Indentation behavior of a semi-infinite piezoelectric semiconductor under a rigid flat-ended cylindrical indenter

This paper theoretically studies the axisymmetric frictionless indentation of a transversely isotropic piezoelectric semiconductor(PSC)half-space subject to a rigid flatended cylindrical indenter.The contact area and other surface of the PSC half-space are assumed to be electrically insulating.By the Hankel integral transformation,the problem is reduced to the Fredholm integral equation of the second kind.This equation is solved numerically to obtain the indentation behaviors of the PSC half-space,mainly including the indentation force-depth relation and the electric potential-depth relation.The results show that the effect of the semiconductor property on the indentation responses is limited within a certain range of variation of the steady carrier concentration.The dependence of indentation behavior on material properties is also analyzed by two different kinds of PSCs.Finite element simulations are conducted to verify the results calculated by the integral equation technique,and good agreement is demonstrated.

Nonlinear free vibration of piezoelectric semiconductor doubly-curved shells based on nonlinear drift-diffusion model

In this paper, the nonlinear free vibration behaviors of the piezoelectric semiconductor(PS) doubly-curved shell resting on the Pasternak foundation are studied within the framework of the nonlinear drift-diffusion(NLDD) model and the first-order shear deformation theory. The nonlinear constitutive relations are presented, and the strain energy, kinetic energy, and virtual work of the PS doubly-curved shell are derived.Based on Hamilton's principle as well as the condition of charge continuity, the nonlinear governing equations are achieved, and then these equations are solved by means of an efficient iteration method. Several numerical examples are given to show the effect of the nonlinear drift current, elastic foundation parameters as well as geometric parameters on the nonlinear vibration frequency, and the damping characteristic of the PS doublycurved shell. The main innovations of the manuscript are that the difference between the linearized drift-diffusion(LDD) model and the NLDD model is revealed, and an effective method is proposed to select a proper initial electron concentration for the LDD model.

The mechanism to reform dynamic performance of an elastic wave-front in a piezoelectric semiconductor by the wave-carrier interaction induced from static biasing fields

The propagation of an elastic wave(EW)in a piezoelectric semiconductor(PSC)subjected to static biasing fields is investigated.It is found that there exist two coupling waves between electric field and charge carriers.One is stimulated by the action of the polarized electric field in the EW-front on charge carriers(EFC),and the other is stimulated by the action of initial electric field in biasing fields on dynamic carriers(IEC).Obviously,the latter is a man-made and tunable wave-carrier interaction.A careful study shows that IEC can play a leading role in remaking dynamic performance of the wave-front and an inter-medium role in transferring energy from biasing fields to EW-fronts.Hence,a method is proposed to reform the EW performance by biasing-fields:reforming the dispersivity of EW-fronts by promoting competition between IEC and EFC and inverting the dissipation by the IEC to transfer energy from biasing fields to EWfronts.The corresponding tuning laws on the phase-frequency characteristics of an EW show that the wave velocity can be regulated smaller than the pure EW velocity at a lowfrequency and larger than the pure piezoelectric wave velocity at a high-frequency.As for regulating the amplitude-frequency characteristics of the EW by the IEC,analyses show that EWs can obtain amplification only for those with relatively high vibration frequencies(small wave lengths).The studies will provide guidance for theoretical analysis of waves propagating in PSCs and practical application and design of piezotronic devices.

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.

PROPAGATION BEHAVIORS OF SHEAR HORIZONTAL WAVES IN PIEZOELECTRIC-PIEZOMAGNETIC PERIODICALLY LAYERED STRUCTURES

This paper investigates shear horizontal （SH） waves propagating in a periodically layered structure that consists of piezoelectric （PE） layers perfectly bonded with piezomagnetic （PM） layers alternately. The explicit dispersion relations are derived for the two cases when the propagation directions of SH waves are normal to the interface and parallel to the interface, respectively. The asymptotic expressions for dispersion relations are also given when the wave number is extremely small. Numerical results for stop band effect and phase velocity are presented for a periodic system of alternating BaTiO3 and Terfenol-D layers. The influence of volume fraction on stop band effect and dispersion behaviors is discussed and revealed.

Effects of electric/magnetic impact on the transient fracture of interface crack in piezoelectric-piezomagnetic sandwich structure: anti-plane case

Due to the incompatibility of the interlaminar deformations,the interface debonding or cracking usually happens in a layered magnetoelectric(ME)structure under an applied load.In this paper,the transient responses of the anti-plane interface cracks in piezoelectric(PE)-piezomagnetic(PM)sandwich structures are studied by the standard methods of the integral transform and singular integral equation.Discussion on the numerical examples indicates that the PE-PM-PE structure under electric impact is more likely to fracture than the PM-PE-PM structure under a magnetic impact.The dynamic stress intensity factors(DSIFs)are more sensitive to the variation of the active layer thickness.The effects of the material constants on the DSIFs are dependent on the roles played by PE and PM media during the deformation process.

A full-coupling model of PN junctions based on the global-domain carrier motions with inclusion of the two metal/semiconductor contacts at endpoints

A full-coupling model on the current-voltage(J-V)characteristics of PN junctions is put forward in the paper by taking into account both the whole junction and the two electrode regions consisting of metal/semiconductor(M/S)contacts.The depletion layer assumption proposed by the Shockley model is discarded.Gauss’law on the electric potential and the electric field is applied in the whole junction region such that the majority-carrier currents inside and outside the P/N barrier region are able to be exactly defined and clearly calculated.Then,the stable continuity equations of the electron and hole currents are established to show the current conversion between minority-and majority-carriers inside the whole PN junction region.By analyzing all the conversion procedure,the J-V characteristics of a PN junction are obtained with good agreement to the experimental results,which are closely dependent on the minority-carrier lifetime and doping concentrations.Obviously,the study on this topic possesses referential significance to mechanically tuning the performance of piezoelectric PN junctions and piezotronic devices.

Propagation of Rayleigh-type surface waves in a layered piezoelectric nanostructure with surface effects

This work investigates the dispersion properties of Rayleigh-type surface waves propagating in a layered piezoelectric nanostructure composed of a piezoelectric nanofilm over an elastic substrate.As one of the most important features of nanostructures,surface effects characterized by surface stresses and surface electric displacements are taken into account through the surface piezoelectricity theory and the nonclassical mechanical and electrical boundary conditions.Concrete expressions of the dispersion equation are derived,and numerical results are provided to examine the effects of several surface-related parameters,including the surface elasticity,surface piezoelectricity,surface dielectricity,surface density,as well as surface residual stress,on the dispersion modes and phase velocity.The size-dependent dispersion behaviors occurring with surface effects are also predicted,and they may vanish once the thickness of the piezoelectric nanofilm reaches a critical value.

Shear-horizontal waves in periodic layered nanostructure with both nonlocal and interface effects

The propagation of shear-horizontal(SH)waves in the periodic layered nanocomposite is investigated by using both the nonlocal integral model and the nonlocal differential model with the interface effect.Based on the transfer matrix method and the Bloch theory,the band structures for SH waves with both vertical and oblique incidences to the structure are obtained.It is found that by choosing appropriate interface parameters,the dispersion curves predicted by the nonlocal differential model with the interface effect can be tuned to be the same as those based on the nonlocal integral model.Thus,by propagating the SH waves vertically and obliquely to the periodic layered nanostructure,we could invert,respectively,the interface mass density and the interface shear modulus,by matching the dispersion curves.Examples are further shown on how to determine the interface mass density and the interface shear modulus in theory.

Propagation behavior of SH waves in a piezomagnetic substrate with an orthorhombic piezoelectric layer

The dispersion behavior of the shear horizontal （SH） waves in the coupled structure consisting of a piezomagnetic substrate and an orthorhombic piezoelectric layer is investigated with different cut orientations. The surface of the piezoelectric layer is mechanically free, electrically shorted, or open, while the surface of the piezomagnetic substrate is mechanically free, magnetically open, or shorted. The dispersion relations are derived for four electromagnetic boundary conditions. The dispersion characteristics are graphically illustrated for the layered structure with the PMN-PT layer perfectly bonded on the CoFe2O4 substrate. The effects of the PMN-PT cut orientations, the electromagnetic boundary conditions, and the thickness ratio of the layer to the substrate on the dispersion behavior are analyzed and discussed in detail. The results show that, （i） the effect of the cut orientation on the dispersion curves is very obvious, （ii） the electrical boundary conditions of the PMN-PT layer dominate the propagation feature of the SH waves, and （iii） the thickness ratio has a significant effect on the phase velocity when the wave number is small. The results of the present paper can provide valuable theoretical references to the applications of piezoelectric/piezomagnectic structure in acoustic wave devices.

DECAY RATE OF SAINT-VENANT END EFFECTS FOR PLANE DEFORMATIONS OF PIEZOELECTRIC-PIEZOMAGNETIC SANDWICH STRUCTURES

This paper is concerned with the decay of Saint-Venant end effects for plane deformations of piezoelectric （PE）-piezomagnetic （PM） sandwich structures, where a PM layer is located between two PE layers with the same material properties or reversely. The end of the sandwich structure is subjected to a set of self-equilibrated magneto-electro-elastic loads. The upper and lower surfaces of the sandwich structure axe mechanically free, electrically open or shorted as well as magnetically open or shorted. Firstly the constitutive equations of PE mate- rials and PM materials for plane strain are given and normalized. Secondly, the simplified state space approach is employed to arrange the constitutive equations into differential equations in a matrix form. Finally, by using the transfer matrix method, the characteristic equations for eigen- values or decay rates axe derived. Based on the obtained characteristic equations, the decay rates for the PE-PM-PE and PM-PE-PM sandwich structures are calculated. The influences of the electromagnetic boundary conditions, material properties of PE layers and volume fraction on the decay rates are discussed in detail.

ENERGY TRAPPING OF THICKNESS-SHEAR AND THICKNESS-TWIST MODES IN A PARTIALLY ELECTRODED AT-CUT QUARTZ RESONATOR

The thickness-shear and thickness-twist vibrations of a finite and partially elec- troded AT-cut quartz resonator are investigated. The equations of anisotropic elasticity are used with the omission of the small elastic constant c56. An analytical solution is obtained using Fourier series from which the free vibration resonant frequencies, mode shapes, and energy trapping are calculated and examined.

Magnetoelectric Properties of Piezoelectric—Piezomagnetic Composites with Elliptical Nanofibers

Based on the surface/interface theory,the effective magnetoelectric(ME)properties of piezoelectric(PE)-piezomagnetic(PM)composites with elliptical nanofibers are investigated analytically.Using the complex function theory,conformal mapping and the Mori-Tanaka mean-field method,the solutions of magneto-electro-elastic(MEE)fields are obtained,which satisfy both the interface and the single-valued conditions.The closed-form expression of the ME coefficient of the composites shows that the effect of ME coefficient is related to the interface parameters,elliptical aspect ratio,material properties of both fiber and matrix and the fiber volume fraction.Numerical calculation shows that by properly selecting some of these parameters,the effective ME coefficient could be substantially enhanced.

SH Waves in(1-x)Pb(Mg_(1/3)Nb_(2/3))O_(3-x)PbTiO_3 Piezoelectric Layered Structures Loaded with Viscous Liquid

The velocity dispersion and attenuation of shear horizontal（SH） waves in a layered piezoelectric structure loaded with viscous liquid is studied,where the（1- x）Pb（Mg（1/3）Nb（2/3））O（3-x）PbTiO3[PMN-xPT]single crystal is chosen as the piezoelectric layer.The PMN-xPT is being polarized along[011]c and[001]c so that the macroscopic symmetries are mm 2 and 4 mm,respectively.For the nonconductive liquid,the electrically open and shorted conditions at the interface between the liquid and the piezoelectric layer are considered.The phase velocity equations are derived analytically.The effects of the electrically boundary condition,the viscous coefficient and mass density of liquid as well as the thickness of the PMN-xPT layer on the phase velocity and attenuation are graphically illustrated.The results show that the phase velocity for the[011]c polarized PMN-0.29 PT is much smaller than that for the[001]c polarized PMN-0.33 PT,and the effects of viscous coefficient and piezoelectric layer thickness on the phase velocity for the[011]c case are stronger than that for the[001]c case.In addition,the electrical boundary conditions have an obvious influence on the propagation behaviors.These results can be useful for the designs and applications of acoustic wave devices and liquid biosensors.