On three-dimensional elastic problems of one-dimensional hexagonal quasicrystal bodies

Based on rigorous operator theory, a general solution of the three-dimensional elasticity equations of equilibrium for 1D hexagonal quasicrystals is obtained. The solution is expressed in terms of four quasiharmonic functions, which is very simple and useful. The point phonon (phason) force solution of an infinite 1D hexagonal quasicrystal body is derived, all in terms of elementary functions. They can play an important role in numerical simulations such as boundary element method.     

Three-dimensional interfacial fracture analysis of a one-dimensional hexagonal quasicrystal coating

In this paper, the three-dimensional (3D) interfacial fracture is analyzed in a one-dimensional (1D) hexagonal quasicrystal (QC) coating structure under mechanical loading. A planar interface crack with arbitrary shape is studied by a displacement discontinuity method. Fundamental solutions of interfacial concentrated displacement discontinuities are obtained by the Hankel transform technique, and the corresponding boundary integral-differential equations are constructed with the superposition principle. Green’s functions of constant interfacial displacement discontinuities within a rectangular element are derived, and a boundary element method is proposed for numerical simulation. The singularity of stresses near the crack front is investigated, and the stress intensity factors (SIFs) as well as energy release rates (ERRs) are determined. Finally, relevant influencing factors on the fracture behavior are discussed.     

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

The interaction between a screw dislocation and an elliptical hole with two asymmetrical cracks in a one-dimensional(1 D) 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.     

Bending and vibration of two-dimensional decagonal quasicrystal nanoplates via modified couple-stress theory

Based on the modified couple-stress theory, the three-dimensional(3D)bending deformation and vibration responses of simply-supported and multilayered twodimensional(2D) decagonal quasicrystal(QC) nanoplates are investigated. The surface loading is assumed to be applied on the top surface in the bending analysis, the tractionfree boundary conditions on both the top and bottom surfaces of the nanoplates are used in the free vibration analysis, and a harmonic concentrated point loading is applied o...     

The general solution of one-dimensional hexagonal quasicrystal

A general solution is given for three-dimensional dynamic problems in 1D hexagonal quasicrystalline material with Laue class 6/m_hmm. In the general solution, the phonon and phason displacements and stresses are controlled by two displacement functions Ψ and F, which satisfy a second-order partial differential equation, and a sixth-order partial differential equation, respectively. The general solution for static equilibrium problems is treated as a special case.     

Effective electroelastic constants for three-phase confocal elliptical cylinder model in piezoelectric quasicrystal composites

A three-phase confocal elliptical cylinder model is proposed to analyze micromechanics of one-dimensional hexagonal piezoelectric quasicrystal (PQC) composites. Exact solutions of the phonon, phason, and electric fields are obtained by using the conformal mapping combined with the Laurent expansion technique when the model is subject to far-field anti-plane mechanical and in-plane electric loadings. The effective electroelastic constants of several different composites made up of PQC, quasicrystal (QC), and piezoelectric (PE) materials are predicted by the generalized self-consistent method. Numerical examples are conducted to show the effects of the volume fraction and the cross-sectional shape of inclusion (or fiber) on the effective electroelastic constants of these composites. Compared with other micromechanical methods, the generalized selfconsistent and Mori-Tanaka methods can predict the effective electroelastic constants of the composites consistently.     

POLYNOMIAL SOLUTIONS TO PIEZOELECTRIC BEAMS (Ⅱ)——ANALYTICAL SOLUTIONS TO TYPICAL PROBLEMS

IntroductionThis paper is a continuation of Ref.[1],in which a series of orthotropic piezoelectricplane problems was solved and the corresponding exact solutions were obtained with the trial-and-error method,on the basis of the general solution expressed …     

Study on a straight dislocation in an icosahedral quasicrystal with piezoelectric effects

An electro-elastic analysis is performed on an icosahedral quasicrystal with piezoelectric effects containing a straight dislocation. The closed-form expressions for the elastic and electric fields are obtained using the extended Stroh formalism. The effects of piezoelectric constant on the phonon displacement, phason displacement, and electric potential are discussed in detail.     

一维六方准晶压电材料含运动螺型位错弹性问题分析

借助复变函数方法,研究了点群6mm 一维六方准晶压电材料中运动螺型位错,得到位错芯附近的应力、位移、能量的解析表达式.分析发现,在靠近运动螺型位错芯处,声子场和相位子场应力的分量表现出(x2+y2)-1的奇异性.当不考虑相位子场的影响时,文中得到的结果可以退化为含运动螺型位错的压电材料中的结果;当不考虑电场的影响时,退...     

Analytical solution of a simply supported piezoelectric beam subjected to a uniformly distributed loading

IntroductionIntelligentstructureisakindofnewstructuremodelsandhasbeenreceivedmuchattentioninrecentyears.Usedaspiezoelectricsensorsandactuators,thiskindofintelligentstructureshasmanyadvantagessuchasthepromptnessofresponseandtheconvenienceforthesignalcontrol.Soitisfollowedwithinterestbothinthetheoreticalstudyandintheengineeringapplications[1].Forexample ,theresearchoffundamentalsolution[2 ,3]andellipsoidalinclusion[4 ]forthree_dimensionalpiezoelectricmaterialbyuseofFouriertransformation ;thestu…     

Exact solutions for free vibration of transversely isotropic piezoelectric circular plates

By employing the general solution for coupled three-dimensional equations of a transversely isotropic piezoelectric body, this paper investigates the free vibration of a circular plate made of piezoelectric material. Three-dimensional exact solutions are then obtained under two specified boundary conditions, which can be used for both axisymmetric and non-axisymmetric cases. Numerical results are finally presented. The project supported by the National Natural Science Foundation of China (No. 19872060)     

Two-dimensional electroelastic fundamental solutions for general anisotropic piezoelectric media

I.IntroductionDuetotheirintrinsiccouplingeffectbetweenmechanicalandelectricalfields,piezoelectricmaterialshavebeenwidelyusedintechnologyastransducersandsensorsand,morerecently,asactuatorsinsmartstructures.lnordertooptimizetheirmicrostructuresandunderstand…     

含直对称裂纹的一维六方压电准晶对SH波的散射Scattering of SH wave by a linear symmetric crack at one-dimensional piezoelectric hexagonal quasicrystals

利用积分变换技术,结合Copson方法,研究了含直线型对称裂纹的一维六方压电准晶对SH波的散射问题。通过求解对偶积分方程,得到声子场、相位子场应力、位移及电场电位移分量的解析解。定义了裂纹尖端应力强度因子及电位移强度因子,给出了电非渗透性条件下应力强度因子及电位移强度因子的解析解。此研究结果对压电准晶材料的工程应用有一定的理论价值。     

Electro-elastic fundamental solutions of anisotropic piezoelectric materials with an elliptical hole

By using Stroh' complex formalism and Cauchy's integral method, the electro-elastic fundamental solutions of an infinite anisotropic piezoelectric solid containing an elliptic hole or a crack subjected to a line force and a line charge are presented in closed form. Particular attention is paid to analyzing the characteristics of the stress and electric displacement intensity factors. When a line force-charge acts on the crack surface, the real form expression of intensity factors is obtained. It is shown through a special example that the present work is correct. The project supported by the Fund of the State Education Commission of China for Excellent Young Teachers     

The fundamental solutions for the plane problem in piezoelectric media with an elliptic hole or a crack

1.IntroductionItiswell-knownthatthefundame,ltalsolutionsorGreen'sfunctionsplayanimportantroleilllinearelasticity.Forexample,theycanbeusedtoconstructmanyanalyticalsolutionsofpracticalproblems.Itismoreimportantthattheyareusedasthefundamentalsolutionsintheboundaryelementmethod(BEM)tosolvesomecomplicatedproblem.Withthewidely-increasingapplicationofpiezoelectricmaterialsinengineeringproblems,thestudyregardingtheGreen'sfLlnctionsinpiezoelectricsolidshasreceivedmuchinterest.The3DGreen'sfunctionsi…     

一种具有新型动力放大器压电悬臂梁俘能器计算模型和解析解

为了提高压电振动能量俘获的效率,提出了一种新型的压电悬臂梁俘能器。新的压电俘能器在悬臂梁固定端安装一个新型动力放大器系统,另一端带有一个有限尺寸的质量块。新型动力放大器由平移及转动约束的弹簧-质量块系统组成。考虑有限尺寸质量块的质量分布效应和平移及转动约束的弹簧刚度等结构参数的影响,利用广义Hamilton原理,针对带有新型动力放大器的压电式悬臂梁俘能器,建立了分布参数型运动微分方程,获得了相应的特征函数,分析了自振频率和能量俘获效果。分析结果表明,考虑质量块偏心距和转动惯量可提高能量俘获效率的预测精度;合理选择动力放大器的平移及转动弹簧刚度可提高能量俘获的效率,降低俘能器的共振频率。     

Analytical modeling of sandwich beam for piezoelectric bender elements

Piezoelectric bender elements are widely used as electromechanical sensors and actuators.An analytical sandwich beam model for piezoelectric bender elements was developed based on the first-order shear deformation theory(FSDT),which assumes a single rotation angle for the whole cross-section and a quadratic distribution function for coupled electric potential in piezoelectric layers,and corrects the effect of transverse shear strain on the electric displacement integration.Free vibration analysis of simply- supported bender elements was carried out and the numerical results showed that,solu- tions of the present model for various thickness-to-length ratios are compared well with the exact two-dimensional solutions,which presents an efficient and accurate model for analyzing dynamic electromechanical responses of bender elements.     

Several three-dimensional solutions for transversely isotropic functionally graded material plate welded with circular inclusion

The problem of a transversely isotropic functionally graded material (FGM) plate welded with a circular inclusion is considered. The analysis starts with the generalized England-Spencer plate theory for transversely isotropic FGM plates, which expresses a three-dimensional (3D) general solution in terms of four analytic functions. Several analytical solutions are then obtained for an infinite FGM plate welded with a circular inclusion and subjected to the loads at infinity. Three different cases are considered, i.e., a rigid circular inclusion fixed in the space, a rigid circular inclusion rotating about the x-, y-, and z-axes, and an elastic circular inclusion with different material constants from the plate itself. The static responses of the plate and/or the inclusion are investigated through numerical examples.     

Life-span of classical solutions for one-dimensional hydromagnetic flow

The paper concerns Cauchy, problem for one-dimensional hydromagnetic dynamics with dissipative terms. When the dissipation coefficient is equal to zero it is shown that the smooth solutions develop shocks in the finite time if the initial amounts of entropy and magnetic field are smaller than those of sound waves; when it is larger than zero, and the initial amounts of entropy, this dissipation coefficient and the magnetic field in each period are smaller than those of sound waves, then the smooth solutions blow up in the finite time. Moreover, the life-span of the smooth solution is given.