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We study the bending of a magnetically saturated ferromagnetoelastic plate. The plate is rectangular and simply-supported along its edges. It is under a local distribution of normal mechanical load on its top surface, simulating a mechanical probe or manipulation of the magnetization field. The three-dimensional equations of saturated ferromagnetoelasticity for small fields superposed on finite biasing fields due to spontaneous magnetization are used. The plate is effectively piezomagnetic under the biasing fields. A trigonometric series solution is obtained. The perturbation of the magnetization field by the mechanical load is calculated and examined. It is found that the magnetization is sensitive to the mechanical load, particularly near the loading area. The perturbation of the magnetization is found to be associated with the transverse shear stresses in bending. [ABSTRACT FROM AUTHOR]

We study electromechanical responses of a flexoelectric semiconductor plate in bending under mechanical loads. A two-dimensional theory for classical bending without shear deformation is derived from the three-dimensional macroscopic theory of flexoelectric semiconductors. A simple solution is obtained for pure bending. A combination of physical and geometric parameters is introduced as a measure of the strength of the coupling between the mechanical load and the redistribution of charge carriers. A trigonometric series solution is obtained for a simply supported rectangular plate under a local normal mechanical load, which shows concentration of mobile charges and the formation of electric potential barriers near the loading area. The results are fundamental to the mechanical manipulation of charge carriers in these plates. We also analyze the buckling of a simply supported rectangular plate under in-plane compressive forces. A series of buckling loads and modes are obtained. Numerical results show that flexoelectric coupling exhibits a stiffening effect and increases the buckling load, while semiconduction weakens the flexoelectric stiffening. The distributions of mobile charges in the first few buckling modes are presented. [ABSTRACT FROM AUTHOR]

We study the response of a composite beam (unimorph) with a piezomagnetic layer and a piezoelectric semiconductor layer under a transverse magnetic field. A one-dimensional model for coupled bending and extension of the beam is derived from the three-dimensional theory. A simple and analytical solution of the model is obtained, showing that various electromechanical fields develop in the beam through piezomagnetic and piezoelectric couplings as well as semiconduction. In particular, the mobile charges in the semiconductor layer redistribute themselves under the magnetic field. A coupling coefficient is defined to describe the strength of this magneto-semiconduction coupling. The effects of physical and geometric parameters on the fields and the coupling coefficient are examined. The results are fundamental to piezotronics when magnetic effects are involved. [ABSTRACT FROM AUTHOR]

We study electric currents in a piezoelectric semiconductor fiber under a constant voltage and time-dependent axial stresses applied locally. From a nonlinear numerical analysis based on a one-dimensional phenomenological model using the commercial software COMSOL, it is found that pulse electric currents can be produced by periodic or time-harmonic stresses. The pulse currents can be tuned by the amplitude and frequency of the applied stress. The result obtained provides a new approach for the mechanical control of electric currents in piezoelectric semiconductor fibers and has potential applications in piezotronics. [ABSTRACT FROM AUTHOR]

We study the electrical response of a multiferroic composite semiconductor fiber consisting of a piezoelectric semiconductor layer and two piezomagnetic layers under a transverse magnetic field applied locally to a finite part of the fiber. The phenomenological theory of piezomagnetic-piezoelectric semiconductors is employed. A one-dimensional model is derived for magnetically induced extension of the fiber. For open-circuit boundary conditions at the two ends of the fiber, an analytical solution is obtained from the model linearized for small carrier perturbations. The solution shows a local electric polarization and a pair of local electric potential barrier-well. When the two ends of the fiber are under a voltage, a nonlinear numerical solution shows that the potential barrier and well forbid the passage of currents when the voltage is low. The results have potential applications in piezotronic devices when magnetic fields are involved for manipulating the devices or sensing and transduction. [ABSTRACT FROM AUTHOR]

We study transient bending vibration of a ZnO piezoelectric semiconductor nanofiber fixed at one end with a suddenly applied shear force at the other end. A one-dimensional model based on the phenomenological theory of piezoelectric semiconductors consisting of the equations of piezoelectricity coupled to the continuity equation of electrons is used. An approximate theoretical analysis is performed, accompanied by a finite element analysis using COMSOL. The evolutions of deflection, electric potential and electron distribution are calculated and examined. It is found that when the fiber reaches its largest deflection, the distributions of the electromechanical fields are qualitatively similar to those in the case of static loading under the same shear force, but the amplitudes of the fields are about twice as large roughly. [ABSTRACT FROM AUTHOR]

Abstract We study the bending of a composite fiber of piezoelectric dielectrics and nonpiezoelectric semiconductors. The top and bottom piezoelectric layers are polarized in the opposite directions. A theoretical analysis is performed using a one-dimensional model. It is shown that mechanical loads trigger the redistribution of mobile charges in such a composite fiber. Thus the composite fiber exhibits piezotronic couplings like a homogeneous piezoelectric semiconducting fiber. The couplings are not a direct effect, but similar to a product property due to the particular design of the present composite. The electromechanical and semiconducting behaviors of the composite fiber and the effects of various parameters on piezotronic couplings are calculated and examined. It is observed that piezotronic couplings in these composite fibers are sensitive to material and geometric parameters and can be optimized through design. Different from the previous work on ZnO fiber where the mobile charges are driven to the top and bottom surfaces of the fiber, in the present composite fiber the mobile charges are driven to the two ends of the fiber. The present theoretical analysis of the composite fiber offers an important method for developing novel piezotronic devices. Graphical abstract The tuning effect of the mechanical force on piezotronic effects via product property are theoretically demonstrated in the bending of the cantilever composite fiber of PZT-5A and silicon with the reference concentrations of p 0 = n 0 = 10 23 / m 3 and the shear force F = 20 pN. The holes and electrons in the composite fiber move towards the two ends, respectively, and then reach a new equilibrium state under the induced polarization electric field when the shear force is applied. fx1 Highlights • Piezotronic effect in a bended composite fiber is theoretically demonstrated. • The mobile charges in the composite fiber with bending deformation are driven to the two ends. • The piezotronic coupling is sensitive to material and geometric parameters and can be optimized through design. [ABSTRACT FROM AUTHOR]

Abstract Some piezoelectric materials, such as zinc oxide, are semiconductors simultaneously. Usually, the semiconductive property of these materials is omitted in the study of piezoelectric characteristics. However, due to the small sizes of some piezoelectric devices, such as nanogenerators, the semiconductive property may have an appreciable impact on the wave motion characteristics and potential output. In this paper, we study the influence of semiconductive property for the improvement of nanogernerators through the propagation of shear-horizontal waves in a piezoelectric semiconductor plate of 6 mm class crystals by using wave mode approach. Some interesting results are observed from the points of both mechanical and electrical views. Mechanically, the semiconductive property will reduce the frequencies of waves (decrease the kinetic energy of waves), and cause new size-dependent wave modes due to the drift of electrons and holes. Meanwhile, a size-dependent acoustic loss is generated, where the acoustic loss becomes greater when the size gets smaller. Electrically, by comparing the magnitudes and distributions of potential between the cases with and without semiconduction, it is presented that energy can be harvested not only when the deformations are generated but also when the deformations are recovering. Further, the potential output in piezoelectric semiconductor can be improved by increasing strain and reducing conductivity. These results are useful for the design of piezoelectric semiconductor devices. They are also good corrections to the theoretical analyses of some piezoelectric devices in which semiconductive property is omitted, especially for the devices with small sizes. Graphical abstract The influences of semiconductive effect on the wave motion and potential output of piezoelectric semiconductor nanoplate were studied. The dispersion curves for different plate thicknesses were obtained, along with detailed distributions of displacements, electric potential, and concentrations of holes and electrons. Results show semiconductive property will result in size-dependent acoustic energy loss. Meanwhile, new size-dependent wave modes appear whose predominant energy is caused by holes and electrons with negligible mechanical energy. On the other hand, the semiconductive property will also reduce potential output significantly, and the detailed mechanical and electrical influence factors on piezoelectric potential are studied for the improvement of the potential output. This work studied a steady state process of wave propagating in nanoplate involving both electron and hole using a fully coupled constitutive equation, which is a more realistic picture for revealing intrinsic characteristics of semiconductive piezoelectric materials. fx1 Highlights • Displacement, electric potential and carrier concentration profiles were obtained. • Semiconductive effect will cause size-dependent acoustic energy loss. • New wave modes appear whose predominant energy is caused by holes and electrons. • Potential magnitudes can be improved by increasing strain and reducing conductivity. • Energy can be harvested in the recovery of deformation as well. [ABSTRACT FROM AUTHOR]

We study electromechanical fields near the interface between a circular piezoelectric semiconductor cylinder and another piezoelectric semiconductor in which it is embedded. The cylinder is p-doped. The surrounding material is n-doped. The phenomenological theory of piezoelectric semiconductors consisting of the equations of piezoelectricity and the conservation of charge for holes and electrons is used. The theory is linearized for small carrier concentration perturbations. An analytical solution is obtained, showing the formation of a PN junction near the interface. Various electromechanical fields associated with the junction are calculated. The effects of a few physical parameters are examined. [ABSTRACT FROM AUTHOR]

We study a ZnO piezoelectric semiconductor nanowire in bending vibration with shear deformation for energy harvesting application. The wire is a cantilever fixed at one end and is driven by a time-harmonic transverse shear force at the other end. A theoretical analysis is performed using one-dimensional equations based on the phenomenological theory of piezoelectric semiconductors consisting of the momentum equation, the charge equation of electrostatics, and the conservation of charge for holes and electrons. An analytical solution is obtained. The distributions of the electric potential and carrier concentration near resonances are calculated. The fields at the first resonance are qualitatively similar to the static fields. At the second and higher resonances the fields reverse their directions when crossing the nodal points of the vibration modes. The results obtained are fundamental to the development and optimization of energy harvesters and other devices based on the bending vibration of ZnO nanowires. [ABSTRACT FROM AUTHOR]

This paper presents a derivation of the equations of linear momentum, angular momentum, and energy of an electroelastic body using a composite particle consisting of two differential elements based on Tiersten's two-continuum model. The differential derivation shows the physics involved in a way different from the integral approach in the literature. Like the integral approach, it also produces the expressions of the electric body force, couple, and power which are fundamental to the development of the nonlinear macroscopic theory of an electroelastic body. [ABSTRACT FROM AUTHOR]

This paper presents a procedure for the derivation of the expressions for electric body force, couple, and power in a nonlinear electroelastic body under electromechanical loads. The derivation is based on Tierseten's two-continuum model but much simplified. [ABSTRACT FROM AUTHOR]

We study the effects of mechanical nonlinearity arising from large thickness-shear deformation on the transient process of an AT-cut quartz plate resonator. Mindlin's two-dimensional plate equation is used, from which a system of first-order nonlinear differential equations governing the evolution of the vibration amplitude is obtained. Numerical solutions by the Runge-Kutta method show that in common operating conditions of quartz resonators the nonlinear effect varies from noticeable to significant. As resonators are to be made smaller and thinner in the future with about the same power requirement, nonlinear effects will become more important and need more understanding and consideration in resonator design. [ABSTRACT FROM AUTHOR]

Abstract: Exact solutions for free vibration frequencies and modes are obtained for thickness-shear and thickness-twist vibrations of unelectroded circular AT-cut quartz plates governed by the two-dimensional scalar differential equation derived by Tiersten and Smythe. Comparisons are made with experimental results and the widely-used perturbation solution by Tiersten and Smythe under the assumption of weak in-plane anisotropy. Our solution is found to be much closer to the experimental results than the perturbation solution. For the frequency of the fundamental thickness-shear mode, the error of the perturbation method is 0.4549%, significant in resonator applications. [Copyright &y& Elsevier]

Abstract: We study free vibration of a thickness-shear mode crystal resonator of AT-cut quartz. The resonator is a rectangular plate partially and symmetrically electroded at the center with rectangular electrodes. A single-mode, three-dimensional equation governing the thickness-shear displacement is used. A Fourier series solution is obtained. Numerical results calculated from the series show that there exist trapped thickness-shear modes whose vibration is mainly under the electrodes and decays rapidly outside the electrodes. The effects of the electrode size and thickness on the trapped modes are examined. [Copyright &y& Elsevier]

Abstract: The thickness-shear and thickness-twist vibrations of a finite and partially electroded AT-cut quartz resonator are investigated. The equations of anisotropic elasticity are used with the omission of the small elastic constant c 56. An analytical solution is obtained using Fourier series from which the free vibration resonant frequencies, mode shapes, and energy trapping are calculated and examined. [Copyright &y& Elsevier]

Abstract: We study shear-horizontal (SH) waves in a rotated Y-cut quartz plate carrying an isotropic elastic layer of finite thickness. The three-dimensional theories of anisotropic elasticity and isotropic elasticity are used for the quartz plate and the elastic layer, respectively. A transcendental frequency equation that determines the dispersion relations of the waves is obtained. The dispersion relations are obtained and plotted by solving the frequency equation using MATLAB. Approximate dispersion relations are also obtained analytically for two special cases. One is for long waves whose wavelength is much larger than the plate thickness. The other is for the case of a very thin elastic layer. The effects of the elastic layer on the dispersion relations are examined. The results obtained are fundamental and useful to acoustic wave sensors for measuring the mechanical and geometric properties of the elastic layer. [Copyright &y& Elsevier]

ABSTRACT: We study experimentally the microstructure and mechanical behavior of natural cow leather. Tensile tests are performed using leather strips to observe their deformation, creep and failure. It is found that the microstructure of cow leather is a layered, complicated network of fibers of different sizes from a few to a few hundreds of nanometers in diameter. They show nonlinear stress-strain relations and viscoelastic behavior. The effect of humidity is also examined. A simple theoretical model of a multilayered beam is proposed to describe the most basic behavior in tension. [Copyright &y& Elsevier]

We study the effects of a local temperature change on the electrical behaviors of a piezoelectric semiconductor fiber in extensional deformation. A one-dimensional model for thin fibers derived previously from the macroscopic theory of thermopiezoelectric semiconductors is used. Through a combined theoretical and numerical analysis, it is shown that a local temperature change produces a local electric potential barrier and a potential well, which prohibits the flow of currents along the fiber unless the voltage is above a temperature-dependent critical value. The results are useful for thermally manipulating the currents in the fiber and have potential applications in piezotronics. Image 1 • The effects of a local temperature change on the electrical behaviors of a PS fiber in extension are investigated. • A local temperature change causes local polarization and thereby produces a local potential barrier and well. • The potential barrier and well forbid the flow of currents along the fiber at low voltages. • The local temperature change behaves mainly like a switch, and sometimes like a diode. [ABSTRACT FROM AUTHOR]