Effective elastic properties of piezoelectric composites with radially polarized cylinders

Effective elastic properties of piezoelectric composites containing an infinitely long, radially polarized cylinder embedded in an isotropic non-piezoelectric matrix are theoretically investigated under an external strain field. Analytical solutions of elastic displacement and electric potentials are exactly derived, and the effective elastic responses are formulated in the dilute limit. Meanwhile, a vanishing piezoelectric response mechanism is revealed in the piezoelectric composite containing radially polarized cylinders. Furthermore, it is shown that the effective elastic properties can be enhanced (or reduced) due to the increase of the piezoelectric (or dielectric) constants of the cylinders.     

Receiving sensitivity and transmitting voltage response of a fluid loaded spherical piezoelectric transducer with an elastic coating

A method is presented to determine the response of a spherical acoustic transducer that consists of a fluid-filled piezoelectric sphere with an elastic coating embedded in infinite fluid to electrical and plane-wave acoustic excitations. The exact spherically symmetric, linear, differential, governing equations are used for the interior and exterior fluids, and elastic and piezoelectric materials. Under acoustic excitation and open circuit boundary condition, the equation governing the piezoelectric sphere is homogeneous and the solution is expressed in terms of Bessel functions. Under electrical excitation, the equation governing the piezoelectric sphere is inhomogeneous and the complementary solution is expressed in terms of Bessel functions and the particular integral is expressed in terms of a power series. Numerical results are presented to illustrate the effect of dimensions of the piezoelectric sphere, fluid loading, elastic coating and internal material losses on the open-circuit receiving sensitivity and transmitting voltage response of the transducer.     

Electromechanical response of 2-2 layered piezoelectric composites: A micromechanical model based on the asymptotic homogenization method

A micromechanical model based on the asymptotic homogenization technique has been developed to predict the complete elastic, dielectric and piezoelectric properties of a general 2-2 layered piezoelectric composite where the constituent phases are elastically anisotropic and piezoelectrically active. Two classes of layered piezoelectric composites (i.e. longitudinally and transversely layered) are considered in two widely different ceramic- and polymer-based systems and their effective properties are obtained in the limits of both large-volume (i.e. bulk) and small-volume (i.e. thin-film) systems. It is demonstrated that: (i) in the bulk, ceramic–ceramic layered composite system, the elastic, piezoelectric, and dielectric properties of the composites vary linearly with volume fraction of the second phase, while in the bulk ceramic–polymer layered composite system, the corresponding properties vary non-linearly with volume fraction of the second phase; (ii) in the prismatic (thin-film) layered piezoelectric composite system, the non-vanishing, effective elastic, piezoelectric and dielectric properties vary linearly with the volume fraction of the second phase for both the longitudinally and transversely layered composite structures in the ceramic–ceramic and the ceramic–polymer composite systems; (iii) the ceramic–polymer piezoelectric layered composites that incorporate a low density polymeric phase with lower acoustic impedance generally exhibit enhanced piezoelectric coupling constants and lowered acoustic impedance; (iv) the longitudinally layered composites exhibit higher piezoelectric coupling constants and lower acoustic impedance compared to that of the transversely layered composites; and (v) the best combination of properties for applications such as hydrophones (i.e. the highest piezoelectric coupling constants and the lowest acoustic impedance) is obtained in the ceramic–polymer, longitudinally layered, thin-film, piezoelectric composites.     

Isotropic and anisotropic physical properties of quasicrystals

Since quasicrystals have positional and orientational long-range order, they are essentially anisotropic. However, the researches show that some physical properties of quasicrystals are isotropic. On the other hand, quasicrystals have additional phason degrees of freedom which can influence on their physical behaviours. To reveal the quasicrystal anisotropy, we investigate the quasicrystal elasticity and other physical properties, such as thermal expansion, piezoelectric and piezoresistance, for which one must consider the contributions of the phason field. The results indicate that: for the elastic properties, within linear phonon domain all quasicrystals are isotropic, and within nonlinear phonon domain the planar quasicrystals are still isotropic but the icosahedral quasicrystals are anisotropic. Moreover, the nonlinear elastic properties due to the coupling between phonons and phasons may reveal the anisotropic structure of QCs. For the other physical properties all quasicrystals behave like isotropic media except for piezoresistance properties of icosahedral quasicrystals due to the phason field.     

A unified optical theorem for scalar and vectorial wave fields

The generalized optical theorem is an integral relation for the angle-dependent scattering amplitude of an inhomogeneous scattering object embedded in a homogeneous background. It has been derived separately for several scalar and vectorial wave phenomena. Here a unified optical theorem is derived that encompasses the separate versions for scalar and vectorial waves. Moreover, this unified theorem also holds for scattering by anisotropic elastic and piezoelectric scatterers as well as bianisotropic (non-reciprocal) EM scatterers.     

Effective Anisotropic Dielectric Properties of Crystal Composites

Transformation fieM method （TFM） is developed to estimate the anisotropic dielectric properties of crystal composites having arbitrary shapes and dielectric properties of crystal inclusions, whose principal dielectric axis are different from those of anisotropic crystal matrix. The complicated boundary-value problem caused by inclusion shapes is circumvented by introducing a transformation electric field into the crystal composites regions, and the effective anisotropic dielectric responses are formulated in terms of the transformation field. Furthermore, the numerical results show that the effective anisotropie dielectric responses of crystal composites periodically vary as a function of the rotating angle between the principal dielectric axes of inclusion and matrix crystal materials. It is found that at larger inclusion volume fraction the inclusion shapes induce profound effect on the effective anisotropic dielectric responses.     

Singular variation property of elastic constants of piezoelectric ceramics shunted to negative capacitance

Piezoelectric shunt damping has been widely used in vibration suppression, sound absorption, noise elimination, etc.In such applications, the variant elastic constants of piezoelectric materials are the essential parameters that determine the performances of the systems, when piezoelectric materials are shunted to normal electrical elements, i.e., resistance,inductance and capacitance, as well as their combinations. In recent years, many researches have demonstrated that the wideband sound absorption or vibration suppression can be realized with piezoelectric materials shunted to negative capacitance. However, most systems using the negative-capacitance shunt circuits show their instabilities in the optimal condition, which are essentially caused by the singular variation properties of elastic constants of piezoelectric materials when shunted to negative capacitance. This paper aims at investigating the effects of negative-capacitance shunt circuits on elastic constants of a piezoelectric ceramic plate through theoretical analyses and experiments, which gives an rational explanation for why negative capacitance shunt circuit is prone to make structure instable. First, the relationships between the elastic constants c_(11), c_(33), c_(55) of the piezoelectric ceramic and the shunt negative capacitance are derived with the piezoelectric constitutive law theoretically. Then, an experimental setup is established to verify the theoretical results through observing the change of elastic constant c_(55) of the shunted piezoelectric plate with the variation of negative capacitance.The experimental results are in good agreement with the theoretical analyses, which reveals that the instability of the shunt damping system is essentially caused by the singular variation property of the elastic constants of piezoelectric material shunted to negative capacitance.     

Stretchable electromagnetic interference shielding and antenna for wireless strain sensing by anisotropic micron-steel-wire based conductive elastomers

We prepare stretchable elastic electromagnetic interference(EMI) shielding and stretchable antenna for wireless strain sensing using an elastic composite comprising commercial steel wool as a conducting element. The prepared elastic conductor shows anisotropic electrical properties in response to the external force. In the stretchable range, the electrical resistance abnormally decreases with the increase of tensile deformation. The EMI shielding effectiveness of the elastic conductor can reach above-30 d B under 80% tensile strain. The resonance frequency of the dipole antenna prepared by the elastic conductor is linearly correlated with the tensile strain, which can be used as a wireless strain sensor. The transmission efficiency is stable at about-15 d B when stretched to 50% strain, with attenuation less than 5%. The current research provides an effective solution for stretchable EMI shielding and wireless strain sensing integrated with signal transmission by an antenna.     

Elasticity and inelasticity of the SiC/Al-13Si-9Mg biomorphic metal ceramics

The acoustic investigations of the elastic (Young’s modulus) and microplastic properties of a composite material, the SiC/Al-13Si-9Mg biomorphic metal ceramic, were performed. The ceramic was prepared by infiltration of the Al-13Si-9Mg melt into porous silicon carbide derived from wood of two species of trees, beech and sapele. The measurements were performed with a composite piezoelectric vibrator under resonance conditions, with rod-shaped samples vibrated longitudinally at about 100 kHz over a wide range of vibrational strain amplitudes, which included both the linear (amplitude-independent) and nonlinear (microplastic) regions. It was shown that the Young’s modulus and the microplastic properties of the composite are anisotropic and depend substantially on the tree species, particularly when longitudinal vibrations are excited in samples cut along the tree fibers.     

FREE VIBRATIONS OF SIMPLY SUPPORTED AND MULTILAYERED MAGNETO-ELECTRO-ELASTIC PLATES

Analytical solutions are derived for free vibrations of three-dimensional, linear anisotropic, magneto-electro-elastic, and multilayered rectangular plates under simply supported edge conditions. For any homogeneous layer, we construct the general solution in terms of a simple formalism that resembles the Stroh formalism, from which any physical quantities can be solved for given boundary conditions. In particular, the dispersion equation that characterizes the relationship between the natural frequency and wavenumber can be obtained in a simple form. For multilayered plates, we derive the dispersion relation in terms of the propagator matrices. The present solution includes all previous solutions, such as piezoelectric, piezomagnetic, and purely elastic solutions as special cases, and can serve as benchmarks to various thick plate theories and numerical methods used for the modelling of layered composite structures. Typical natural frequencies and mode shapes are presented for sandwich piezoelectric/piezomagnetic plates. It is shown clearly that some of the modes are purely elastic while others are fully coupled with piezoelectric/piezomagnetic quantities, with the latter depending strongly upon the material property and stacking sequence. These frequency and mode shape features could be of particular interest to the analysis and design of various “smart” sensors/actuators constructed from magneto-electro-elastic composite laminates.     

Relation between the electric response and the characteristics of elastic waves under shock excitation of heterogeneous dielectric materials with piezoelectric inclusions

A physicomathematical model is proposed for the electric response to elastic shock excitation of piezo-containing heterogeneous materials. The parameters of the electric signal under a pulsed action on a dielectric sample containing a piezoelectric inclusion are calculated theoretically using the apparatus of the mechanics of continuous media, and the conformity to experimental results is observed.     

Study on the reflectivity properties of spherically bent analyser crystals

Theoretical and experimental studies are presented on properties of spherically bent analyser crystals for high‐resolution X‐ray spectrometry. A correction to the bent‐crystal strain field owing to its finite surface area is derived. The results are used to explain the reflectivity curves and anisotropic properties of Si(660) and Si(553) analysers in near‐backscattering geometry. The results from the calculation agree very well with experimental results obtained using an inelastic X‐ray scattering synchrotron beamline.     

Simulation of elastic wave propagation in cylindrical structures including excitation by piezoelectric transducers

The development and optimization of non-destructive testing procedures usually needs experimental data. As experiments are time-consuming and expensive to conduct, we would like to use numerical data instead. This is admissible, if the simulation describes the physical experiments accurately. A three-dimensional displacement-stress finite-difference model is presented for a piezoelectric transducer coupled to an anisotropic tube. The allocation of the displacement and stress components on a staggered grid leads to a stable scheme. A full piezoelectric model of the transducer is used, including transverse isotropy in the elastic, dielectric, and piezoelectric constants. Similar to an experiment, elastic waves are excited in the corresponding simulation by applying a voltage signal to the electrodes of the piezoelectric transducer. Predictions of the simulation model for a piezoelectric ring transducer coupled to a carbon-fibre-reinforced shell are compared to experimental results to test the validity of the numerical data.     

Orientational contribution to the piezoelectric constants of BaTiO3 ceramic in ferroelectric phases with various symmetries

A self-consistent method based on the interaction of a piezoelectric sphere with a piezoelectric medium that has anisotropic elastic and dielectric properties is used to calculate the components of the tensor piezoelectric modulus of BaTiO₃ ceramic in all three ferroelectric modifications. A comparison of the calculated and measured piezoelectric moduli shows that at least 60–70% of the piezoelectric effect in BaTiO₃ ceramic is caused by domain boundary movement throughout the entire ferroelectric region. Fiz. Tverd. Tela (St. Petersburg) 41, 1080–1083 (June 1999)     

Prediction of the properties of two-phase composites with a piezoactive component

The effective dielectric, piezoelectric, and elastic constants of two-phase macroscopically piezoactive 3-0 and 3-3 composites are calculated. It is assumed that one of the components is a polarized ferroelectric ceramic material and the other is an inactive material with variable elastic properties. The limiting case when the elastic compliances of the inactive material tend to infinity (porous ferroelectric ceramics) is considered. The adequacy of this model to production technologies of piezoelectric composites is discussed. Computational results are compared with experimental data.     

A Piezoelectric Screw Dislocation Interacting with an Elliptical Piezoelectric Inhomogeneity Containing a Confocal Elliptical Rigid Core

The electro-elastic interaction between a piezoelectric screw dislocation and an elliptical piezoelectric inhomogeneity, which contains an electrically conductive confocal elliptical rigid core under remote anti-plane shear stresses and in-plane electrical load is dealt with. The analytical solutions to the elastic field and the electric field, the interfacial stress fields of inhomogeneity and matrix under longitudinal shear and the image force acting on the dislocation are derived by means of complex method. The effect of material properties and geometric configurations of the rigid core on interfacial stresses generated by a remote uniform load, rigid core and material electroelastic properties on the image force is discussed.     

Two-dimensional shear waves scattering by a large rigidity strip with interface crack

A two-dimensional problem of shear horizontal (SH) waves scattering by a finite width planar elastic (piezoelectric) inclusion partially debonded from its surrounding elastic matrix is investigated using the effective boundary conditions and singular integral equations technique. The case of large rigidity inclusions with blunted tips is considered, in which the upper face of the inclusion is perfectly bonded to the matrix. The debonding region is modeled as interface crack with non-contacting faces. Using the Green theorem the mixed boundary value problem is reduced to a system of the hypersingular integral equations. Numerical results of the scattering fields characteristics are presented. The effects of incidence direction, various material parameters of the strip on the scattering field are discussed and phenomenon of the non-specular reflection of SH waves is considered. The accuracy of the numerical results is confirmed by the use of analytical approximate problem solution of high-frequency SH waves scattering on a finite hard/soft inclusion.     

Minimal Geometric Deformation: the inverse problem

In this paper we show that any static and spherically symmetric anisotropic solution of the Einstein field equations can be thought as a system sourced by certain deformed isotropic system in the context of Minimal Geometric Deformation-decoupling approach. To be more precise, we developed a mechanism to obtain an isotropic solution from any anisotropic solution of the Einstein field equations. As an example, we implement the method to obtain the sources of a simple static anisotropic and spherically symmetric traversable wormhole.     

Anisotropic fluid spheres in general relativity

A procedure is developed to find static solutions for anisotropic fluid spheres from known static solutions for perfect fluid spheres. The method is used to obtain four exact analytical solutions of Einstein’s equations for spherically symmetric self-gravitating distribution of anisotropic matter. The solutions are matched to the Schwarzschild exterior metric. The physical features of one of the solutions are briefly discussed. Many previously known perfect fluid solutions are derived as particular cases.     

An Analytical Method for Calculating P-SV Acoustical Field Excited by a Piezoelectric Strip with Finite Width and Thickness

A piezoelectric strip with finite width and thickness is placed on top of an isotropic elastic half-space. Acoustical field can be excited when a voltage is across the piezoelectric strip. An analytical method is presented to calculate the acoustical field by the dynamics characteristics of the piezoelectric strip. Considering the piezoelectric strip as an anisotropic material of the 6 mm-type crystal system, we study the two-dimensional P-SV acoustical fields inside the piezoelectric strip and the isotropic half-space. The displacement and stress distributions are analysed thoroughly. The effects of the width and thickness of the piezoelectric strip and other parameters on the acoustical field are also analysed.