Volume Fraction Of Piezoelectric Phase Research Articles

Vibration analysis of magneto-electro-elastic sandwich plate with auxetic graphene reinforced metal matrix composite core

This research addresses analytical solutions for vibration performance of simply supported sandwich plate subjected to coupled mechanical-electric-magnetic-thermal loads. The plate is made of graphene reinforced metal matrix composite (GRMMC) core and magneto-electro-elastic (MEE) face sheets. Three graphene distribution patterns, FG-X, FG-O, and UD are considered for evaluating the reinforcement efficiency of graphene. The Reddy’s higher order shear deformation plate theory and Hamilton’s principle are employed to formulate the equations of motion of the sandwich plate. Then, using double trigonometric functions for variables and applying Bubnov–Galerkin procedure, the system of nonlinear second-order differential equations is constructed to reveal the natural frequency, frequency ratio, and dynamic response of the sandwich plate. The influences of graphene distribution patterns and volume fraction, magnetic and electric potentials, temperature change, and volume fraction of piezoelectric phase are discussed in details. This research provides basis for the design of sandwich composite structures, especially smart structures and devices.

3D frictional contact of graded magneto-electro-elastic film-substrate system under electromagnetic fields

The 3D frictional contact model of graded magneto-electro-elastic (MEE) film-substrate system under electromagnetic fields is presented. The semi-analytical method (SAM) is used to solve this multi-physical contact problem. Firstly, the frequency response functions (FRFs) for every layer of MEE material subjected to unit mechanical, electric and magnetic loads are derived. Conjugate gradient method (CGM) is then employed to obtain contact responses with Discrete convolution-fast Fourier transformation (DC-FFT) speeding related calculations. Finally, multilayered model is used to approximate graded film with two types of grads, exponentially varying grad (EVG) and volume-fraction varying grad (FVG), the effects of the type and thickness of graded film and the friction coefficient are investigated. The results show that EVG film with gradient index less than one or FVG film with smaller volume fraction of piezoelectric phase at the surface are preferred for the MEE film-substrate systems.

Nonlinear vibration characteristics of refined higher-order multi-phase piezo-magnetic nanobeams

This paper studies nonlinear dynamic characteristics of a nonlocal two-phase piezo-magnetic beam based on a refined higher-order beam formulation and piezoelectric reinforcement scheme. The piezoelectric reinforcement can cause an enhanced vibration behavior of smart nanobeams under magnetic field. Nonlinear governing equations of a smart nanobeam are derived based on refined beam theory, and a numerical trend is provided to obtained nonlinear vibration frequency. This research shows that changing the volume fraction of piezoelectric phase in the material has a great influence on vibration behavior of smart nanobeam under electric and magnetic fields. Also, it can be seen that nonlinear vibration behavior of smart nanobeam is dependent on the magnitude of exerted electric voltage, magnetic potential, hardening elastic foundation and shear deformation.

Magneto-electric effects on nonlocal nonlinear dynamic characteristics of imperfect multi-phase magneto-electro-elastic beams

This paper studies nonlinear dynamic characteristics of a nonlocal two-phase piezo-magnetic beam including geometric imperfections by considering piezoelectric reinforcement scheme. The piezoelectric reinforcement can cause an enhanced vibration behavior of smart nanobeams under magnetic field. All of prior papers on piezo-magnetic nanobeams ignore the influence of geometric imperfections which are substantial because a nanobeam is not ever ideal. Nonlinear governing equations of a smart nanobeam are derived based on refined beam theory and a numerical trend is provided to obtained nonlinear vibration frequency. This research shows that changing the volume fraction of piezoelectric phase in the material has a great influence on vibration behavior of smart nanobeam under electric and magnetic fields. Also, it can be seen that nonlinear vibration behavior of smart nanobeam is dependent on the magnitude of exerted electric voltage, magnetic potential, hardening elastic foundation and geometrical imperfection.

Active control for ratios of strains in functionally graded piezoelectric composites

Poisson’s ratio measured by the ratio of transverse strain to longitudinal strain is an important intrinsic property of materials. Imitating the definition of Poisson’s ratio, we define that the ratio of strains is denoted by the ratio of any two normal strains. Nowadays, some design methods have been proposed to tailor the ratios of strains by changing Poisson’s ratio in materials. However, the ranges of the ratios of strains by available methods are too narrow, the technology can provide materials with tailorable ratios of strains over an extremely wide range is rarely studied. To this end, we propose that the ratios of strains in piezoelectric composites can be active-controlled by simultaneously tailoring force and electric fields. The analytical solutions for different ratios of strains in piezoelectric composites subjected to force and electric fields are presented. It is demonstrated that the range of tunable ratios of strains can be from giant negative to giant positive. Moreover, the ratios of strains in any location of FG piezoelectric composites can be greatly affected by force field, electric field, polarization direction, volume fraction of piezoelectric phase. The present study may open up a new routine to design materials possessing extraordinary and programmable mechanical behaviors.

Analyzing large-amplitude vibration of nonlocal beams made of different piezo-electric materials in thermal environment

The present article researches large-amplitude thermal free vibration characteristics of nonlocal two-phase piezo-magnetic nano-size beams having geometric imperfections by considering piezoelectric reinforcement scheme. The piezoelectric reinforcement can cause an enhanced vibration behavior of smart nanobeams under magnetic field. All previous studies on vibrations of piezoelectric-magnetic nano-size beams ignore the influences of geometric imperfections which are crucial since a nanobeam is not always ideal or perfect. Nonlinear governing equations of a smart nanobeam are derived based on classical beam theory and an analytical trend is provided to obtain nonlinear vibration frequency. This research shows that changing the volume fraction of piezoelectric phase in the material has a great influence on vibration behavior of smart nanobeam under electric and magnetic fields. Also, it can be seen that nonlinear vibration behaviors of smart nanobeam is dependent on the magnitude of exerted electric voltage, magnetic imperfection amplitude and substrate constants.

Computational model for power optimization of piezoelectric vibration energy harvesters with material homogenization

Piezoelectric vibration power harvesters are being studied in the literature since they have high energy conversion from mechanical vibrations. A computational model that optimizes piezoelectric vibration energy harvester output power using homogenization of piezoelectric material is presented in this work. This computational model allows piezoelectric material tailoring to create piezoelectric vibrational energy harvesters capable of producing higher electrical power. The materials considered in the study are single crystal and polycrystals of BaTiO3 and PZN-4.5%PT, and piezopolymer PVDF-TrFE and the piezocomposites of these materials. The computational model is used to optimize the harvester power output of the unimorph vibration harvester configuration. The harvesters are modelled using the finite element method which is validated comparing analytical results for four traditional harvester configurations, viz., unimorph, bimorph, longitudinal generator and transverse generator. Single crystals, polycrystals and piezocomposites made by piezoceramic and piezopolymer materials are considered in the optimization procedure. Polycrystalline and piezocomposite properties are computed through a computational model based in the homogenization theory, which is implemented using the finite element method. Electrical resistance is used as the surrogate for the electrical machine connected to the harvesters. The design variables considered are the crystal orientation for single crystal materials, microstructural orientation distribution of the grains for polycrystalline materials, the piezoceramic material volume fraction and piezopolymer orientation for piezocomposites and/or the circuit resistance. A simulated annealing algorithm based in Metropolis algorithm is used as the optimizer. Several examples are presented and discussed considering excitations near as well as far away from resonance frequency. Harvesters with material composites having optimal material configurations that deliver enhanced electrical power have been identified.

Theoretical study on nonlinear magnetoelectric effect and harmonic distortion behavior in laminated composite

A theoretical model is established for nonlinear magnetoelectric (ME) effect and harmonic distortion behavior in laminated composite, in which the complex nonlinear mechanical-thermo-magnetic characteristics of magnetostrictive phase are taken into consideration. Both the low-frequency and the resonant ME effects are derived by the elastic mechanics method. In this model, the output ME voltage is divided into three parts: a dc term, a linear ac term and a nonlinear ac term. Considering the temperature effect, this model is adopted to predict the dependences of ac voltages on bias magnetic field, frequency of ac magnetic field, the volume fraction of piezoelectric phase and interfacial parameter. Then, the competition relationship between linear and nonlinear ac voltages is discussed. To clearly describe the nonlinear characteristics of the proposed sample, a distortion factor θ is used for characterizing the harmonic distortion behaviors. The dependences of θ on the frequency of ac magnetic field and temperature under different ac magnetic fields are also studied. Finally, the predictions of harmonic distortion behaviors with changing bias magnetic field are obtained. The calculated linear ME coefficient shows a good agreement with the previous experimental data. It showed that: linear ac voltage and linear piezomagnetic coefficient present the same trend as the bias magnetic field increases, and nonlinear ac voltage shows the same trend as the absolute value of nonlinear piezomagnetic coefficient with increasing bias magnetic field; with temperature increasing, the output ME voltages decrease; operating temperature has a minimal effect on the required magnetic field corresponding to the optimal value of the output ME voltages, while it cannot alter the optimal value of piezoelectric phase's volume fraction; the nonlinear ac voltage presents more resonant frequencies than the linear one in the same range. Also, a definite multiple relationship is observed between the corresponding resonant frequencies of linear and nonlinear voltages; a larger θ leads to a more serious harmonic distortion, which is influenced by the frequency of ac magnetic field and temperature; bias magnetic field can be applied to adjust the harmonic distortion behaviors.

Design, fabrication, and properties of 2-2 connectivity cement/polymer based piezoelectric composites with varied piezoelectric phase distribution.

The laminated 2-2 connectivity cement/polymer based piezoelectric composites with varied piezoelectric phase distribution were fabricated by employing Lead Zirconium Titanate ceramic as active phase, and mixture of cement powder, epoxy resin, and hardener as matrix phase with a mass proportion of 4:4:1. The dielectric, piezoelectric, and electromechanical coupling properties of the composites were studied. The composites with large total volume fraction of piezoelectric phase have large piezoelectric strain constant and relative permittivity, and the piezoelectric and dielectric properties of the composites are independent of the dimensional variations of the piezoelectric ceramic layer. The composites with small total volume fraction of piezoelectric phase have large piezoelectric voltage constant, but also large dielectric loss. The composite with gradually increased dimension of piezoelectric ceramic layer has the smallest dielectric loss, and that with the gradually increased dimension of matrix layer has the largest piezoelectric voltage constant. The novel piezoelectric composites show potential applications in fabricating ultrasonic transducers with varied surface vibration amplitude of the transducer.

Electro-elastic constants calculation of active piezoelectric damping composites by finite element method

Currently, the active piezoelectric damping composites (APDC) with obliquely embedded piezoelectric rods have been considered as an effective means for controlling vibration and noise. How to model the unit cell of APDC with orientation angle between 0° and 90° that meets the theoretical restrictions and assumptions using finite element method (FEM) is a difficult problem that needs to be solved. In this paper, an alternative method to model the unit cell of APDC is proposed to overcome that difficulty. The effects of the orientation angle and the volume fraction of piezoelectric phase on the studied constants [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], e33, e34 and the electromechanical coupling coefficients are analyzed and some special and useful conclusions are summarized. The simulation results show good agreement with the theoretical and experimental results, which confirms the validity of the proposed alternative finite element method in modeling and analyzing the APDC.

Elastomechanical Study of Magnetoeletric Coupling in Bilayer of Lithium Zinc Ferrite and Lead Zirconate Titanate

A theoretical model based on the constitutive equations of piezoelectrics and magnetostrictor is introduced to discuss the magnetoelectric (ME) coupling in freebody bilayer containing magnetostrictive and piezoelectric phases. The ME coupling at low frequency of Ni0.8Zn0.2Fe2O4–PZT bilayer have been studied by using the model and the corresponding material parameters of individual phases. The results show that the ME voltage coefficients can increase to a maximum at a given volume fraction of piezoelectric phase. An approximately linear increase of the maximum has been obtained with strengthening interface coupling. Analysis shows that large magnetostriction, appropriate volume fraction and ideal interface coupling are key ingredients for obtaining excellent ME performance.

Analysis of a dielectric crack in a magnetoelectroelastic layer

Within the theory of linear magnetoelectroelasticity, the fracture analysis of a magneto-electrically dielectric Griffith crack embedded in a magnetoelectroelastic layer is investigated under in-plane magneto-electro-mechanical loadings. The semi-permeable crack-face magnetoelectric boundary conditions are utilized to simulate the case of an opening dielectric crack. Applying the Fourier transform technique, the boundary-value problem is reduced to solving three coupling singular integral equations. Field intensity factors of stress, electric displacement, magnetic induction and crack opening displacement (COD) are further determined by the Lobatto-Chebyshev collocation method. The electric displacement and magnetic induction of crack interior are discussed in detail. The obtained results reveal that the magnetoelectric field inside the crack is dependent on the material properties, applied loadings, the dielectric permeability of crack interior, and the ratio of the crack length and the layer width. Numerical computations are carried out to present that the volume fraction of piezoelectric phase in BaTiO 3 – CoFe 2 O 4 composites has great influences on the magnetoelectric field inside the dielectric crack. Based on the COD intensity factor, the analysis for the growth of a dielectric crack in a magnetoelectroelastic layer is examined. The proposed procedure can be reduced to dealing with the case of a dielectric crack in a piezoelectric layer and the obtained results can be verified by the experimental observations.

The theoretical model of 1-3-2 piezocomposites

A theoretical model is proposed to calculate the equivalent model the electromechanical properties of (1-3-2) piezocomposite. Piezoelectric equations of state were derived in terms of equivalent parameters based on linear electromechanical response and uniform field theories. Equivalent parameters (g31, g33, beta33, d31, d33, epsilon33) of 1-3-2 piezocomposite were obtained. The computed g31 is -19.9 x 10(-3) V x m/N(-1), g33 is 68.4 x 10(-3) V x m/N(-1), d31 is -98 x 10(-12) C/N, d33 is 336 x 10(-12) C/N, and epsilonT33/epsilon0 is 555, while the volume fraction of piezoelectric phase nu1 is 0.4 and nu2 is 0.1. The variation of composite properties with volume fraction of piezoelectric phase have been modeled and experimentally verified. The computed d31, d33, and epsilon33 are within 12.5, 6.7, and 8.4% of experimental values, respectively.

Elastomechanical study of interface coupling in magnetoelectric bilayers

A theoretical model is introduced to derive the ME voltage coefficients of bilayer in free state according to the constitutive equations of magnetostrictive and piezoelectric phases. Using this model, the ME voltage coefficients of La07Sr03MnO3(LSMO)-PZT and Tb1-xDyxFe2-y (TDF)-PZT bilayers have been calculated and analyzed using the corresponding material parameters of individual phases. The results show that the ME voltage coefficient increases to a maximum at a given volume fraction of piezoelectric phase. With increasing interface coupling parameter k, an approximately linear increase of the maximum ME voltage coefficient have been observed. The maximum ME voltage coefficient for TDF-PZT bilayer reaches 19Vcm-1Oe-1, while for LSMO-PZT bilayer, the maximum value is only 165mVcm-1Oe-1. The theoretical results of ME voltage coefficients versus bias magnetic field for LSMO-PZT bilayer have been found to agree well with the measured data when k=02. Analysis shows that large magnetostriction, appropriate volume fraction and adequate interface coupling are key facters for obtaining excellent ME performance.

Theoretical modelling of a conducting crack in a magnetoelectroelastic solid

A theoretical study of a magnetoelectroelastic composite plane with a single conducting crack is presented. Crack is assumed to be arbitrarily oriented with respect to the poling direction of the medium. General solutions for fully coupled magnetoelectroelasticity expressed in term of complex potential functions are used to formulate the problem. The formulation of a conducting crack is reduced to a classical Riemann-Hilbert problem and explicit analytical solutions are derived for the field intensity factors, total and mechanical energy release rates and crack tip hoop stress. The formulation is then extended to obtain common fracture parameters of an arbitrarily oriented permeable crack. Selected numerical results are presented for a conducting and a permeable crack in magnetoelectroelastic composite BaTiO3-CoFe2O4. It is found that crack orientation, volume fraction of piezoelectric phase and magnitude of electro-magnetic and mechanical loading have a significant influence on fracture parameters.