Table of Content

01 May 2022, Volume 43 Issue 5

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Articles

Effects of mechanical loadings on the performance of a piezoelectric hetero-junction

Wanli YANG, Renzhong HONG, Yunbo WANG, Yuantai HU

2022, 43(5):  615-626.  doi:10.1007/s10483-022-2848-7

Abstract ( 1393 )   HTML ( 39)   PDF (2255KB) ( 127 )  

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A fully-coupled model for a piezoelectric hetero-junction subjected to a pair of stresses is proposed by discarding the depletion layer approximation. The effect of mechanical loadings on PN junction performance is discussed in detail. Numerical examples are carried out for a p-Si/ZnO-n hetero-junction under a pair of stresses acting on the ntype ZnO portion near the PN interface, where ZnO has the piezoelectric property while Si is not. It is found that the bottom of conduction band is lowered/raised near the two loading points due to the decrease/increase in the electron potential energy there induced by a tensile-stress mode via sucking in majority-carriers from two outside regions, which implies appearance of a potential barrier and a potential well near two loading points. Furthermore, the barrier height and well depth gradually become large with increasing tensile stress such that more and more electrons/holes are inhaled in loading region from the n-/p-zone, respectively. Conversely, rising/dropping of conduction band bottom is brought out near the two loading points by a compressive-stress mode due to the increase/decrease in the potential energy of electrons by pumping out the majority-carriers from the loading region to the two outside regions. Therefore, a potential well and a potential barrier are induced near the two loading points, such that more and more electrons/holes are driven away from the loading region to the n-zone/p-zone, respectively, with the increasing compressive stress. These effects are important to tune the carrier recombination rate near the PN interface. Thus, the present study possesses great referential significance to piezotronic devices.

Near-zero Poisson's ratio and suppressed mechanical anisotropy in strained black phosphorene/SnSe van der Waals heterostructure: a first-principles study

Qi REN, Xingyao WANG, Yingzhuo LUN, Xueyun WANG, Jiawang HONG

2022, 43(5):  627-636.  doi:10.1007/s10483-022-2844-7

Abstract ( 1227 )   HTML ( 9)   PDF (2551KB) ( 114 )  

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Black phosphorene (BP) and its analogs have attracted intensive attention due to their unique puckered structures, anisotropic characteristics, and negative Poisson's ratio. The van der Waals (vdW) heterostructures assembly by stacking different materials show novel physical properties, however, the parent materials do not possess. In this work, the first-principles calculations are performed to study the mechanical properties of the vdW heterostructure. Interestingly, a near-zero Poisson's ratio v_zx is found in BP/SnSe heterostructure. In addition, compared with the parent materials BP and SnSe with strong in-plane anisotropic mechanical properties, the BP/SnSe heterostructure shows strongly suppressed anisotropy. The results show that the vdW heterostructure has quite different mechanical properties compared with the parent materials, and provides new opportunities for the mechanical applications of the heterostructures.

Well-posedness of two-phase local/nonlocal integral polar models for consistent axisymmetric bending of circular microplates

Hai QING

2022, 43(5):  637-652.  doi:10.1007/s10483-022-2843-9

Abstract ( 1083 )   HTML ( 4)   PDF (5723KB) ( 87 )  

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Previous studies have shown that Eringen's differential nonlocal model would lead to the ill-posed mathematical formulation for axisymmetric bending of circular microplates. Based on the nonlocal integral models along the radial and circumferential directions, we propose nonlocal integral polar models in this work. The proposed strainand stress-driven two-phase nonlocal integral polar models are applied to model the axisymmetric bending of circular microplates. The governing differential equations and boundary conditions (BCs) as well as constitutive constraints are deduced. It is found that the purely strain-driven nonlocal integral polar model turns to a traditional nonlocal differential polar model if the constitutive constraints are neglected. Meanwhile, the purely strain-and stress-driven nonlocal integral polar models are ill-posed, because the total number of the differential orders of the governing equations is less than that of the BCs plus constitutive constraints. Several nominal variables are introduced to simplify the mathematical expression, and the general differential quadrature method (GDQM) is applied to obtain the numerical solutions. The results from the current models (CMs) are compared with the data in the literature. It is clearly established that the consistent softening and toughening effects can be obtained for the strain-and stress-driven local/nonlocal integral polar models, respectively. The proposed two-phase local/nonlocal integral polar models (TPNIPMs) may provide an e-cient method to design and optimize the plate-like structures for microelectro-mechanical systems.

Nonlinear thickness-shear vibration of an infinite piezoelectric plate with flexoelectricity based on the method of multiple scales

Yang ZHENG, Bin HUANG, Lijun YI, Tingfeng MA, Longtao XIE, Ji WANG

2022, 43(5):  653-666.  doi:10.1007/s10483-022-2842-7

Abstract ( 1183 )   HTML ( 7)   PDF (297KB) ( 110 )  

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This paper presents a nonlinear thickness-shear vibration model for onedimensional infinite piezoelectric plate with flexoelectricity and geometric nonlinearity. The constitutive equations with flexoelectricity and governing equations are derived from the Gibbs energy density function and variational principle. The displacement adopted here is assumed to be antisymmetric through the thickness due to the thickness-shear vibration mode. Only the shear strain gradient through the thickness is considered in the present model. With geometric nonlinearity, the governing equations are converted into differential equations as the function of time by the Galerkin method. The method of multiple scales is employed to obtain the solution to the nonlinear governing equation with first order approximation. Numerical results show that the nonlinear thickness-shear vibration of piezoelectric plate is size dependent, and the flexoelectric effect has significant influence on the nonlinear thickness-shear vibration frequencies of micro-size thin plates. The geometric nonlinearity also affects the thickness-shear vibration frequencies greatly. The results show that flexoelectricity and geometric nonlinearity cannot be ignored in design of accurate high-frequency piezoelectric devices.

Elliptical inclusion in an anisotropic plane: non-uniform interface effects

Pengyu PEI, Ming DAI

2022, 43(5):  667-688.  doi:10.1007/s10483-022-2845-5

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We study the plane deformation of an elastic composite system made up of an anisotropic elliptical inclusion and an anisotropic foreign matrix surrounding the inclusion. In order to capture the influence of interface energy on the local elastic field as the size of the inclusion approaches the nanoscale, we refer to the Gurtin-Murdoch model of interface elasticity to describe the inclusion-matrix interface as an imaginary and extremely stiff but zero-thickness layer of a finite stretching modulus. As opposed to isotropic cases in which the effects of interface elasticity are usually assumed to be uniform (described by a constant interface stretching modulus for the entire interface), the anisotropic case considered here necessitates non-uniform effects of interface elasticity (described by a non-constant interface stretching modulus), because the bulk surrounding the interface is anisotropic. To this end, we treat the interface stretching modulus of the anisotropic composite system as a variable on the interface curve depending on the specific tangential direction of the interface. We then devise a unified analytic procedure to determine the full stress field in the inclusion and matrix, which is applicable to the arbitrary orientation and aspect ratio of the inclusion, an arbitrarily variable interface modulus, and an arbitrary uniform external loading applied remotely. The non-uniform interface effects on the external loading-induced stress distribution near the interface are explored via a group of numerical examples. It is demonstrated that whether the nonuniformity of the interface effects has a significant effect on the stress field around the inclusion mainly depends on the direction of the external loading and the aspect ratio of the inclusion.

Two-step homogenization for the effective thermal conductivities of twisted multi-filamentary superconducting strand

Yongbin WANG, Huadong YONG, Youhe ZHOU

2022, 43(5):  689-708.  doi:10.1007/s10483-022-2846-9

Abstract ( 1185 )   HTML ( 6)   PDF (8414KB) ( 273 )  

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For the accurate prediction of the effective thermal conductivities of the twisted multi-filamentary superconducting strand, a two-step homogenization method is adopted. Based on the distribution of filaments, the superconducting strand can be decomposed into a set of concentric cylinder layers. Each layer is a two-phase composite composed of the twisted filaments and copper matrix. In the first step of homogenization, the representative volume element (RVE) based finite element (FE) homogenization method with the periodic boundary condition (PBC) is adopted to evaluate the effective thermal conductivities of each layer. In the second step of homogenization, the generalized self-consistent method is used to obtain the effective thermal conductivities of all the concentric cylinder layers. The accuracy of the developed model is validated by comparing with the local and full-field FE simulation. Finally, the effects of the twist pitch on the effective thermal conductivities of twisted multi-filamentary superconducting strand are studied.

Fundamental solutions of critical wedge angles for one-dimensional piezoelectric quasicrystal wedge

Xiang MU, Xiaoyu FU, Liangliang ZHANG, Zhaowei ZHU, Jinming ZHANG, Yang GAO

2022, 43(5):  709-728.  doi:10.1007/s10483-022-2847-6

Abstract ( 1203 )   HTML ( 2)   PDF (3170KB) ( 89 )  

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Two problems of a one-dimensional (1D) piezoelectric quasicrystal (QC) wedge are investigated, i. e., the two sides of the wedge subject to uniform tractions and the wedge apex subject to the concentrated force. By virtue of the Stroh formalism and Barnett-Lothe matrices, the analytical expressions of the displacements and stresses are derived, and the generalized solutions for the critical wedge angles are discussed. Numerical examples are given to present the mechanical behaviors of the wedge in each field. The results indicate that the effects of the uniform tractions and the concentrated force on the phonon field displacement are larger than those on the phason field.

Effects of local thickness defects on the buckling of micro-beam

Andi LAI, Bing ZHAO, Xulong PENG, Chengyun LONG

2022, 43(5):  729-742.  doi:10.1007/s10483-022-2855-7

Abstract ( 1230 )   HTML ( 4)   PDF (584KB) ( 60 )  

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A buckling model of Timoshenko micro-beam with local thickness defects is established based on a modified gradient elasticity. By introducing the local thickness defects function of the micro-beam, the variable coe-cient differential equations of the buckling problem are obtained with the variational principle. Combining the eigensolution series of the complete micro-beam with the Galerkin method, we obtain the critical load and buckling modes of the micro-beam with defects. The results show that the depth and location of the defect are the main factors affecting the critical load, and the combined effect of boundary conditions and defects can significantly change the buckling mode of the micro-beam. The effect of defect location on buckling is related to the axial gradient of the rotation angle, and defects should be avoided at the maximum axial gradient of the rotation angle. The model and method are also applicable to the static deformation and vibration of the micro-beam.

Modeling and analysis of magnetic spring enhanced lever-type electromagnetic energy harvesters

Ning YU, Xiangyi FEI, Chuanyu WU, Bo YAN

2022, 43(5):  743-760.  doi:10.1007/s10483-022-2849-9

Abstract ( 1232 )   HTML ( 4)   PDF (6791KB) ( 70 )  

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This study presents a novel enhanced monostable lever-type electromagnetic energy harvester (L-EEH). According to the positions of the coil and the lever pivot, four configurations are discussed to realize a better harvesting performance of the L-EEHs. On the basis of establishing the theoretical model of the L-EEH, the corresponding analytical solutions can be obtained by applying the harmonic balance method. The effects of the nonlinear coe-cient, the lever ratio, the mass ratio, and the circuit parameters on the energy harvesting performance of L-EEHs are analyzed and discussed. The numerical and experimental efforts are carried out to verify the theoretical model and the energy harvesting performance. The results demonstrate that the maximum output voltage can be achieved with an appropriate lever ratio. Furthermore, the L-EEH possesses a considerable energy harvesting performance under a smaller lever ratio compared with the other three configurations. The output power can also be improved by adjusting the tip mass of the lever. The proposed L-EEH has a considerable operating bandwidth and an output power, which can reach 146.6 mW under the excitation amplitude of 0.3g.

Flutter analysis of rotating beams with elastic restraints

Lüsen WANG, Zhu SU, Lifeng WANG

2022, 43(5):  761-776.  doi:10.1007/s10483-022-2850-6

Abstract ( 1186 )   HTML ( 8)   PDF (553KB) ( 276 )  

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The aeroelastic stability of rotating beams with elastic restraints is investigated. The coupled bending-torsional Euler-Bernoulli beam and Timoshenko beam models are adopted for the structural modeling. The Greenberg aerodynamic model is used to describe the unsteady aerodynamic forces. The additional centrifugal stiffness effect and elastic boundary conditions are considered in the form of potential energy. A modified Fourier series method is used to assume the displacement field function and solve the governing equation. The convergence and accuracy of the method are verified by comparison of numerical results. Then, the flutter analysis of the rotating beam structure is carried out, and the critical rotational velocity of the flutter is predicted. The results show that the elastic boundary reduces the critical flutter velocity of the rotating beam, and the elastic range of torsional spring is larger than the elastic range of linear spring.