introduction to Sandwich Construction, Engineering Materials
Advisory Services Ltd, UK.
3. Finite Element modeling of hybrid active-passive vibration damping of multilayer
piezoelectric sandwich beams by M.A. Trindade, A. Benjeddou and R. Ohayon
4. A.Benjeddou. Advances in piezoelectric finite element modeling of adaptive structural
elements: a survey 2000.Computers and Structures 76 (2000) 347-349.
5. Aldraihem OJ, Wetherhold RC. Mechanics and control of coupled bending and twisting
vibration of laminated beams. Smart Mater Struct 1997;6:123-33.
6. Allik H, Hughes TJR. Finite element method for piezoelectric vibration. Int J Num Methods
Engrg 1970;2:151-7.
7. Bahrami H, Tzou HS. Design and analysis of a precision multi-dof placement device. In: Brei
D, Sirkis J, editors. Adaptive Struct Mater Syst ASME 1997;AD-54:1-7.
8. Brian p. Baillargeon, Senthil S.Vel. Active Vibration Suppression of Sandwich Beams using
Piezoelectric Shear Actuators: Experiments and Numerical Simulations 2005. Journal of
intellegent material systems and structures.Vol 16.pg518-521.
9. Aldraihem, O.J. and Khdeir, A.A. 2003. „„Exact Deflection Solutions of Beams with Shear
Piezoelectric Actuators,‟‟ International Journal of Solids and Structures, 40:1–12.
10. Baillargeon, B.P. and Vel, S.S. 2005. „„Exact Solution for the Vibration and Active Damping
of Composite Plates with Piezoelectric Shear Actuators,‟‟ Journal of Sound and Vibration,
282:781–804.
11.Jingjun Zhang, Lili He, Ercheng Wang, Ruizhen Gao. Active Vibration Control of Flexible
Structures Using Piezoelectric Materials 2008.IEEE.international conference for advanced
computer control.pg540,544.
Page | 31
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
12. Aoustin Y., et al., “Experirnental results for the end effector control of a single flexible
robotic arm”, IEEE Trans. Control System Technology, vol.2, no.4, 1994, pp. 371-381.
13. Sun D. and Mills J. K., “Application of smart material actuators for control of a single-link
flexible manipulator”, Proc. of International Federation of Automatic Control (IFAC), 1999.
14. J. L. Fanson and T.K. Caughey, “Positive position feedback control for large space
structures”, AIAA. J. vol.28, 1990, pp. 717-724.
15. Anna Markidou, Wan Y. Shih and Wei-Heng Shih. Soft-materials elastic and shear moduli
measurement using piezoelectric cantilevers.Review of scientific instruments 76, 064302:1-3
(2005)
16. P. S. Wellman, R. D. Howe,
biorobotics.harvard.edu/pubs/mechprops.pdf>
E.
Dalton,
and
K.
A.
Kern,
<http://
17. W.H.Liao and K.W.Wang. On the analysis of viscoelastic materials for active constrained
layer damping treatments 1997. Journal of Sound and Vibration (1997) 207(3), 319-321.
18. S. Raja, Gangan Prathap and P. K. Sinha. Modelling, Simulation and Validation for Active
Vibration Control of Smart Sandwich Beam with Piezoelectric Actuation, 2002.pg 49.
19. Zeki KIRAL, Levent MALGACA, Murat AKDAG. Active control of residual vibration of a
cantilever smart beam 2007. Turkish J. Eng. Env. Sci.
32 (2008) , pg51 – 52,56.
20. ANSYS software ANSYS Inc., Canonsburg, PA, USA, (2006). (www.ansys.com).
21. Bruant, I., Coffignal, G., Lene, F. and Verge, M., “Active Control of Beam Structures with
Piezoelectric Actuators and Sensors: Modeling and Simulation”, Smart Materials and
Structures,10, 404-408, 2001.
22. D. A. van den Ende, P. de Almeida, Sybrand van der Zwaag. Piezoelectric and mechanical
properties of novel composites of PZT and a liquid crystalline thermosetting resin. J Mater Sci
(2007) 42:6417–6425.
23. Jaffe B, Cook WR, Jaffe H (1971) Piezoelectric ceramics. Academic, New York, pp 253–267
24. Yamada T, Ueda T, Kitayama T (1982) J Appl Phys 53:4328
25. Chih-Liang Chua, Bing-SongWua and Yih-Hwang Lin. Vibration control of flexible beam
mounted on elastic base 2006. Finite element in analysis and design.
www.elsevier.com/locate/finel.
Page | 32
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
26. M.J. Cunningham, D.F.L. Jenkins, W.W. Clegg, M.M. Bakush, Active vibration control and
actuation of a small cantilever for applications in scanning probe instruments, Sensor. Actuator.
(1995) 147–150.
27. C. Mei. Hybrid wave/mode active control of bending vibrations in beams based on the
advanced Timoshenko theory 2008. Journal of Sound and Vibration 322 (2009) 29–38.
28. L.Meirovitch, FundamentalsofVibrations, McGrawHillHigherEducation,NewYork,2001.
29. K.F.Graff, Wave MotioninElasticSolids, OhioStateUniversityPress,1975.
30. L.Cremer,M.Heckl,E.E.Ungar, Structure-borneSound, Springer,Berlin,1987.
31. C.M.A. Vasques and J. Dias Rodrigues. Active vibration control of smart piezoelectric
beams: Comparison of classical and optimal feedback control strategies. Computers and
Structures 84 (2006) 1402–1405.
32. Chopra I. Review of state of art of smart structures and integrated systems.
AIAA J 2002;40(11):2145–87.
33. Tzou HS, Anderson GL, editorsIntelligent structural systems. Solid mechanics and its
applications, vol. 13. Dordrecht: Kluwer Academic Publishers; 1992.
34. Bahrami H, Tzou HS. Design and analysis of a precision multi-dof placement device .In:
Brei D, Sirkis J, editors. Adaptive Struct Mater Syst ASME 1997; AD-54:1-7.
35. www.Sciencedirect.com/pdf
36. www.pdf-freedownload.com/pdf
37.Benjeddou, A., Trindade, M.A. and Ohayon “ New shear actuated smart structure beam
finite element” AIAA Journal Vol 37
38.Baillargeon, B. P. and Vel, S. S. (2003): .Exact solution for the vibration and active damping
of composite plates with piezoelectric shear actuators.
39. Aoustin Y., et al., “Experirnental results for the end effector control of a single flexible
robotic arm, IEEE Trans. Control System Technology, vol.2, no.4, 1994, pp. 371-381.
40.Zhang, X.D. and Sun, C.T. (1996): .Formulation of an adaptive sandwich beam., Smart
Materials and Structures, Vol 5, pp. 814-823.
Page | 33
DYNAMIC BEHAVIOR OF SANDWICH BEAM WITH PIEZOELECTRIC 2011
LAYERS
41. Benjeddou, A., Trindade, M.A. and Ohayon, R. (1999): .New shear actuated smart structure
beam finite element., AIAA Journal, Vol 37, pp.378-383.
42. Arockiasamy, M. and Neelakanta, P. S. and Sreenivasan, G.,Vibration Control of Beams with
Embedded Smart Composite Material. Journal of Aerospace Engineering, Vol. 5, no. 4, 492-498
(1992).
Page | 34
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Related manuals

Download PDF

advertisement