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2020年 第41卷 第6期    刊出日期：2020-06-01

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论文

Electronic band energy of a bent ZnO piezoelectric semiconductor nanowire

Wanli YANG, Yuantai HU, E. N. PAN

2020, 41(6):  833-844.  doi:10.1007/s10483-020-2619-7

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The electric band energy variation in a bent piezoelectric semiconductor (PSC) nanowire of circular cross-section induced by the mechanical force is analyzed based on a six-band k·p method. The electric-mechanical fields are first obtained analytically in a cantilever bent PSC nanowire by solving the fully-coupled electro-mechanical equations. Then, the band energy is acquired numerically via the six-band Hamiltonian. By considering further the nonlinear coupling between the piezoelectric and semiconducting quantities, the contribution of the redistribution carriers to the electric field is analyzed from the Gauss's law. Numerical examples are carried out for an n-type ZnO nanowire in different locations induced by an applied concentrated end force. They include the electric potential, heavy hole (HH), light hole (LH), spin-orbit split-off (SO), and conduction band (CB) edges along the axial and thickness directions. Our results show that the applied force has a significant effect on the band energies. For instance, on the bottom surface along the axial direction, the bandgaps near the fixed end are greater than those near the loading end, and this trend is reversed on the top surface. Moreover, at a fixed axial location, the energy level of the lower side can be enhanced by applying a bending force at the end. The present results could be of significant guidance to the electronic devices and piezotronics.

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

Wanli YANG, Jinxi LIU, Yongliang XU, Yuantai HU

2020, 41(6):  845-858.  doi:10.1007/s10483-020-2617-9

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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.

Vibration analysis of piezoelectric sandwich nanobeam with flexoelectricity based on nonlocal strain gradient theory

Shan ZENG, Kaifa WANG, Baolin WANG, Jinwu WU

2020, 41(6):  859-880.  doi:10.1007/s10483-020-2620-8

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A nonlocal strain gradient theory (NSGT) accounts for not only the nongradient nonlocal elastic stress but also the nonlocality of higher-order strain gradients, which makes it benefit from both hardening and softening effects in small-scale structures. In this study, based on the NSGT, an analytical model for the vibration behavior of a piezoelectric sandwich nanobeam is developed with consideration of flexoelectricity. The sandwich nanobeam consists of two piezoelectric sheets and a non-piezoelectric core. The governing equation of vibration of the sandwich beam is obtained by the Hamiltonian principle. The natural vibration frequency of the nanobeam is calculated for the simply supported (SS) boundary, the clamped-clamped (CC) boundary, the clamped-free (CF) boundary, and the clamped-simply supported (CS) boundary. The effects of geometric dimensions, length scale parameters, nonlocal parameters, piezoelectric constants, as well as the flexoelectric constants are discussed. The results demonstrate that both the flexoelectric and piezoelectric constants enhance the vibration frequency of the nanobeam. The nonlocal stress decreases the natural vibration frequency, while the strain gradient increases the natural vibration frequency. The natural vibration frequency based on the NSGT can be increased or decreased, depending on the value of the nonlocal parameter to length scale parameter ratio.

Jacobian-free Newton-Krylov subspace method with wavelet-based preconditioner for analysis of transient elastohydrodynamic lubrication problems with surface asperities

N. M. BUJURKE, M. H. KANTLI

2020, 41(6):  881-898.  doi:10.1007/s10483-020-2616-8

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This paper presents an investigation into the effect of surface asperities on the over-rolling of bearing surfaces in transient elastohydrodynamic lubrication (EHL) line contact. The governing equations are discretized by the finite difference method. The resulting nonlinear system of algebraic equations is solved by the Jacobian-free Newtongeneralized minimal residual (GMRES) from the Krylov subspace method (KSM). The acceleration of the GMRES iteration is accomplished by a wavelet-based preconditioner. The profiles of the lubricant pressure and film thickness are obtained at each time step when the indented surface moves through the contact region. The prediction of pressure as a function of time provides an insight into the understanding of fatigue life of bearings. The analysis confirms the need for the time-dependent approach of EHL problems with surface asperities. This method requires less storage and yields an accurate solution with much coarser grids. It is stable, efficient, allows a larger time step, and covers a wide range of parameters of interest.

Interaction between a screw dislocation and an elliptical hole with two asymmetrical cracks in a one-dimensional hexagonal quasicrystal with piezoelectric effect

Lianhe LI, Xiaowei CUI, Junhong GUO

2020, 41(6):  899-908.  doi:10.1007/s10483-020-2615-6

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The interaction between a screw dislocation and an elliptical hole with two asymmetrical cracks in a one-dimensional (1D) hexagonal quasicrystal with piezoelectric effect is considered. A general formula of the generalized stress field, the field intensity factor, and the image force is derived, and the special cases are discussed. Several numerical examples are given to show the effects of the material properties and the dislocation position on the field intensity factors and the image forces.

Thomson and rotation effects during photothermal excitation process in magnetic semiconductor medium using variable thermal conductivity

K. LOTFY, A. K. KHAMIS, A. A. EL-BARY, M. H. AHMED

2020, 41(6):  909-926.  doi:10.1007/s10483-020-2613-9

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This study investigates a strong magnetic field acting over an elastic rotator semiconductor medium. The Thomson effect due to the magnetic field during the photothermal transport process is studied, and the thermoelectricity theory is used to explain the behavior of waves in the homogenous and isotropic medium under the effect of variable thermal conductivity. The variable thermal conductivity is considered as a linear function of the temperature. The two-dimensional deformation equations are used to describe the overlaps among plasma, electrical, thermal, and magneto-elastic waves. The charge density of inertia-particles is considered as a function of time for studying the induced electric current. The normal mode analysis is used to obtain the exact solutions of the physical field distributions as part of this phenomenon. To obtain the complete solutions of the physical field quantities, the certain mechanical loads, electromagnetic effects, thermal effects, and plasma recombination process are applied herein. The results of the physical distributions are graphically depicted and discussed in consideration of the internal heat source, rotation, and Peltier coefficient.

Analysis of thermal responses in a two-dimensional porous medium caused by pulse heat flux

T. SAEED, I. A. ABBAS

2020, 41(6):  927-938.  doi:10.1007/s10483-020-2612-8

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In this article, the generalized model for thermoelastic waves with two relaxation times is utilized to compute the increment of temperature, the displacement components, the stress components, and the changes in the volume fraction field in a two-dimensional porous medium. By using the Fourier-Laplace transform and the eigenvalue method, the considered variables are obtained analytically. The derived approach is estimated with numerical outcomes which are applied to the porous media with a geometrical simplification. The numerical results for the considered variables are performed and presented graphically. Finally, the outcomes are represented graphically to display the difference among the classical dynamical (CD) coupled, the Lord-Shulman (LS), and the Green-Lindsay (GL) models.

Design and fluid-structure interaction analysis for a microfluidic T-junction with chemo-responsive hydrogel valves

E. KHANJANI, A. HAJARIAN, A. KARGAR-ESTAHBANATY, N. ARBABI, A. TAHERI, M. BAGHANI

2020, 41(6):  939-952.  doi:10.1007/s10483-020-2618-6

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Due to the deformation ability even under small loads, hydrogels have been widely used as a type of soft materials in various applications such as actuating and sensing, and have attracted many researchers to study their behaviors. In this paper, the behavior of hydrogel micro-valves with reverse sensitivity to the pH inside a T-junction flow sorter is investigated. With the fluid-structure interaction (FSI) approach, the effects of various parameters such as the inlet pressure and the pH value on the stress and deformation of the micro-valves are examined, and the results with and without FSI, including the flow rate and the closure pH, are compared. In order to reduce the response time of hydrogels, the effects of three different patterns on the performance of the microvalves are explored. Eventually, it is concluded that FSI is a key influential factor in designing and analyzing the behaviors of hydrogels.

Assessment of force models on finite-sized particles at finite Reynolds numbers

Ruyang LI, Weixi HUANG, Lihao ZHAO, Chunxiao XU

2020, 41(6):  953-966.  doi:10.1007/s10483-020-2621-9

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Finite-sized inertial spherical particles are fully-resolved with the immersed boundary projection method (IBPM) in the turbulent open-channel flow by direct numerical simulation (DNS). The accuracy of the particle surface force models is investigated in comparison with the total force obtained via the fully-resolved method. The results show that the steady-state resistance only performs well in the streamwise direction, while the fluid acceleration force, the added-mass force, and the shear-induced Saffman lift can effectively compensate for the large-amplitude and high-frequency characteristics of the particle surface forces, especially for the wall-normal and spanwise components. The modified steady-state resistance with the correction effects of the acceleration and the fluid shear can better represent the overall forces imposed on the particles, and it is a preferable choice of the surface force model in the Lagrangian point-particle method.

A highly-efficient method for stationary response of multi-degree-of-freedom nonlinear stochastic systems

Lincong CHEN, J. Q. SUN

2020, 41(6):  967-982.  doi:10.1007/s10483-020-2614-7

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Analytical and numerical studies of multi-degree-of-freedom (MDOF) nonlinear stochastic or deterministic dynamic systems have long been a technical challenge. This paper presents a highly-efficient method for determining the stationary probability density functions (PDFs) of MDOF nonlinear systems subjected to both additive and multiplicative Gaussian white noises. The proposed method takes advantages of the sufficient conditions of the reduced Fokker-Planck-Kolmogorov (FPK) equation when constructing the trial solution. The assumed solution consists of the analytically constructed trial solutions satisfying the sufficient conditions and an exponential polynomial of the state variables, and delivers a high accuracy of the solution because the analytically constructed trial solutions capture the main characteristics of the nonlinear system. We also make use of the concept from the data-science and propose a symbolic integration over a hypercube to replace the numerical integrations in a higher-dimensional space, which has been regarded as the insurmountable difficulty in the classical method of weighted residuals or stochastic averaging for high-dimensional dynamic systems. Three illustrative examples of MDOF nonlinear systems are analyzed in detail. The accuracy of the numerical results is validated by comparison with the Monte Carlo simulation (MCS) or the available exact solution. Furthermore, we also show the substantial gain in the computational efficiency of the proposed method compared with the MCS.