Theoretical study on dynamic effective electroelastic properties of random piezoelectric composites with aligned inhomogeneities

The closed-form solutions of the dynamic problem of heterogeneous piezoelectric materials are formulated by introducing polarizations into a reference medium and using the generalized reciprocity theorem.These solutions can be reduced to the ones of an elastodynamic problem.Based on the effective medium method,these closedform solutions can be used to establish the self-consistent equations about the frequencydependent effective parameters,which can be numerically solved by iteration.Theoretical predictions are compared with the experimental results,and good agreement can be found.Furthermore,the analyses on the effects of microstructure and wavelength on the effective properties,resonance frequencies,and attenuation are also presented,which may provide some guidance for the microstructure design and analysis of piezoelectric composites.

Test on Sensor Effect of Cement Matrix Piezoelectric Composite

A novel cement matrix smart piezoelectric composite and its application as sensing element are presented.A cement matrix smart piezoelectric composite piece encapsulated in a cement mortar formed a practical sensor, and it was tested on material test system with cyclic loading.According to the theoretical analysis, the function of the cement matrix piezoelectric sensor output voltage was expressed in terms of the magnitude of the input cyclic loading amplitude and frequency.The curve fitting of gain function that is defined as sensor′s gain factor under different frequencies of input loading was carried out. From the results of curve fitting, it is found that the cement matrix smart piezoelectric composite has a simple relationship between input loading and output voltage.Therefore the cement matrix piezoelectric composite sensor is suitable to be applied in structural health monitoring.

Preparation and Electromechanical Properties of PVDF Matrix Piezoelectric Composites Containing Highly Oriented BaTiO_3 Whiskers

The piezoelectric composites containing highly oriented BaTiO3 whiskers as active phase and PVDF as matrix have been prepared by micro-hole extrusion and orientation in carried fibers. The morphology of oriented BaTiO3 whiskers and microstructure of the composites were observed by SEM. As for its electromechanical properties, it is found that the dielectric constant, piezoelectric constant and remnant of polarization in the BaTiO3 whisker-PVDF composite are considerably higher than that in the BaTiO3 powders-PVDF composite, while the loss factors follow the opposite trend. For the BaTiO3 whisker-PVDF composite, the values of ε, d33 and Pr parallel to the whisker orientation (normal specimen) are much higher than that perpendicular to the whisker orientation (parallel specimen). The significant effects of the connective passages of active phase on electromechanical properties of the piezoelectric composites has also been investigated.

Effective property of piezoelectric composites containing coated nano-elliptical fibers with interfacial debonding

Based on both the spring layer interface model and the Gurtin-Murdoch surface/interface model,the anti-plane shear problem is studied for piezoelectric composites containing coated nano-elliptical fibers with imperfect interfaces.By using the complex function method and the technique of conformal mapping,the exact solutions of the electroelastic fields in fiber,coating,and matrix of piezoelectric nanocomposites are derived under far-field anti-plane mechanical and in-plane electrical loads.Furthermore,the generalized self-consistent method is used to accurately predict the effective electroelastic moduli of the piezoelectric nanocomposites containing coated nano-elliptical fibers with imperfect interfaces.Numerical examples are illustrated to show the effects of the material constants of the imperfect interface layers,the aspect ratio of the fiber section,and the fiber volume fraction on the effective electroelastic moduli of the piezoelectric nanocomposites.The results indicate that the effective electroelastic moduli of the piezoelectric nanocomposites can be significantly reduced by the interfacial debonding,but it can be improved by the surface/interface stresses at the small scale,which provides important theoretical reference for the design and optimization of piezoelectric nanodevices and nanostructures.

The Role of PZT in Flexible 1-3 Piezoelectric Composite for Smart Structure

Piezoelectric composite materials have the ability to perform both sensing and actuating functions.It is a viable candidate for smart actuation in underwater noise controlling with its higher coupling factor and lower acoustic impedance, when the piezoelectric rods are inclined to control its both the shear and the compression damping characteristics.In this paper, a simple physical model of 1-3 piezoelectric composite is advanced for maximizing the electromechanical coupling factor,the acoustic impedance,and the hydrophone figure of merit.

Tunable Band Gap in Piezoelectric Composite Rod Based on the Inter-Coupling Effect

The longitudinal wave propagating in one-dimensional periodic piezoelectric composite rod with inter-coupling between different piezoelectric segments is investigated. The analytical formulae for such a structure are shown and the dispersion relation is calculated. The results show that, by introducing the inter-coupling between the different piezoelectric segments, which is accomplished by serially connecting every n piezoelectric segment into supercells, some tunable Bragg band gaps can accordingly be opened in the low frequency region. The investigation could provide a new guideline for the tunable phononic crystal under passive control.

Parity-time symmetric acoustic system constructed by piezoelectric composite plates with active external circuits

Researches on parity-time(PT)symmetry in acoustic field can provide an efficient platform for controlling the travelling acoustic waves with balanced loss and gain.Here,we report a feasible design of PT-symmetric system constructed by piezoelectric composite plates with two different active external circuits.By judiciously adjusting the resistances and inductances in the external circuits,we obtain the exceptional point due to the spontaneous breaking of PT symmetry at the desired frequencies and can observe the unidirectional invisibility.Moreover,the system can be at PT exact phase or broken phase at the same frequency in the same structure by merely adjusting the external circuits,which represents the active control that makes the acoustic manipulation more convenient.Our study may provide a feasible way for manipulating acoustic waves and inspire the application of piezoelectric composite materials in acoustic structures.

Elastic properties of spherically anisotropic piezoelectric composites

Effective elastic properties of spherically anisotropic piezoelectric composites, whose spherically anisotropic piezoelectric inclusions are embedded in an infinite non-piezoelectric matrix, are theoretically investigated. Analytical solu- tions for the elastic displacements and the electric potentials under a uniform external strain are derived exactly. Taking into account of the coupling effects of elasticity, permittivity and piezoelectricity, the formula is derived for estimating the effective elastic properties based on the average field theory in the dilute limit. An elastic response mechanism is revealed, in which the effective elastic properties increase as inclusion piezoelectric properties increase and inclusion dielectric properties decrease. Moreover, a piezoelectric response mechanism, of which the effective piezoelectric response vanishes due to the symmetry of spherically anisotropic composite, is also disclosed.

Nonlinear analysis on electrical properties in a bended composite piezoelectric semiconductor beam

In this paper,the interactions between the transverse loads and the electrical field quantities are investigated based on the nonlinear constitutive relation.By considering a composite beam consisting of a piezoelectric semiconductor and elastic layers,the nonlinear model is established based on the phenomenological theory and Euler’s beam theory.Furthermore,an iteration procedure based on the differential quadrature method(DQM)is developed to solve the nonlinear governing equations.Before analysis,the convergence and correctness are surveyed.It is found that the convergence of the proposed iteration is fast.Then,the transverse pressure induced electrical field quantities are investigated in detail.From the calculated results,it can be found that the consideration of nonlinear constitutive relation is necessary for a beam undergoing a large load.Compared with the linear results,the consideration of the nonlinear constitutive relation breaks the symmetry for the electric potential,the electric field,and the perturbation carrier density,and has little influence on the electric displacement.Furthermore,the non-uniform pressures are considered.The results show that the distributions of the electric field quantities are sensitively altered.It indicates that the electrical properties can be manipulated with the design of different transverse loads.The conclusions in this paper could be the guidance on designing and manufacturing electronic devices accurately.

Porous, multi-layered piezoelectric composites based on highly oriented PZT/PVDF electrospinning fibers for high-performance piezoelectric nanogenerators

Piezoelectric nanogenerators(PENGs)that can harvest mechanical energy from ambient environment have broad prospects for multi-functional applications.Here,multi-layered piezoelectric composites with a porous structure based on highly oriented Pb(Zr_(0.52)Ti_(0.48))O_(3)/PVDF(PZT/PVDF)electrospinning fibers are prepared via a laminating method to construct high-performance PENGs.PZT particles as piezoelectric reinforcing phases are embedded in PVDF fibers and facilitate the formation of polarβphase in PVDF.The multi-layered,porous structure effectively promotes the overall polarization and surface bound charge density,resulting in a highly efficient electromechanical conversion.The PENG based on 10 wt%PZT/PVDF composite fibers with a 220µm film thickness outputs an optimal voltage of 62.0 V and a power of 136.9μW,which are 3.4 and 6.5 times those of 10 wt%PZT/PVDF casting film-based PENG,respectively.Importantly,the PENG shows a high sensitivity of 12.4 V·N^(−1),presenting a significant advantage in comparison to PENGs with other porous structures.In addition,the composites show excellent flexibility with a Young’s modulus of 227.2 MPa and an elongation of 262.3%.This study shows a great potential application of piezoelectric fiber composites in flexible energy harvesting devices.

Effective properties of coated fibrous piezoelectric composites with spring-type interfaces under anti-plane mechanical and in-plane electrical loads

In this paper,we investigate the effective properties of three-phase(matrix/coating/fiber)cylindrical piezoelectric composites with imperfect interfaces under anti-plane mechanical and in-plane electrical loads.By using the electromechanically coupling spring-type interface model and the generalized self-consistent method(GSM),we analytically derived the effective electroelastic moduli.The present solutions include as special cases the three-phase cylindrical piezoelectric composites with perfect interfaces as well as the two-phase(matrix/fiber)case with imperfect or perfect interfaces.Selected calculations are graphically shown to demonstrate dependence of the effective moduli on the interfacial properties.The particular size-dependent characteristic due to the interfacial imperfection is also discussed.

Dielectric and Piezoelectric Properties of 0-3 PZT/PVDF Composite Doped with Polyaniline

Lead zirconate titanate （ PZT ） / polyvinylidene fluoride （PVDF） 0-3 piezoelectric composites doped with polyaniline （PANI） were obtained by hot-press method. The polarization properties of the composites were characterized by XRD and P- E hysteresis loops at room temperature. And the dielectric and piezoelectric properties were also measured. The results show that the poling of PZT could be effectively carried oat and the dielectric constant e, and dissipation tanδ increase monatonously by increasing the volume fraction of PANI in the composite. The piezoelectric constant d33, and the planar electromechanical coupling factor kp increase while the mechanical quality factor Qm decreases with the increase in the content of PANI. The d33, kp and Qm show the extremum values at 8 vol%-10 vol% PANI.

Fabrication and Performances of 1-3-2 Piezoelectric Ceramic/Polymer Composite

A novel 1-3-2 piezoelectric composite has been developed,which consists of piezoelectric ceramic plate and 1-3 piezoelectric composite.The composite was fabricated by dicing PZT ceramic along mutual perpendicular two directions and then filling epoxy into grooves.The piezoelectric and electromechanical properties of the novel composite were determined. The results show a coefficient d_ (33) of 405pC/N,a vibration displacement of 113.5pm,an acoustic impendence of 13.3 Mraly, a bandwidth of 12kHz and a thickness electromechanical coupling coefficient of 0.56.

THE EFFECTIVE PROPERTIES OF PIEZOELECTRIC COMPOSITE MATERIALS WITH TRANSVERSELY ISOTROPIC SPHERICAL INCLUSIONS

The effective properties of piezoelectric composite materials are very important in engineering. In this paper, the closed_form solutions of the constraint_strain and the constraint_electric_field of a transversely isotropic spherical inclusion in an infinite non_piezoelectric matrix are obtained. The dilute solutions of piezoelectric composite materials with transversely isotropic spherical inclusions are also given. The solutions in the paper can be readily utilized in analysis and design of piezoelectric composite materials or smart materials and smart structures.

Numerical Investigation of Ultrasonic Guided Wave Dynamics in Piezoelectric Composite Plates for Establishing Structural Self-Sensing

This article presents a numerical investigation of guided wave generation, propagation, interaction with damage, and reception in piezoelectric composite plates for the purpose of establishing structural self-awareness.This approach employs piezoelectric composite materials as both load bearing structure and sensing elements.Finite element modal analysis of a plate cell with Bloch-Floquet boundary condition(BFBC) is performed to understand the wave propagation characteristics in piezoelectric composite plates. A comparative study is carried out between a standard composite plate and a piezoelectric composite plate to highlight the influence of piezoelectricity on guided wave dispersion relations. Subsequently, a transient dynamic coupled-field finite element model is constructed to simulate the procedure of guided wave generation, propagation, interaction with damage, and reception in a piezoelectric composite plate. Active sensing array is designed to capture the structural response containing the damage information. Three engineering scenarios, including a pristine case, a one-damage-location case and a two-damage-location case, are considered to demonstrate the ultrasonic sensing capability of the piezoelectric composite system. Finally, time-reversal method is utilized to locate and image the damage zones. This research shows that piezoelectric composite material possesses great potential to establish structural self-awareness, if it serves both as the load bearing and structural sensing components.

Variational bounds of the effective moduli of piezoelectric composites

The classical Hashin-Shtrikman variational principle was re-generalized to the heterogeneous piezoelectric materials.The auxiliary problem is very much simplified by selecting the reference medium as a linearly isotropic elastic medium.The electromechanical fields in the inhomogeneous piezoelectrics are simulated by introducing into the homogeneous reference medium certain eigenstresses and eigen electric fields.A closed-form solution can be obtained for the disturbance fields,which is convenient for the manipulation of the energy functional.As an application,a two-phase piezoelectric composite with nonpiezoelectric matrix is considered.Expressions of upper and lower bounds for the overall electromechanical moduli of the composite can be developed.These bounds are shown better than the Voigt-Reuss type ones.

The Ritz-Sublaminate Generalized Unified Formulation approach for piezoelectric composite plates

This paper extends to composite plates including piezoelectric plies the variable kinematics plate modeling approach called Sublaminate Generalized Unified Formulation(SGUF).Two-dimensional plate equations are obtained upon defining a priori the through-thickness distribution of the displacement field and electric potential.According to SGUF,independent approximations can be adopted for the four components of these generalized displacements:an Equivalent Single Layer(ESL)or Layer-Wise(LW)description over an arbitrary group of plies constituting the composite plate(the sublaminate)and the polynomial order employed in each sublaminate.The solution of the two-dimensional equations is sought in weak form by means of a Ritz method.In this work,boundary functions are used in conjunction with the domain approximation expressed by an orthogonal basis spanned by Legendre polynomials.The proposed computational tool is capable to represent electroded surfaces with equipotentiality conditions.Free-vibration problems as well as static problems involving actuator and sensor configurations are addressed.Two case studies are presented,which demonstrate the high accuracy of the proposed Ritz-SGUF approach.A model assessment is proposed for showcasing to which extent the SGUF approach allows a reduction of the number of unknowns with a controlled impact on the accuracy of the result.

WAVE PROPAGATION IN PIEZOELECTRIC/PIEZOMAGNETIC LAYERED PERIODIC COMPOSITES

This paper is concerned with the dynamic behaviors of wave propagation in layered periodic composites consisting of piezoelectric and piezomagnetic phases. The dispersion relations of Lamb waves axe derived. Dispersion curves and displacement fields are calculated with different piezoelectric volume fractions. Numerical results for BaTiO3/CoFe2O4 composites show that the dispersion curves resemble the symmetric Lamb waves in a plate. Exchange between the longitudinal （i.e. thickness） mode and coupled mode takes place at the crossover point between dispersion curves of the first two branches. With the increase of BaTiO3 volume fraction, the crossover point appears at a lower wave number and wave velocity is higher. These findings are useful for magnetoelectric transducer applications.

A refined finite element method for bending analysis of laminated plates integrated with piezoelectric fiber-reinforced composite actuators

This research presents a finite element formulation based on four-variable refined plate theory for bending analysis of cross-ply and angle-ply laminated composite plates integrated with a piezoelectric fiber-reinforced composite actuator under electromechanical loading. The four-variable refined plate theory is a simple and efficient higher-order shear deformation theory, which predicts parabolic variation of transverse shear stresses across the plate thickness and satisfies zero traction conditions on the plate free surfaces. The weak form of governing equations is derived using the principle of minimum potential energy, and a 4-node non-conforming rectangular plate element with 8 degrees of freedom per node is introduced for discretizing the domain. Several benchmark problems are solved by the developed MATLAB code and the obtained results are compared with those from exact and other numerical solutions, showing good agreement.

Double Hopf bifurcation of composite laminated piezoelectric plate subjected to external and internal excitations

The double Hopf bifurcation of a composite laminated piezoelectric plate with combined external and internal excitations is studied. Using a multiple scale method, the average equations are obtained in two coordinates. The bifurcation response equations of the composite laminated piezoelectric plate with the primary parameter resonance, i.e., 1：3 internal resonance, are achieved. Then, the bifurcation feature of bifurcation equations is considered using the singularity theory. A bifurcation diagram is obtained on the parameter plane. Different steady state solutions of the average equations are analyzed. By numerical simulation, periodic vibration and quasi-periodic vibration responses of the Composite laminated piezoelectric plate are obtained.