Shape memory alloys (SMA)-textile-based actuators have gained significant attention for their applications in various fields, including soft robotics and wearable devices. Nowadays, soft actuators are created using SMA and macro fiber composites (MFC). SMA is a highly nonlinear material, and textile fiber-wrapped SMA wires are employed to craft shape-morphing structures and actuation sheets through the knitting method. This process requires expertise and time, leading to high costs for producing an actuation sheet. In this research work, ABAQUS is utilized to construct an equivalent unit cell model based on linear constitutive equations for analyzing the behavior of knitted SMA-textile-based actuators. The actuation deformation of the P-loop is obtained using the user material subroutine (UMAT). Strain is the primary output focused on in this study, with elastic material properties and electric field as the input parameters. By incorporating the linear constitutive equations, the actuation of basic patterns and derived patterns is successfully compared with experimental results. The proposed model predicts a similar deformation of the actuation pattern sheets of the SMA-textile-based actuator, justifying the proposed equivalent unit cell model.
Output-only based damage assessment of delaminated smart composite structures is increasingly appealing due to its easy availability in real engineering applications. In this work, structural vibration responses of the pristine and delaminated composite structures are processed via Fast Fourier Transform (FFT) and Convolutional Neural Network (CNN) for the classification of healthy and various damaged cases. The dynamic model for the healthy and delaminated smart composite laminates is developed by incorporating of improved layerwise theory, higher-order electric potential field, and finite element method. Structural vibration responses are obtained through a surface bonded piezoelectric sensor by solving the electromechanically coupled dynamic model in the time domain. FFT is used to construct vibration-based images from the transient responses of the sensor and CCN is used to classify those images into healthy and damaged classes. The confusion matrix of CNN showed physically consistent results and an overall classification accuracy of 90% was obtained. The pre-trained CNN was also tested to predict labels for new cases of delaminations in the smart composite laminates. The essence of the proposed method is that it requires only low-frequency structural vibration responses for the detection and localization of delamination in smart composite laminates.
Separation along the interfaces of layers (delamination) is a principal mode of failure in laminated composites and its detection is of prime importance for structural integrity of composite materials. In this work, structural vibration response is employed to detect and classify delaminations in piezo-bonded laminated composites. Improved layerwise theory and finite element method are adopted to develop the electromechanically coupled governing equation of a smart composite laminate with and without delaminations. Transient responses of the healthy and damaged structures are obtained through a surface bonded piezoelectric sensor by solving the governing equation in the time domain. Wavelet packet transform (WPT) and linear discriminant analysis (LDA) are employed to extract discriminative features from the structural vibration response of the healthy and delaminated structures. Dendrogram-based support vector machine (DSVM) is used to classify the discriminative features. The confusion matrix of the classification algorithm provided physically consistent results.
This paper presents a comparative study of different classification algorithms for the classification of various types of inter-ply delaminations in smart composite laminates. Improved layerwise theory is used to model delamination at different interfaces along the thickness and longitudinal directions of the smart composite laminate. The input-output data obtained through surface bonded piezoelectric sensor and actuator is analyzed by the system identification algorithm to get the system parameters. The identified parameters for the healthy and delaminated structure are supplied as input data to the classification algorithms. The classification algorithms considered in this study are ZeroR, Classification via regression, Naïve Bayes, Multilayer Perceptron, Sequential Minimal Optimization, Multiclass-Classifier, and Decision tree (J48). The open source software of Waikato Environment for Knowledge Analysis (WEKA) is used to evaluate the classification performance of the classifiers mentioned above via 75-25 holdout and leave-one-sample-out cross-validation regarding classification accuracy, precision, recall, kappa statistic and ROC Area.
Dynamic characteristics of smart composite laminate with partially debonded piezoelectric sensor are investigated. Improved layerwise theory with Heaviside’s unit step function is used to model the discontinuous displacement field with jumps owing to the in-plane slipping and out-of-plane opening at the debonded interface. Higher order electric potential field is employed to describe the potential variation through the thickness of piezoelectric patches. Finite element method and extended Hamilton’s principle are used to derive the governing equation of motion. The governing equation is solved in time domain using Newmark time integration algorithm. The developed model is numerically implemented on a laminated composite plate with surface bonded piezoelectric actuator and partially debonded sensor. The sensing capability is evaluated in the presence of partial inner and edge debonding in the piezoelectric sensor.
The dynamic characteristics of smart composite laminates with partially debonded piezoelectric actuator are investigated in this work. The proposed work introduces an improved layerwise theory based mathematical modeling with the Heaviside unit step functions to allow the possible sliding of the in-plane displacements and jump of the out-of-plane displacements for the debonded area. The finite element implementation is conducted using the four-node plate element to derive the governing equation. The dynamic characteristics are investigated by the frequency domain and time domain. The influence of actuator debonding to the natural frequencies is subtler for such kind of smart composite structures. The debonding of piezoelectric actuator also decreases its actuation ability that is reflected in the magnitudes of the system response. The proposed method can well predict the responses of the smart composite laminates with actuator debonding failures and it could be applied to the further damage detection methods.
In this present study experimental and finite element analysis of cellulose based electro-active paper energy harvester is presented. Electro-active paper coated with metal electrode is a smart form of cellulose and exhibit piezoelectric effect. Specimens were prepared by depositing electrodes on both sides of the cellulose film. A 50 mm x 50 mm cellulose film coated with aluminum electrodes was bonded on 100 mm x 50 mm x 1 mm aluminum host structure. The voltage output to input acceleration frequency response across a load resistor of 1 MΩ is recorded by conventional energy harvesting experimental setup at the fundamental vibration mode of the EAPap cantilever beam. A coupled piezoelectric-circuit finite element model is developed in which load resistor is directly connected to energy scavenging device. Voltage output FRF is measured for the cases, without proof mass, and by adding a 2 grams proof mass near the tip of the cantilever. The experimental voltage FRF value is 7.6 V/g at 75.1 Hz and is improved to 13.8 V/g at 62.2 Hz when a stainless steel proof mass of 2 grams is added. The presented CPC-FEM model results agree reasonably well with the experimental results. Despite the fact that the electro-mechanical coupling coefficient of electro-active paper is lower than other available piezoelectric materials, it is biocompatible, cheap and naturally occurring polymeric material. It is also very flexible and posses similar piezoelectric characteristics such a PVDF which inspire to use EAPap in energy harvesting applications.
KEYWORDS: Composites, Actuators, Finite element methods, Control systems, Sensors, Matrices, Energy efficiency, Systems modeling, Mechanical engineering, Motion models
Recently, light weight structure becomes an object of attention because increase of energy efficiency becomes the most important global hot issue. Then, composite structures, which have inherent high strength and stiffness to weight ratio, are in the limelight for light weight structures. However, complex failure modes of composite structure are still remains unsolved problem and become main obstacle of wide application of composite structures. Delamination is one of frequent damage phenomenon of laminated composite structure. Delamination can cause reduction of structural stiffness and decrement of natural frequencies. This might induce increase of structural vibration and resonant phenomenon of operating structures. Then, delamination should be detected and complemented. In this work, active control scheme and piezoelectric actuators are used to reduce the delamination effect of damaged composite structure. At first, finite element model for delaminated composite structure is constructed based on improved layerwise theory and then state space control model is established. After design and implementation of active controller, dynamic characteristics and structural performances of damaged composite structure are investigated and effectiveness of active healing is evaluated.
The general class of organic-inorganic hybrid nanocomposites materials is a fast growing area of research. The significant effort is focused on the ability to control the nanoscale structures via organic functional synthetic approaches with inorganic metal oxides. The properties of nanocomposites material depends on the properties of their individual components but also their morphological and interfacial characteristics. This rapidly expanding field is generating many exciting new materials with novel properties. Mainly, cellulose is considered as the richest renewable materials are presently among the most promising candidates for use in photonics due to their versatility, flexibility, light weight, low cost and ease of modification. Cellulose-metal oxide nanomaterials were developed the technologies to manipulate selfassembly and multifunctionallity, of new technologies to the point where industry can produce advanced and costcompetitive cellulose metal oxide hybrid materials. Therefore, the present study is focused on cellulose–functionalized - 4, 4’-(propane-2, 2’-diyl) diphenol-SiO2/TiO2 hybrid nano-composites materials by in-situ sol-gel process. The chemical and morphological properties of cellulose-functionalized SiO2/TiO2 materials via covalent crosslinking hybrids were characterized by FTIR, XRD, TGA, DSC, SEM, TEM and optical properties.
In the recent times, cellulose-based Electro-Active Paper (EAPap) has been investigated to have electro-mechanical coupling and piezoelectric effects which are promising characteristics for a smart material. In this paper, the effects of electrodes of EAPap are investigated for vibration energy harvesting. Although piezopolymers have smaller value of electro-mechanical coupling constants as compared to the piezoceramics, but are very flexible, which motivates to use these materials as potential media for flexible energy harvesting. Cellulose based Electro-active papers are deposited with different metal electrodes like aluminum, gold and silver. The fabricated samples are tested with aluminum cantilever beam under an input excitation. The effects of area of electrodes are also investigated by comparing the output voltage at the different area of electrodes ranging from 400mm2 to 1200mm2. EAPap cantilever are tested at lowest resonant frequency and under varying acceleration amplitude to maximize the output voltage. From the experimental results, it is concluded that the potential of EAPap as a flexible energy harvester are very promising.
The possibility as a vibration sensor of Electro-Active paper (EAPap) based on piezoelectricity was investigated in the
present paper. The EAPap was fabricated by regenerating and tape casting cellulose. The gold, silver and aluminum were
deposited on both sides of the cut cellulose film using a thermal evaporator. The sample was coated by thin laminating
film for packaging. The simple aluminum cantilevered beam was used for the vibration testing and EAPap was attached
on the beam. The original EAPap sensor without grounding and shielding has greatly affected by the surrounding noise
such as power noise especially. The power noise reduced dramatically with grounding and shielding of EAPap. The
impulsive response of EAPap provided correct dynamic characteristics of the beam. Forced response of EAPap presented
that gold and silver electrodes are suitable for EAPap sensor but aluminum electrode provides too many noise due to
high resistance. PVDF provided similar characteristics of EAPap, which results EAPap has high potential as a vibration
sensor.
A stress function based method is proposed to analyze the interlaminar stresses at the free edge of a piezo-bonded
composite laminated structure. Two piezoelectric actuators are symmetrically surface bonded on composite laminate.
Same electric fields are applied to the two symmetric piezoelectric actuators which can generate induced strain, resulting
in pure extension on the laminated plate. The stresses that satisfy the traction-free boundary conditions at the free edge
and at the top and bottom surfaces of the laminate were obtained by using the complementary virtual work principle.
Cross-ply and angle-ply laminates were analyzed. To verify the proposed method, the stress concentrations predicted by
the present method were compared with those analyzed by the finite element method. The results provided that the stress
function based analysis of piezo-bonded laminated composite structure is an efficient and accurate method for initial
design stage of piezo-composite structure.
In this paper, the possibility of EAPap as a piezoelectric sensor was investigated by the vibration control of the
cantilevered beam. The EAPap sample was attached at the root of the cantilevered beam and used as a vibration sensor.
The piezoceramic patch was also attached at the root of the beam and played as an actuator. The voltage output of
EAPap showed same trend of that measured by the piezoceramic patch. The frequency bandwidth and quality factor of
EAPap were similar to those of piezoceramic patch, which results EAPap has similar sensing capability of piezoceramic
patch. To find the application of EAPap sensor, beam vibration control was performed. EAPap sensor output was
considered as a position error of the cantilevered beam system and a simple PID controller was designed to suppress the
vibration of the beam. The EAPap sensor output provided clear time response of the beam. The controlled system
showed good vibration control performance of the beam. The results provided that EAPap has great potential as a
piezoelectric vibration sensor.
The possibility as a vibration sensor of Electro-Active paper (EAPap) based on piezoelectricity was investigated in the
present paper. The EAPap was fabricated by regenerating and tape casting cellulose. The sample was coated by thin
laminating film for packaging. The capacitance of EAPap was measured and compared with commercial PVDF. Relative
permittivity of EAPap was 12, which was same as commercially available PVDF. This reveals that EAPap has similar
sensing potential of synthetic piezo polymer film. The simple aluminum cantilevered beam was used for the vibration
testing and EAPap was attached on the beam. The original EAPap sensor without grounding and shielding has greatly
affected by the surrounding noise such as power noise especially. The power noise reduced dramatically with grounding
and shielding of EAPap. The impulsive response of EAPap provided correct dynamic characteristics of the beam.
Especially, twisting mode of the beam was clearly observed even though the EAPap was attached at the center of the
beam. This is because the sensing capability of EAPap is based on piezoelectricity which is bidirectional strain
characteristics. EAPap sensor based on piezoelectricity provided a great potential as a vibration sensor.
Understanding of creep effects on actuating mechanisms is important to precisely figure out the behavior of
material. Creep behaviors of cellulose based Electro-Active Paper (EAPap) were studied under different constant loading
conditions. We found the structural modification of microfibrils in EAPap after creep test. Structural differences of as-prepared
and after creep tested samples were compared by SEM measurements. From the measured creep behaviors by
different loading conditions, two different regions of induced strain and current were clearly observed as the
measurement time increased. It is consider that local defects may occur and becomes micro-dimple or micro-crack
formations in lower load cases as localized deformation proceeds, while the shrinkage of diameter of elongated fibers
was observed only at the high level of loading. Therefore, cellulose nanofibers may play a role to be against the creep
load and prevent the localized structural deformations. The results provide useful creep behavior and mechanism to
understand the mechanical behavior of thin visco-elastic EAPap actuator.
Electro-active paper (EAPap) is a new smart material that has a potential to be used in biomimetic actuator and sensor. It
is made by cellulose that is very abundant material in nature. This material is fascinating with its biodegradability,
lightweight, large displacement, high mechanical strength and low actuation voltage. It has been reported that ionic and
piezoelectric effects play a dominant roll in the actuation mechanism. However, the electromechanical actuation
mechanisms are not clearly established yet. This paper presents the modeling of the actuation behavior of water infused
cellulose samples and their composite dielectric constant calculated by Maxwell- Wagner theory. Electro-mechanical
forces are calculated using Maxwell stress tensor method. Also, bending deflection is evaluated from simple beam model
and compared with experimental observation.
Piezoelectricity is one of major actuating mechanisms of a cellulose-based Electro-Active paper (EAPap). Wet drawn
stretching method was introduced in the fabrication process of cellulose film to increase piezoelectricity of EAPap. The
characteristics of wet drawn cellulose were studied by scanning electron microscope (SEM), X-ray diffractogram (XRD)
and pull test. The performance of EAPap was evaluated by measuring bending displacement and piezoelectric charge
constant. The performance of EAPap was sensitive to the fabrication process and material orientation of cellulose film.
Aligning cellulose fibers in the fabrication process was a critical parameter to improve mechanical and electromechanical
properties of EAPap. The experimental results provided that wet drawn stretching is an effective fabrication method to
improve mechanical stiffness and piezoelectricity of EAPap.
To improve the piezoelectricity of cellulose electro-active paper (EAPap), electrical field and magnetic field
alignments were investigated. EAPap is made with cellulose by dissolving cotton pulp and regenerating cellulose with
aligned cellulose fibers. EAPap made with cellulose has piezoelectric property due to its structural crystallinity.
Noncentro-symmetric crystal structure of EAPap, which is mostly cellulose II, can exhibit piezoelectricity. However,
EAPap has ordered crystal parts as well as disordered parts of cellulose. Thus, well alignment of cellulose chains in
EAPap is important to improve its piezoelectricity.
In this paper, uniaxial alignments of cellulose chains were investigated by applying electric field and magnetic field.
As exposing different fields to EAPap samples, the changed characteristics were analyzed by X-Ray diffractometer
(XRD) and Scanning electron microscopy (SEM). Finally, the piezoelectricity of EAPap samples was evaluated by
comparing their piezoelectric charge constant [d31]. As increasing applied electric field up to 40V/mm, d31 value was
gradually improved due to increased cellulose crystallinity as well as alignment of cellulose chains. Also the alignment
of cellulose chains was improved with increasing the exposing time to magnetic field (5.3T) and well alignment was
achieved by exposing EAPap sample on the magnetic field for 180min.
Electro-Active Paper(EAPap) actuator materials based on cellulose has been discovered as a smart material that has merits in terms of low voltage operation, lightweight, dryness, low power consumption, bio-degradability, abundance and low price. Since EAPap material requires low power consumption, a remotely driven actuator has been proposed by using microwave power transmission. This concept is attractive for many biomimetic systems such as crawling micro-insect robots, flying objects like dragon fly, and smart wall papers. However, the actuation performance of EAPap is sensitive to humidity. Thus, in this paper, a new EAPap that is less sensitive to humidity is studied. The fabrication of EAPap is explained and the actuations are shown with actuating voltage, frequency, humidity level and time. The fabrication process includes dissolving cellulose fibers, eliminating solvent and Li ions with DI (deionized) water and IPA (Isopropyl alcohol) mixture, washing with water, drying and gold coating. Morphology of the fabricated EAPap is analyzed by taking scanning electron microscope images and X-ray diffractogram. The actuator performance is tested in terms of bending displacement with frequency and humidity level.
KEYWORDS: Actuators, Microsoft Foundation Class Library, Sensors, Electrodes, Vibration control, Finite element methods, Structured optical fibers, Composites, Modal analysis, Ceramics
Dynamic modeling of smart hull structure with advanced piezoelectric actuator; macro-fiber composite (MFC) actuator,
is developed and control performance to suppress structural vibration of the system is studied. Finite element technique
is used to ensure application to practical geometry and boundary conditions of smart hull structure. Modal analysis is
conducted to investigate the dynamic characteristics of smart hull structure. For the verification of the proposed finite
element model, numerical results of modal analysis are compared with those of experimental modal test results. Modal
mass and stiffness matrix of smart hull structure are extracted for the controller design. Active controller is designed to
suppress structural vibration of smart hull structure and control performance is evaluated in the resonance and non-resonance
regions.
This paper investigates the applications of the piezoelectric acoustic sensors for
real time detection of crack initiation and propagation in ceramic composites. In the first
case this paper presents a smart method to detect and track the ceramic cell crack
initiation and propagating in real time when the solid oxide fuel cell (SOFC) system is in
operation with extremely high temperature (>750 deg. C). The main sources of fracture
and delamination are the ceramic cell interlayers and interfaces during high temperature
thermocycling. This research work is to successfully discern the damages during
assembly, initial damages at first thermocycle and damage propagation, if any, at later
cycles. This paper demonstrates that the AE signals generated from cell cracking and
fracture in the stack modules can be successfully captured by commercially off the shelf
(COTS) AE experimental hardware. The distinguishing characteristics of the cell crack
AE signal and the metal impact AE signals will be presented in the paper. The second
case successfully demonstrates the application of acoustic emission sensors to detect the
first crack initiated due to crushing load on ceramic balls. A comprehensive strategy to
capture the crushing load with respect to first crack initiation has been developed and
would be presented in this paper. The crack is initiated when the Hertzian contact
stresses are higher than the crushing load limit. Some initial results on signal processing
to distinguish between first and second crack initiation would be presented.
In-plane piezoelectric charge constant of Electro-Active paper (EAPap) was investigated based on direct and converse
piezoelectric effects. EAPap samples were made with cellulose film with very thin gold electrode coated on both sides of
the film. To characterize direct piezoelectricity of EAPap, induced charge was measured when mechanical stress was
applied to EAPap. In-plane piezoelectric charge constant was extracted from the relation between induced charge and
applied in-plane normal stress. To investigate converse piezoelectricity, induced in-plane strain was measured when
electric field was applied to EAPap. Piezoelectric charge constant was also extracted from the relation of induced inplane
strain and applied electric field. Piezoelectric charge constants obtained from direct and converse piezoelectricity
are 31 pC/N and 178 x 10-12m/V for 45 degree sample, respectively. Measured piezoelectric charge constants of EAPap
provide promising potential as a piezoelectric material.
Material properties of Electro-active paper (EAPap) actuator were investigated under different environmental conditions
such as humidity and temperature. Understanding of humidity and temperature effects on the material behavior of
EAPap during visco-elastic deformation regime provided useful information on structural changes of EAPap by
environmental factors. The pulling test results showed that the humidity and temperature heavily impact the mechanical
properties of EAPap. Electro-mechanical coupling effects were investigated by applying electric field during the pulling
test. Change of elastic modulus under different electric fields provides directional dependency of EAPap and strong
shear electro-mechanical coupling. Creep behavior of cellulose paper was studied to figure out mechanical strength of
EAPap under different ambient conditions. Tests under different humidity levels with fixed temperature and different
temperatures with fixed humidity provided the coupled hygrothermal effects on the performance of EAPap.
In this paper, mechanical properties and piezoelectric effects of cellulose based Electro-Active Paper (EAPap) actuators were investigated. Typical pulling tests of cellulose paper, which is a basic material of EAPap actuator, showed distinct elastic modulus and bifurcation point followed by plastic modulus at ambient conditions. The mechanism of this distinct phenomenon was examined to obtain better understanding of EAPap actuator. After that, in-plane strain of EAPap actuator under constant electric field was experimentally investigated to understand piezoelectricity of EAPap. EAPap samples were made by coating very thin gold electrodes on both sides of cellophane film. When external DC voltages were applied, in-plane contractions were induced due to the converse piezoelectric effect of EAPap. It was observed that the EAPap sample with 45° orientation exhibited the largest in-plane strain compared to other orientation samples.
KEYWORDS: Ferroelectric materials, Structural design, Chemical elements, Aluminum, Finite element methods, Dielectrics, Piezoelectric effects, Electromechanical design, Circuit switching, Control systems
In this paper, admittance is introduced to represent electro-mechanical characteristics of piezoelectric structures and to predict the performance of piezoelectric shunt system. It is shown that admittance of the piezoelectric structure is proportional to the dissipated energy in the shunt circuit. Admittance is used as a design index to construct the piezoelectric shunt system and obtained by finite element method. Vibration reduction of the piezoelectric structure with shunt circuit is realized by experiments. Damped system response of piezoelectric structure in frequency and time domain proved that admittance is proportional to the performance of piezoelectric shunt system. Therefore, a new design method of piezoelectric shunt system using admittance analysis is proposed to save design cost of the piezoelectric structure.
Presently there exists no way for direct measurement of strain at high temperature in engine components such as combustion chamber, exhaust nozzle, propellant lines and turbine blades and shaft. Existing fatigue and life prediction studies for high temperature zones in propulsion systems depend on strain/stress values computed from indirect measurements of temperature, flow velocity, pressure, et al. Thermomechanical fatigue (TMF) prediction, which is a critical element for blade design, is a strong function of the temperature and strain profiles. Major uncertainties arise from the inability of current instrumentation to measure temperature and strain at the critical locations. This prevents the structural designer from optimizing the blade design high temperature environment, which is a significant challenging problem in engine design. Ability to measure directly strains in different high temperature zones would deeply enhance the effectiveness of aircraft propulsion systems for fatigue damage assessment and life prediction. State of the art for harsh environment high temperature sensors has improved considerably for the past few years. This paper lays down specifications for high temperature sensors and does the technological assessment of these new sensing technologies. This paper presents a review of the recent advances made in harsh environment sensing systems and takes a peek at the future of such technologies.
In this paper, piezoelectric smart panels featuring shunt damping are designed and tested for broadband noise reduction. Electrical admittance is introduced to represent electro-mechanical characteristics of piezoelectric smart structures and to predict the performance of piezoelectric shunt damping as a design index of the system. The location and size of piezoelectric patches on the host panel are optimized by taking the admittance as a cost function and by using Taguchi method. The admittance is calculated by finite element method in the design stage and experimentally verified after the optimal configuration is found. Shunt performance of smart panel is realized by vibration reduction in frequency domain. In order to illuminate the effect of noise reduction in the shunt system, a standard test setup according to SAE J1400 is used to measure the transmission loss and sound pressure distribution for the smart panel. In this paper, a broadband shunt technique for increasing transmission loss is experimentally investigated.
The possibility of silkworm (Bombyx mori) protein as a base material of biomimetic actuator was investigated in this paper. Silkworm films were prepared from high concentrations of regenerated fibroin in aqueous solution. Films with thickness of about 100 μm were prepared for coating electrodes. The cast silk films were coated by very thin gold electrode on both sides of the film. Tensile test of cast film showed bi-modal trend, which is typical stress-strain relation of polymeric film. As the test of a possible biomimetic actuator, silkworm film actuator provides bending deformations according to the magnitude and frequency of the applied electric filed. Although the present bending deformation of silkworm film actuator is smaller than that of Electro-Active Paper actuator, it provides the possibility of biomimetic actuator.
The transient response of delaminated smart composite laminates is studied using an improved layerwise laminate theory. The theory is capable of capturing interlaminar shear stresses that are critical to delamination. The Fermi-Dirac distribution function is combined with an improved layerwise laminate theory to model a smooth transition in the displacement and the strain fields of the delaminated interfaces during “breathing” of delaminated layers. Stress free boundary conditions are enforced at all free surfaces. Continuity in displacement field and transverse shear stresses are enforced at each ply level. In modeling piezoelectric composite plates, a coupled piezoelectric-mechanical formulation is used in the development of the constitutive equations. Numerical analysis is conducted to investigate the effect of nonlinearity in the transient vibration of bimodular behavior caused by the contact impact of delaminated interfaces. Composite plate with surface-bonded or embedded sensors, subject to external loads, are also investigated to study the effects on transient responses due to various sizes and locations of delamination.
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