Non-Linear transient dynamic Behavior of Composite Specimens with Macro Fiber Composite patch as actuators.

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Academic year 2016/2017

Department of Civil and Industrial Engineering

Master of Science in Aerospace Engineering

NONLINEAR TRANSIENT DYNAMIC RESPONSE OF

COMPOSITE FIBER SPECIMEN

WITH

MACRO FIBER COMPOSITE PATCH AS ACTUATOR.

Supervisor:

Candidate:

Prof. Mario Rosario Chiarelli

Nidish Narayanan

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Abstract

The thesis presents the nonlinear dynamic behavior of composite fiber beam with Macro Fiber Composite glued onto them. The composite material employed are made of thin Carbon/Epoxy or Glass/Epoxy prepreg fabric with 0.25 mm thickness. The piezoelectric patches employed here are Macro Fiber composite (MFC) with 0.3 mm thickness. The Macro Fiber Composites (MFC) are glued onto the surface of the composite material on top and on the bottom. High temperature wires were soldered on to the piezoelectric patch to provide them with electric voltage excitation. MFC is composed of ceramic fibers that can bend or flex when a current is applied to it-much like a muscle. The Macro Fiber Composite also generates a current when it is vibrated or flexed, giving us the ability to use the MFC as a next-gen vibration detector as well.

The aim of the project is to study the transient structural response of the hybrid structure. The transient structural response has been studies using the FEM software ANSYS. A flexible method is developed and implemented in this work based on ANSYS Parametric Design Language. In this project, composite panel is modeled with 3D 20-node solid element and the Macro Fiber composite is modeled with a 3D 20-node coupled-field solid element. The geometry for the hybrid structure is designed keeping in mind the bending and torsional specification of the MFC provided by the manufacturer. The mesh for the structure is a conformal/mapped mesh which gives emphasis on uniform shape and size of elements which gives better connectivity for the elements sharing the edge nodes.

The specimens used for this project were specially manufactured from the Smart Material Corp. (SMC) developed within the European Collaborative project titled “FutureWings”. The composite fiber beams have four different fiber orientations. The specimens were tested for bending and torsion tests with different values of voltage excitations and impulse loads. These results are validated with the experiments carried out on the specimens in the Aerospace Department laboratory. The transient study of the structure allowed us to evaluate the real modes of vibration of the hybrid structure which were then compared with the result obtained from the experimental analysis through the use of Fast Fourier Transform(FFT) and Frequency Response(FR) of the system. The study also highlights the stiffening/softening effect of the Piezoelectric actuators on the specimen dynamic response.

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Chapter 1 Introduction

In the recent decades, a lot of research has been carried out on integrating piezoelectric material, which can be used as actuators and sensors into base structure to control the structure. The Macro Fiber composite is one such piezoelectric structure.

The thesis focuses on understanding the dynamic behavior of Hybrid structure, preliminary experimental validation of the Hybrid structure having the capability to change its shape. This is achieved through the use of piezoelectric fibers embedded into laminates of composite material called Macro Fiber Composites. The Hybrid Structure is made up of a Composite fiber beam with Macro fiber composite patch glued onto the top and bottom face. Such a hybrid structure is capable of deforming on command, which means that implementation of these hybrid structures on aircraft will allow us to manipulate the aerodynamic forces acting on the aircraft structure.

The Macro Fiber Composite (MFC) actuator is an emerging technology that strives to improve the current state of art for structural actuation, which relies on monolithic piezoceramic materials. The MFC is a layered, planar actuation device that employs rectangular cross-section, unidirectional piezoceramic fibers (PZT) embedded in a thermosetting polymer matrix. This active, fibre –reinforced layer is then sandwiched between copper-clad Kapton film layers that have an etched interdigitated electrode pattern. During manufacturing, these layers are laid by hand and then cured in a vacuum hot press. After the epoxy matrix that bonds the package together is fully cured, a high DC voltage (1500V) is applied to the electrodes, thereby poling the piezoceramic material in the plane of the actuator and establishing the poling direction parallel to the PZT fibers.

The primary use of MFC has been in the helicopter blade research and vibration monitoring on the Space Shuttle launch pad. Non-aerospace application includes wind turbine blades, noise cancellation in commercial grade appliances, vibration dampening in performance sporting equipment such as skis, and even active vibration damping in the Audi TT drive shaft.

The hybrid structure is composed of carbon/epoxy composite material and Macro Fiber composite glued onto the top and bottom surface of the carbon/epoxy composite material. The carbon/epoxy composite material is a four-layered carbon/epoxy prepreg with a thickness of 0.25mm each, with two different stacking sequences for the layer 45-0-0-45 and 0-45-45-0. The Macro Fiber Composite which is glued on top and bottom surface is supplied by Smart material corp.(SMC). The material is M8557-F1, with fiber orientation of 45 degree for the torsion specimen.

A deformed shape of the structure is obtained quasi-statically, activating the piezoelectric layers, giving us the possibility of a low electric power level.it is therefore expected that a very low voltage values will be able to command the hybrid structure. The test is performed on the specimens manufactured solely for this experimentation form Smart Material Corp.(SMC). In this project, the majority of the work has been dedicated to the simulation of realistic hybrid specimen made of Composite material and Macro Fiber Composite (MFC) patches. Torsion specimen is studied in detail using the non-linear finite element analysis.

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The majority of the work was focused on numerical simulation of the structure with Finite Element Analysis and Computer Aided Engineering software ANSYS to generate model, which provided the dynamic response of the hybrid structure. The transient structural analysis provides us with the information of how the hybrid structure responds to dynamic loading and helps us understand how the nonlinearity affects it. These numerical simulation gives us a pretty good idea of natural frequency and mode shapes of the structure so that we can assess at what frequency it is best to operate them if they are incorporated into Space or similar structural fields.

The first few sections gives a brief background on Piezoelectricity and Macro Fiber Composites and the governing equation followed by the numerical and experimental discussion and concluding with comparison of numerical simulation results and experimental data.

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3

Piezoelectricity

Piezoelectricity, also called the piezoelectric effect, is the ability of certain materials to generate an AC (alternating current) voltage when subjected to mechanical stress or vibration, or to vibrate when subjected to an AC voltage. The most common piezoelectric material is quartz. Certain ceramics, Rochelle salts, and various other solids also exhibit this effect. Piezoelectric materials are therefore used to convert electrical energy into mechanical energy (such as actuators) and vice versa (such as sensors). The behavior of piezoelectric materials has been analyzed through the document. They are multi-functional material, that can be used to realize adaptable structural systems. They can be distinguished from the type of excitation mechanism, from the field of application and the status of development. In this section, the piezoelectric effect and its constituent elements will be examined in detail.

Origin

The pyroelectric effect by which a material generates an electric potential in response to a variation of temperature, was studied by Carl Linnaeus and Franz Aepinus in the mid-18th century. Starting from these studies, both René Just Ha\"uy and Antoine César Becquerel examined the relationship between the mechanical stress and the electric charge. The first demonstration of the direct piezoelectric effect was processed in 1880 by the brothers Pierre and Jaques Curie. They combined their knowledge of pyroelectricity with the understanding of the underlying crystal structures to predict crystal behavior and they could demonstrate its effect using quartz, topaz, cane sugar and Rochelle salt. The Curies, however, did not predict the inverse piezoelectric effect. The latter was mathematically deduced by fundamental thermodynamic principles by Gabriel Lippmannin in 1881. The Curies immediately confirmed the existence of inverse effect and went to obtain quantitative proof of the complete reversibility of the electro-elastomechanical deformations in piezoelectric crystals. In 1910 with the publication of the work done by Woldemar Voigt: Lehrbuch der Kristqallphysik (Textbook on Crystal Phisics) were described the 20 natural crystal classes capable of piezoelectricity. He rigorously defined the piezoelectric elements using tensor analysis. The first practical application for piezoelectric devices was the sonar, developed during the First World War. In France in 1917 Paul Langevin and his coworkers developed an ultrasonic submarine detector. The detector consisted of a transducer, made of thin quartz crystals carefully glued between two steel plates, and a hydrophone to detect the returned echo. By emitting a high-frequency pulse from the transducer and measuring the amount of time it takes to hear the echo from sound waves bouncing on an object, the distance to that object can be calculated. Over the next few decades, new piezoelectric materials and new applications were explored and developed: ultrasonic transducers allowed easy measurements of viscosity and elasticity in fluids and solids; ultrasonic time-domain refractometers (which send an ultrasonic pulse through a material and measure reflections from discontinuities) could find flaws inside cast metal and stone objects, improving structural safety. During Second World War, independent research groups in USA, Russia and Japan discovered a new class of synthetic materials called ferroelectrics, which exhibited piezoelectric constants many times higher than the natural ones.

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Structure

Piezoelectric effect arises from a crystal structure. The piezoelectric effect is exhibited by 20 out of 32 crystal classes and is always associated with noncentrosymmetric crystals. Naturally occurring materials, such as quartz, exhibit this effect as a result of their crystalline structure. Engineered materials, like lead zirconate titanate (PZT) for instance, are subjected to a process called poling to impart the piezoelectric behavior.

A typical noncentrosymmetric crystal structure such as a perovskite (calcium titanate — CaTiO3) has a net non-zero charge in each unit cell of the crystal. However, as a result of the titanium ion sitting slightly off-center inside the unit cell, an electrical polarity develops, thereby turning the unit cell effectively into an electric dipole. A mechanical stress on the crystal further shifts the position of the titanium ion, thus changing the polarization strength of the crystal. This is the source of the direct effect. When the crystal is subjected to an electric field, it also results in a relative shift in the position of the titanium ion, leading to the distortion of the unit cell and making it more (or less) tetragonal. This is the source of the inverse effect.

Poling

Piezoelectric properties are due to crystalline structure of the materials. In a macroscopic crystalline structure that comprises several such unit cells, the dipoles are by default found to be randomly oriented. When the material is subjected to a mechanical stress, each dipole rotates from its original orientation toward a direction that minimizes the overall electrical and mechanical energy stored in the dipole. If all the dipoles are initially randomly oriented (i.e. a net polarization of zero), their rotation may not

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5

significantly change the macroscopic net polarization of the material, hence the piezoelectric effect exhibited will be negligible. Therefore, it is important to create an initial state in the material such that most dipoles will be more-or-less oriented in the same direction. Such an initial state can be imparted to the material by poling it. The direction along which the dipoles align is known as the poling direction.

During poling, the material is subjected to a very high electric field that orients all the dipoles in the direction of the field. Upon switching off the electric field, most dipoles do not return back to their original orientation as a result of the pinning effect produced by microscopic defects in the crystalline lattice. This gives us a material comprising numerous microscopic dipoles that are roughly oriented in the same direction. It is noteworthy that the material can be de-poled if it is subjected to a very high electric field oriented opposite to the poling direction or is exposed to a temperature higher than the Curie temperature of the material.

Figure 2 Alignment of electric dipoles represented by arrows in a material prior to poling (left), during the poling process (middle) and at the end of poling (right).

Macro Fiber Composite

The Macro Fiber Composite (MFC) was invented by NASA in 1996[]. Smart Material started commercializing the MFC as the licensed manufacturer and distributor of the patented invention worldwide in 2002. The MFC consists of rectangular piezo-ceramic rods sandwiched between layers of adhesive, electrodes and polymide film. The electrodes are attached to the film in an interdigitated pattern which transfers the applied voltage directly to and from the ribbon shaped rods. As a thin surface, it can be applied (normally bonded) to various types of structures or embedded in a composite structure. If a voltage is applied, it will bend or distort the material, counteract vibrations or generate them. If no voltage is applied, it can work as a very sensitive strain gauge, sensing deformations, noise and vibrations. The MFC is also an excellent device to harvest energy from vibrations. In our applications P1 type MFC for the bending specimens and F1 type MFC for the torsion ones have been used. The P1 and F1 exploit the d33 effect for actuation and elongate up to 1800 ppm if they operate at maximum allowed voltage-500 V, 1500 V. The schematics of the MFCs is shown in the figure:

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Application of Macro Fiber Composites

Macro Fiber Composite offers high performance, flexibility, reliability and low cost. The fact that it can be bonded as thin surface-conformable sheet to several structures makes it easy to be used. On application of electric excitation or voltage it will bend or distort material, counteract vibration or generate vibration. It can also be used as a strain gauge to sense vibration, noise and to harvest energy from the vibrations. In the recent years the Macro fiber composites have found applicability in numerous fields ranging from Aerospcae/civil strutures to Sonar application in submarines. Some of the prominent application include,

Deformation of wing using MFC (1)

Macro Fiber composites were used on the upper and lower surface of the wing to change its shape. The geometry of the wing is similar to NACA0014. The Macro Fiber Composites are bonded to the inside and become an integral part of the wing surface. Various wind tunnel experimental were carried in still-air and various flow regimes to understand the effect the change of shape of airfoil.

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7 Figure 5 Airfoil with MFC patch

on the inner surface (left) and MFC patch on the (right).

Energy Harvesting

System using

Piezo-Electric Macro Fiber

Composite (2)

The MFC with properties like flexibility, anisotropy and long-term stability is used in energy harvesting system. MicroStrain reports on its next generation wireless sensors, which eliminate battery maintenance by using piezoelectric materials to convert strain energy to stored electrical energy. Stored energy is used

to measure, record, and transmit strain and load information. A prototype energy harvesting wireless pitch link sensing system has been developed. Under low usage level helicopter operating conditions, the energy consumed was less than the energy harvested, enabling strain & load sensors to operate perpetually without battery maintenance. Breaking down the barriers to monitoring helicopter rotating components, this technology has the potential to greatly improve future HUMS capabilities.

Figure 4 Helicopter rotor assembly showing the position of piezo-electric strain gauge.

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Energy Harvest for Unmanned aerial Vehicle. (3)

The piezoelectric patch applied onto the surface of unmanned aerial vehicle is used to generate energy from vibration. The energy generated by the use of piezoelectric patch and that by photovoltaic cell were compare. It can be concluded that both the

piezoelectric and solar energy harvesting devices have the capability of charging energy storage devices. Preliminary tests show that during a 13-minute flight, the solar panels could charge a 170 mAh battery to 14% capacity and the piezoelectric

patches could charge the EH300 4.6 mJ internal capacitor to 70% capacity.

Fin Buffet Alleviation Using Piezoelectric Actuators (4)

The piezoelectric actuator is used in the development of an autonomous active control system to alleviate the buffet response of vibration modes of the Block-15 F-16 ventral fin during ground and flight test. Strategically mounted to the affected structure they impart directional strain to reduce the negative effect associated with the strain energy of specified modal vibration.

Figure 7 Scaled model of F-16 ventral fin showing position of piezoelectric actuators.

Governing Equation

Mechanical and electrical-strain relationships are described in [2]

The strain vector ε in material Cartesian coordinates is defined in terms of infinitesimal and large displacement components as,





₁₁



₂₂



₃₃



₁₂



₂₃



₁₃





T



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9



































































3 1 3 1 3 1 3 2 3 2 3 2 2 1 2 1 2 1 2 3 2 3 2 3 2 2 2 2 2 2 2 1 2 1 2 1 1 3 2 3 1 2 3 2 1

'

2 /

1 '

'

2 /

1 '

'

2 /

1 '

'

w

v

u

w

v

u

w

v

u

w

v

u

w

v

u

w

v

u

w

u

w

v

u

w

v

u

where u,v.w are the displacement and the apostrophe denote the partial differentiation. Similarly, the electric field vector E is related to the electric potential V by



E

          3 2 1 E E E = -          3 2 1 ' ' ' V V V

Governing equation for the Piezoelectric materials

The Equations governing the linear piezoelectric material are described as 𝝈 ̂ = 𝑪̂𝛆̂ where,

















T

e

C

Cˆ

 

T D  ˆ 







₁₁



₂₂



₃₃



₁₂



₂₃



₁₃

D

₁

D

₂

D

₃



T





T E    ˆ 





₁₁



₂₂



₃₃



₁₂



₂₃



₁₃ E₁ E₂ E₃



T

where, superscript T denotes the transpose of a matrix, ε is the mechanical strain vector, σ is the mechanical stress vector, D is the electric displacement vector and E is the electric field vector.

In principal material direction, the matrix for material stiffness C, the piezoelectric stress matrix e and the dielectric constant matrix ζ for piezoelectric material with orthotropic behavior can be written as:

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10            36 35 34 33 32 31 26 25 24 23 22 21 16 15 14 13 12 11 e e e e e e e e e e e e e e e e e e e            3 2 1 0 0 0 0 0 0



For composite material with orthotropic properties the stiffness matrix is reduced to 9 independent constants.















66 55 44 33 32 31 23 22 21 13 12 11

0

0 C

C

where, Cij=Cji

Coupling equations

The electro-mechanical coupling equations can be given by

E

e

T

d

D

E

d

T

s

T t e

.











Where,            0 0 0 0 0 0 0 0 0 0 0 0 0 33 31 13 15 15 d d d d d

d is the matrix that contains piezoelectric coefficient.

Lagrangian formulation

In the Lagrangian formulation all static and kinematic variables are referred at time t. The principle of virtual work for piezoelectric material is given by:



   _ v t t t t t t t t t t t R dv







,

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11 where,





T z t t t y t t t x t t t xz t t t yz t t t xy t t t zz t t t yy t t t xx t t t t t t

D

                   

_

_

_

_





T z t t t y t t t x t t t xz t t t yz t t t xy t t t zz t t t yy t t t xx t t t t t t

E

                   

_

_

_

_

δ denotes small arbitrary virtual variation,t_{v - volume of body at time t,}t  t_R

is the external virtual work and t t t   _,t t_ t 

 _{denote the generalized stress and strain vector at times t and t+Δt respectively.}

Assuming the loading is deformation independent and can be specified prior to the incremental analysis.The only body force is the inertial D’Alembert force defined by 0_ρt+Δt_{𝒖̈ having a mass density}0_ρ at t=0. The external virtual work is given by,















     T t t t t T T t t

d

Q

V

dv

R

_u

v 0 0 0 0 t t 0





u



u

p

Where u is the displacement vector, t  ₀tp is the boundary traction vector at timet= 0 and t=t+Δt, t ₀tQis the surface charge, 0_{v is the original body volume and}0_{T is the original area on which boundary traction} and electrical charges are prescribed.

The generalized Cauchy stresses tˆ_tt and _tt 0, giving us, , ˆ ˆ    t t t t t t       _ˆ _, ˆ ˆ 1 n t t t t t t















  where    n t tˆ and ˆ

1 _{are linear and nonlinear incremental strain. By substituting the equation for stress,}

strain and external virtual work in to the main equation of principle of virtual work for piezoelectric materials and using approximation t



ˆtCˆt



ˆ 1, and

 1

ˆ ˆ







t  t gives the linearized equation as

     

_

 

_



























T t t t t T T v t t v v t n t t t t

C

dv

u

dv

V

Q

d

v t T t t T T 0 0 0 0 t t 0 1 1 ' 1

ˆ

_ˆ

ˆ

























u



u

p

' ˆ C

t is the tangent material property matrix at time t .

Finite element formulations

Finite element formulations are derived using the updated Lagrangian formulation and principle of virtual work. A 20-Node solid element with electrical degree of freedom is used to analyze the piezoelectric structure.

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12

The displacement at time t+Δt can be written in incremental form as

du u u t

t t  

Where t_{u and du are displacements at time t and its increment at t+Δt respectively.}

The incremental nodal displacement within an element can be explained in terms of nodal displacement as,

 e q N u ₂₀

where, u = [ u v w] T_{and q}(e)_=[u

1 v1 w1 u2 v2 w2 … u20 v20 w20]T,

N20 indicates the matrix for interpolation function for 20 -node solid element and q(e) is the time-dependent nodal displacement vector.

Similarly, the electrical potential within an element can be interpolated using the node electric potential V(e)_as,  e vV N V  where, V(e)_=[V 1 V2 V3 … V20]T and NV=[N1 N2 …. N20] T.

The incremental displacement and electric field within an element are inter-related as ,

 e q N uˆ ˆˆ where,















N

u

uˆ

,

_













V

N

0

0 ˆ

20 and   _{ }















e e e

V

q

qˆ

The linear incremental generalized strain within an element can be represented using nodal displacement increment and electric field as

     e V t t t t e t t t

q

B

q

B

ˆ

0

0 ˆ

ˆ

1

















With

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13  















x t z t x t z t y t z t y t z t x t y t x t y t z t z t y t y t x t x t t t

N

B

, 20 , 20 , 1 , 1 , 20 , 20 , 1 , 1 , 20 , 20 , 1 , 1 , 20 , 1 , 20 , 1 , 20 , 1 1

0 ....

0

0 ....

0

0 ....

0

0 ....

0

0 ....

0

0 ˆ

_,  















z t z t z t y t y t y t x t x t x t V t t

N

B

, 20 , 2 , 1 , 20 , 2 , 1 , 20 , 2 , 1 1

...

ˆ

_, where, N N x N N ytN z Ni tz t i y t t i x t 1,  / , 1,  / , 1,  / As a result, the nonlinear incremental generalized strain becomes,

     e t t t e n t t t

q

G

q

B

ˆ

0

2 /

1 ˆ

ˆ

_

















where

,

0

0 

















x t y t z t x t y t z t y t x t t













u z v z w z



y w y v y u x w x v x u t t t z t t t t y t t t t x t                      / / / , / / / , / / /



and

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14                              z t z t z t z t z t z t y t y t y t y t y t y t x t x t x t x t x t x t t t N N N N N N N N N N N N N N N N N N G , 20 , 1 , 20 , 1 , 20 , 1 , 20 , 1 , 20 , 1 , 20 , 1 , 20 , 1 , 20 , 1 , 20 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ... 0 0 0 0 ... 0 0 .

Substituting the linear generalized strain and nonlinear generalized strain in the principle of virtual work leads to the finite equilibrium equation for each element.

   



   



      , ˆ ˆ ˆ ˆ ˆ ˆ ˆ 1 t ne e t t e t t e t e t t e t t e f r q k k q m       where                         . , ˆ ˆ , ˆ ˆ , 0 0 0 , ˆ ˆ ˆ , 0 0 0 ˆ 33 32 31 23 22 21 13 12 11 1 0 0 1 1 0 0 0                                     



         I I I I I I I I I





t t t t t t t t t t e v t t t e t t e t t t t T e t t e v t t T t t e n t t e v t t t t t e t t e v T e dv B f d Q p N r dv G G k dv B C B k dv N N m t T t t T

Assembling the element into global matrix provides the equation:

 



   



.

ˆ

1

F

R

U

K

U

M

e tt





_tt e



_tt ne



tt



tt

For the case of our simulation the surface of MFC is covered by electrode and the nodal electrical potential is coupled over the top and bottom faces.

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Chapter-2

Description of the Specimen.

The section gives the specification about the bending and torsion specimens used for the test. The specimens are manufactured for test from Smart-Material Corp. The section outlines the main geometric properties of composite specimen and provides a brief description of the Macro Fiber Composites. For this study, two different composite fiber material are chosen, one is Carbon/Epoxy and another one is Glass/Epoxy. The composite materials are manufactured by lay-up of four sheets of fiber-reinforced materials. Furthermore, the MFC patch chosen are M8528-P1 which generates the bending effect and M8557-F1 for the torsion effect the physical properties of the bending and torsion model of MFC are listed below in the Table 1.

M8528-P1 M8557-F1 Active length(mm) 85 85 Active width(mm) 28 57 Overall length(mm) 103 105 Overall width(mm) 35 64 Capacitance(nF) 6.58 13.26 Free strain(ppm) 1800 1750 Blocking Force(N) 454 945

Maximum operating positive Voltage(v) +1500 +1500

Minimum operating negative Voltage(V) -500 -500

Table 1 Physical characteristics of the MFC

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The figure 8 shows the orientation of the fiber in each specimen and some of their characteristics. In the above models the d33 value, which corresponds to the mechanical-electrical coupling effect is inserted in the field corresponding to d31 constant. This is done to facilitate the voltage boundary condition in the numerical simulation. This implies that the voltage is applied along the thickness of the patch in the lateral direction (direction 3), but the strain remains in-plane(direction-1) Figure 9.

Figure 9 Direction 3 indicating the direction in which the MFC is loaded.

The two composite materials used for the tests are Graphite-Fiber/Epoxy-Resin laminate KGBX2508 and the Glass-Fiber/Epoxy-Resin laminate GGBX2808. Each laminate consists of four fabric plies with two different fiber orientations: 0°/90° and +45°/-45° with respect to the length of the specimen. The ply stacking sequence are reported in the Table 2.

Ply N. Sequence N.1 Sequence N.2 Sequence N.3 Sequence N.4

1 +45/-45 0/90 0/90 +45/-45

2 0/90 +45/-45 0/90 +45/-45

3 0/90 +45/-45 0/90 +45/-45

4 +45/-45 0/90 0/90 +45/-45

Table 2 Ply stacking of substrate material

Bending Specimen

These specimens provide bending deformation along the length of the laminate. This is achieved with the help of MFC patches which are glued on the top and bottom surface of the specimens. These MFC patches provide bending deformation for elongator and contractor effect. The piezoelectric fiber direction is set along the length of the substrate laminate. The MFC M8528-P1 patch have 0° orientation, which indicates that the fiber direction is in the same direction as that of the fiber in the laminate. The experimental test provides information on the behavior of the specimen on application of a symmetrical voltage loading. The deformation produced on the application of symmetrical Voltage loading and the time required for the

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specimen to reach steady state is noted down. The specimen is excited with a nodal force while under the influence of voltage excitation to understand transient behavior. The Figure 10 and Figure 11 show the geometry of the bending specimen.

Figure 10 Bending Specimen

Figure 11 Geometric position of MFC patch and dimensions. The substrate laminate of the composite fiber has the following specifications: 400mm×45mm×1mm (4 twill fabrics)

The MFC has active area and passive area, active area being the one with piezoelectric fiber and the passive area constituting the surrounding Kapton.

Overall Length of MFC patch: 103mm×35mm×0.3mm Active area:85mm×28mm

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Torsion Specimen.

The torsion specimen has been designed to obtain pure torsion effect on the substrate laminate. The experimental tests provide information on the deformation of the specimen along its length and maximum displacement at the tip section. The Figure 12 and Figure 13 indicate the positioning of the MFC patch and the dimensions of the specimen and MFC respectively.

Figure 12 Torsion Specimen

Figure 13 Dimension and position of MFC on torsion specimen

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19 400mm×80mm×1mm (four twill fabric)

The MFC dimensional specification are:

Overall length of one MFC patch-105mm×65mm×0.3mm Active area-85mm×57mm.

Figure 14 Cross-sectional view of torsion specimen.

Figure 14 shows the cross-sectional view of the torsion specimen indicating the positions of four twills and the MFC patch on top and bottom. It can be seen that MFC patch has Kapton on its surrounding which constitutes the passive area. The Figure 15 and Figure 16 shows the technical drawing for the bending and torsion specimens respectively.

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Chapter-3

Experimental Set-Up

The chapter gives a brief description of the experimental set-up used to test the specimens. Moreover, a thorough description of the control hardware and software is provided.

Macro Fiber Composite

MFC Characteristic:

M8528-P1 M8557-F1

Maximum Operational Positive Voltage(V)

1500 1500

Maximum Operational Negative Voltage(V) -500 -500 Maximum operating Temperature(°C) 80 80 Operational Lifetime (@ 1kVp-p) (Cycles) 109 ₁₀9 Operational Bandwidth(kHz) 0 -10 0-10 Blocking Force (N) 454 945 Free Strain (ppm) 1800 1750 Capacitance (nF) 6.58 13.26

Volume Density, Active Area (g/cm3)

5.44 5.44

Table 3 Operational Parameter

Tensile Modulus, Ep1(GPa) 30.336

Poisson’s Ratio, νp12 0.31

Poisson’s Ratio, νp21 0.16

Shear Modulus, Gp12 5.515

Table 4 Orthotropic Linear Elastic Properties

High Voltage Power Amplifier

MFC can handle high voltage of the order of 1500V, which requires high voltage power amplifier. The amplifier used in the testing, to provide voltage excitation to the MFC patch is custom model provided by the Smart Material Corporation. The model was developed during the Future wing Project (5). The amplifier is a multi-channel amplifier with up to six independent channels and it is used to control the MFC actuator array.

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Operational Parameters:

Voltage Output Range(V) -500 to 1500

Current Output Range(mA) 0 to ±50 DC or 60 Peak AC

Bandwidth(kHz) 0-10

Slew Rate(V/μs) 50

Voltage Control Input(V) 0-5

Independent Channels 6

Offset Voltage(V) <1

Table 5 High Voltage Power Amplifier Specifications

Test Rig

The test rig holds the specimen and the mechanism that holsters the specimen, sensors, lasers and the modal shaker. The specimen is mounted such that the face that has MFC is perpendicular to the surface of the test rig as shown in the figure. This is done to have minimize the effect of gravity and self-weight on the specimen.

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Figure 18 CAD Model of the Test Rig

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25 • A1: Specimen

• A2: Laser Sensor • A3: Accelerometer • A4: Strain Gauge

• A5: Electrodynamic Modal Shaker • A6: Precision Translation Stage

General Arrangement

The General set up consists of the following main equipment.

• A: Test Rig

• B: Power Supply Group • C: CompactRIO • D: CompactDAQ

• E: Computing Device and User Station

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Laser Distance Measuring Device

The test rig is equipped with two laser sources, which are used for distance measurement based on principle of triangulation measurement. These devices indicate the deformation of the specimen by measuring the deviation from the mean position. OptoNCDT IDL 1402-100 model is used for the test. Its specifications are listed below.

OptoNCDT IDL 1402-100

Measuring range(mm) 100

Start of measuring range (mm) 50

End of measuring range(mm) 150

Resolution(μm) 10

Maximum measuring rate(Hz) 1500

Table 6 Technical specification of the Laser distance measurement device

The second laser device is used as feedback transducer for the control system. The reading that this laser sensor provides is used to obtain displacement produced by the specimen. Figure 21 shows the control point position. The laser position was chosen to optimize the working condition for the control system. The laser is positioned so that it measures displacement produced by the specimen which are within its measuring range.

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Precision Translation Stage

The movement of the laser device on the test rig is done with the help of Precision Translation Stage, Produced by Physik Instrument. It is composed of two M-126.CG1 stages, with a precision of 2.5μm and M-403.8DG stage with a precision of 1μm. The stages are controlled by C+862.10/1 DC motor.

Figure 22 M-403 Translation Stage

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Accelerometer

The 352C22 ICP Accelerometer is fixed to the free tip of the specimen. The sensor is used as feedback for the vibration compensator system. Figure 24 shows the accelerometer. Using the accelerometer, we can find the eigenmodes of the specimen.

352C22 ICP Accelerometer

Measuirng range(mm) 100

Start of measuring range(g) ±500

Sensitivity(mV/g) 10

Frequency range(Hz) 1-10000

Table 7 Technical Specification of Accelerometer

Modal Shaker

The 2007E Electrodynamic Shaker, from the PCB Piezotronics, is used to provide the forced vibration to the system which acts as the external disturbance.

Max force output(Sine)[N] 31 peak

Max force output(Random)[N] 22peak

Maximum force output (Shock: 11ms pulse)[N] 67 peak

Max displacement[m/s] 12.7 peak to peak

Max velocity[m/s] 2

Max acceleration(driven)[m/s2] ₂₆₅ Max acceleration(Shock: 11m/s pulse)[m/s2_] ₁₈₆₃

Frequency range[]kHz] Dc to 9

Table 8 Technical Information-Modal Shaker

Amplifier

The PCB piezotronics Smart Amp 2100E21-100 amplifier is used drive the shaker. The voltage can be regulated using the gain knob in the amplifier. The Table 9 provides the technical information about the model.

Max output voltage [V RMS] 21

Current Limit [A] 18 peak

Output power[W] 100

Frequency response[Hz] 0.4-40000

Max Voltage Gain[dB] 20

Table 9 Technical Information for the Amplifier

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Impedance Head

The mechanical impedance Sensor ICP 288D01 is mounted between the shaker and the stringer, which is connected to the specimen. This device allows us to measure force and acceleration imparted to the specimen and therefore to adjust the input voltage until obtaining the desired level of vibration.

Strain Gauge

The RY93-6/120 strain gauge, produced by Hottinger Baldwin Messtechnik GmbH (HBM) is used to measure the strain in the specimen during the test. The device is a 3-axis rectangular strain gauge rosette and is installed near the fixed end of the specimen.

Digital Multimeter

The Keysight Technologies 34461A Bench Digital Multimeter connected through a high-voltage probe to the CH1 output port of the MFC amplifier

Data acquition I/O platform and computing device

This is used to acquire sensor measurement and to control the system in open as well as in closed loop condition. They are mentioned below.

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NI CompactDAQ-9178

NI CompactDAQ-9178 chassis allows us to receive all signals from the test rig sensor. It also provides voltage output signals for the amplifiers.

NI CompactRIO-9063

The CompactRIO-9603 chassis is an embedded controller. It provides real-time processing running the NI Linux Real-Time OS. The Chassis can receive signals from sensor and provide voltage signals.

NI 9923Modulus

The 9923 Modulus is a terminal block that allows chassis to provide voltage signals. The rig is equipped with two 9923 Moduli.

NI 9215 Modulus

The 9215 Modulus receives four voltage signals through BNC connectors. It can acquire signals of ±10V, upto 100000 samples per second per channel. It receives laser measurements and provides command signals to the MFC and the shaker.

NI 9235 Modulus

The 9235 Quarter-Bridge strain gauge module receives strain measurement from the rosette. Its sampling rate is 10000 samples per second per channel.

Figure 26 CompactDAQD

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Control Software

NI LabVIEW is used to control the chassis. LabView is an integrated development environment. The native graphical language G used in the LabVIEW allows us to visualize, create and code engineering system faster and with less bugs. Moreover, in LabVIEW it is possible to create custom user interface, named Front Panel, for data visualization and operator input. Lastly LabVIEW automatically handles thread allocation and parallel processes and is able to run a control system with high quality performance. A LabVIEW program us termed as Virtual Instrument(VI).

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Chapter 4 Numerical Simulations

The numerical simulation constitutes most of the work done during the thesis. The aim of the numerical simulations is to understand the dynamic behavior of the structure when subjected to dynamic loading and then to validate these results with the experimentally obtained values. Numerical simulation is performed using the Finite Element Analysis(FEA) software ANSYS. These numerical simulations allow us to understand the behavior of the complex structure by not spending money and time on the real specimens or models. The FEA analysis represents the structure with a mathematical model.it then tries to find the solution to the mathematical model numerically.

The Finite Element model comprises of points called “nodes”, which form the shape of the design. The nodes are connected to finite elements, which form the finite element mesh and contain the material and structural properties of the model, defining how the model should behave under certain conditions. The Finite Element Analysis in ANSYS has three main phases:

Pre-Processing phase: This phase allows us to

create the numerical model of the structure we intend to solve. The model is made based on the input we provide such as the element type, material properties, real

constants, coupling and constraint equations. Designing the model, modeling the mesh for the solid model and assigning material properties to the model.

Solution Phase: The numerical model developed with the help of inputs in the pre-processing

phase is solved by the computer. The solver generates the solution to boundary value problems for partial differential equation. This in turn yield approximate values of the unknowns at discreet number of points over the domain. To solver subdivides the domain into smaller finite elements. The individual equation representing each finite element is then assembled together providing a larger system of equation representing the entire model. It is then solved using variational method from the calculus of variation to approximate a solution wherein minimizing the error function.

Post-Processing Phase: The final stage presents the solution generated by the solver such as

stress in the model, or the strain or the displacement produced by the structure. The post processor presents these results with graphical displays, charts and tabled reports.

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Finite Element model

A finite element model of the structure was created. Model of the Specimens were developed as per the specification provided in the chapter two, discussion about the geometry and positioning of the MFC patch. Both the models for the numerical simulation had four plies each. The plies are designed as solid structure and assigned an appropriate element type. The first and fore most task is to assign engineering data to the model. So, in the model we have assigned material properties of Graphite, Glass, Epoxy, Resin and Macro Fiber Composite to the parts that represent the same. The numerical models are without the grip system.

The element type associated with each part of the model has been carefully checked and assigned as per their properties. The Macro Fiber composite is assigned SOLID226 element which is 3-D 20-node coupled field solid. The element has twenty nodes and up to five degrees of free per node. The element has structural, thermal and electrical material properties. KEYOPT(1) determines the Degree of Freedom(DOF) set and the corresponding force labels and reaction solution. KEYOPT(1) is set for 1001 for Piezoelectric analysis. For a Piezoelectric analysis, UX, UY, UZ and VOLT are the DOF labels and force and electric charge are the reaction solution. The rest of the parts (Substrate, Kapton and Resin) have been assigned with SOLID186 element type. SOLID186 is a higher order 3-D 20-nodesolid element that has quadratic displacement behavior. The element has 20 nodes having three degrees of freedom per node: translation in nodal x, y and Z direction

The geometry used for defining the specimen were created shorter in length as compared to the real specimen because the real specimen has a grip which goes inside the holder which reduced the length of the specimen. The geometry used for the numerical modeling was designed in the Design Modeler and shows the unsymmetrical positioning of the MFC along the length. The edge to which the MFC is closest is the edge, which is fixed.

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The Figure 29 shows the geometry of the torsion specimen. The model is made of four plies each 0.25mm in thickness, bonding resin, which has a thickness of 0.075mm and MFC (active and passive area) with a thickness of 0.3mm.

The model consists of multiple parts and ANSYS meshes each part separately with separate mesh with no connections in between them, even though they share faces. So, in order to achieve a conformal

mesh, multiple parts are put into a single part. The conformal mesh allows us to provide same kind of mesh to all the parts as compared to free mesh where the ANSYS assigns each part different mesh and different element shape. The rectangular element shape has been assigned to finite elements by utilizing the edge sizing method and controlling the element shape and size using the number of division assigned to each edge. The bending specimen has been provided with a similar rectangular pattern of mesh to achieve a conformal mesh and the geometry is recreated exactly with the same ideology as that for the torsion specimen.

Transient structural Analysis

The transient structural analysis or the time -history analysis is used to determine the dynamic

response of the structure under the action of any general time-dependent load. For this research study, the time dependent load is an electrical excitation in the form of Voltage which is applied as a ramp and a nodal force. The ANSYS Transient structural block shows the flow of process starting from the engineering data to the final result in the Figure 31.

Figure 31 Transient structural work block in the ANSYS workbench. Figure 30 Mesh for the Torsion specimen

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he transient structural analysis performed on the bending and torsion specimens. For each specimen, there are four different sequences and for each sequence there has been a transient structural analysis with different voltage excitation ranging from 100 V to 1000V and in the negative side with 400V. The following section gives the gives the transient structural analysis on the specimen. The time-dependent response of the free vertex of the specimens has been recorded as the transient voltage load and nodal force act. ANSYS parametric design language is used to provide time-dependent loading and nodal force on the structure.

Figure 32 ANSY commands

The Post-Processor provides the results of the finite element analysis and it has been used to show the time-history of displacement of the tip of the specimen with respect to the transient Voltage loading and the impulse nodal force.

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The nonlinear setting used in the workbench are shown in the figure below.

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Bending Specimen-Graphite Epoxy- Sequence-1

Figure 34 shows the original (wireframe) and the deformed (colored) position of the Bending

Specimen-Graphite/Epoxy specimen at the end of transient loading -20 seconds.

Figure 34 100V Bending Specimen CF Sequence 1

-1.4000E-03 -1.2000E-03 -1.0000E-03 -8.0000E-04 -6.0000E-04 -4.0000E-04 -2.0000E-04 0.0000E+00 2.0000E-04 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 Z-Dis p lace m en t (m ) Time (s)

100 V Time Histroy

Figure 35 Time history of displacement for 100V and nodal force impulse in BS CF SQ1

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Figure 37 200V Bending Specimen Sequence 1

Figure 38 Time history of displacement for 200V and nodal force impulse

Figure 39 Frequency plot for 200V -2.0000E-03 -1.5000E-03 -1.0000E-03 -5.0000E-04 0.0000E+00 5.0000E-04 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 Z-Dis p lace m en t (m ) Time (s)

200 V Time Histroy

4.705882353 1.00E-09 1.00E-07 1.00E-05 1.00E-03 1.00E-01 0 5 10 15 20 25 30 35 40 45 50 PSD Frequency (Hz)

PSD 200 V

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Figure 42 BS CF SQ1 1000V Frequency plot Figure 40 500V Bending Specimen Sequence 1

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Figure 47 -400V Bending Specimen Sequence 1

Figure 48 BS CF SQ1 -400V Frequency Plot

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Bending Specimen-Graphite Epoxy- Sequence-2

Figure 49 shows the original (wireframe) and the deformed position (colored) of the Bending Specimen-Graphite/Epoxy specimen at the end of transient loading -20 seconds.

-8.0000E-04 -7.0000E-04 -6.0000E-04 -5.0000E-04 -4.0000E-04 -3.0000E-04 -2.0000E-04 -1.0000E-04 0.0000E+00 1.0000E-04 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 Z-Dis p lace m en t (m ) Time (s)

100 V Time Histroy

5.882352941 1.00E-12 1.00E-09 1.00E-06 1.00E-03 1.00E+00 0 5 10 15 20 25 30 35 40 45 50 PSD Frequency (Hz)

PSD 100 V

Figure 51 BS CF SQ2 100V Frequency plot

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-1.2000E-03 -1.0000E-03 -8.0000E-04 -6.0000E-04 -4.0000E-04 -2.0000E-04 0.0000E+00 2.0000E-04 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 Z-Dis p lace m en t (m ) Time (s)

200 V Time Histroy

5.882352941 1.00E-13 1.00E-11 1.00E-09 1.00E-07 1.00E-05 1.00E-03 1.00E-01 0 5 10 15 20 25 30 35 40 45 50 PSD Frequency (Hz)

PSD 200 V

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45 -1.20E-03 -1.00E-03 -8.00E-04 -6.00E-04 -4.00E-04 -2.00E-04 0.00E+00 2.00E-04 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 Z-Dis p lace m en t (m ) Time (s)

1000 V Time Histroy

Figure 58 Time history of displacement for 1000V and nodal force impulse in BS CF SQ2 Figure 59 1000V Bending Specimen Sequence 2

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Figure 62 Time history of displacement for -400V and nodal force impulse in BS CF SQ2

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Bending Specimen-Graphite/Epoxy-sequence 3

Figure 64 :100V Bending Specimen Sequence 3

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Figure 67 Time history of displacement for 200V and nodal force impulse in BS CF Figure 68 SQ3200V Bending Specimen Sequence 3

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49 -1.20E-03 -1.00E-03 -8.00E-04 -6.00E-04 -4.00E-04 -2.00E-04 0.00E+00 2.00E-04 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 Z-Dis p lace m en t (m ) Time (s)

500 V Time Histroy

5.882352941 1.00E-14 1.00E-12 1.00E-10 1.00E-08 1.00E-06 1.00E-04 1.00E-02 1.00E+00 0 5 10 15 20 25 30 35 40 45 50 PSD Frequency (Hz)

PSD 500 V

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50 5.882352941 1.00E-14 1.00E-12 1.00E-10 1.00E-08 1.00E-06 1.00E-04 1.00E-02 1.00E+00 0 5 10 15 20 25 30 35 40 45 50 PSD Frequency (Hz)

PSD 1000 V

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5.882352941 1.00E-10 1.00E-08 1.00E-06 1.00E-04 1.00E-02 1.00E+00 0 5 10 15 20 25 30 35 40 45 50 PSD Frequency (Hz)

PSD -400 V

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Bending Specimen-Graphite/Epoxy-Sequence 4

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54 1.00E-10 1.00E-08 1.00E-06 1.00E-04 1.00E-02 1.00E+00 0 5 10 15 20 25 30 35 40 45 50 PSD Frequency (Hz)

PSD 500 V

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Bending Specimen-Glass/Epoxy-sequence-1

-2.00E-03 -1.50E-03 -1.00E-03 -5.00E-04 0.00E+00 5.00E-04 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 Z-Dis p lace m en t (m ) Time (s)

100 V Time Histroy

3.529411765 1.00E-09 1.00E-07 1.00E-05 1.00E-03 1.00E-01 0 5 10 15 20 25 30 35 40 45 50 PSD Frequency (Hz)

PSD 100 V

Figure 94 100V Bending Specimen GE Sequence 1

Figure 95 Time history of displacement for 100V and nodal force impulse in BS GE SQ1

Non-Linear transient dynamic Behavior of Composite Specimens with Macro Fiber Composite patch as actuators.

Academic year 2016/2017

Department of Civil and Industrial Engineering

Master of Science in Aerospace Engineering

NONLINEAR TRANSIENT DYNAMIC RESPONSE OF

COMPOSITE FIBER SPECIMEN

WITH

MACRO FIBER COMPOSITE PATCH AS ACTUATOR.

Supervisor:

Candidate:

Prof. Mario Rosario Chiarelli

Nidish Narayanan

Abstract

Table of Contents

Chapter 1

Introduction

Piezoelectricity

Origin

Structure

Poling

Macro Fiber Composite

Application of Macro Fiber Composites

Deformation of wing using MFC (1)

Energy Harvesting

System using

Piezo-Electric Macro Fiber

Composite (2)

Energy Harvest for Unmanned aerial Vehicle. (3)

Fin Buffet Alleviation Using Piezoelectric Actuators (4)

Governing Equation









































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





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

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



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



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