A coupled Legendre-Laguerre polynomial method with analytical integration for the Rayleigh waves in a quasicrystal layered half-space with an imperfect interface

The Laguerre polynomial method has been successfully used to investigate the dynamic responses of a half-space.However,it fails to obtain the correct stress at the interfaces in a layered half-space,especially when there are significant differences in material properties.Therefore,a coupled Legendre-Laguerre polynomial method with analytical integration is proposed.The Rayleigh waves in a one-dimensional(1D)hexagonal quasicrystal(QC)layered half-space with an imperfect interface are investigated.The correctness is validated by comparison with available results.Its computation efficiency is analyzed.The dispersion curves of the phase velocity,displacement distributions,and stress distributions are illustrated.The effects of the phonon-phason coupling and imperfect interface coefficients on the wave characteristics are investigated.Some novel findings reveal that the proposed method is highly efficient for addressing the Rayleigh waves in a QC layered half-space.It can save over 99%of the computation time.This method can be expanded to investigate waves in various layered half-spaces,including earth-layered media and surface acoustic wave(SAW)devices.

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.

Controllable wave propagation in a weakly nonlinear monoatomic lattice chain with nonlocal interaction and active control

The one-dimensional monoatomic lattice chain connected by nonlinear springs is investigated, and the asymptotic solution is obtained through the Lindstedt-Poincar′e perturbation method. The dispersion relation is derived with the consideration of both the nonlocal and the active control effects. The numerical results show that the nonlocal effect can effectively enhance the frequency in the middle part of the dispersion curve.When the nonlocal effect is strong enough, zero and negative group velocities will be evoked at different points along the dispersion curve, which will provide different ways of transporting energy including the forward-propagation, localization, and backwardpropagation of wavepackets related to the phase velocity. Both the nonlinear effect and the active control can enhance the frequency, but neither of them is able to produce zero or negative group velocities. Specifically, the active control enhances the frequency of the dispersion curve including the point at which the reduced wave number equals zero, and therefore gives birth to a nonzero cutoff frequency and a band gap in the low frequency range. With a combinational adjustment of all these effects, the wave propagation behaviors can be comprehensively controlled, and energy transferring can be readily manipulated in various ways.

Two-dimensional equations for thin-films of ionic conductors

A theoretical model is developed for predicting both conduction and diffusion in thin-film ionic conductors or cables. With the linearized Poisson-Nernst-Planck(PNP)theory, the two-dimensional(2D) equations for thin ionic conductor films are obtained from the three-dimensional(3D) equations by power series expansions in the film thickness coordinate, retaining the lower-order equations. The thin-film equations for ionic conductors are combined with similar equations for one thin dielectric film to derive the 2D equations of thin sandwich films composed of a dielectric layer and two ionic conductor layers. A sandwich film in the literature, as an ionic cable, is analyzed as an example of the equations obtained in this paper. The numerical results show the effect of diffusion in addition to the conduction treated in the literature. The obtained theoretical model including both conduction and diffusion phenomena can be used to investigate the performance of ionic-conductor devices with any frequency.

Coriolis effect on responses of rotating thin piezoelectric hollow cylinder

Coriolis effect is considered in the analysis of a rotating piezoelectric hollow cylinder. An inhomogeneous Bessel equation governing the radial mechanical displacement is derived, which can be approximated as an Euler type differential equation when the cylinder is very thin. Numerical examples show that the Coriolis effect can he significant under certain conditions.

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 general- ized 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.

Exact solutions for axisymmetric flexural free vibrations of inhomogeneous circular Mindlin plates with variable thickness

Circular plates with radially varying thickness, stiffness, and density are widely used for the structural optimization in engineering. The axisymmetric flexural free vibration of such plates, governed by coupled differential equations with variable coefficients by use of the Mindlin plate theory, is very difficult to be studied analytically. In this paper, a novel analytical method is proposed to reduce such governing equations for circular plates to a pair of uncoupled and easily solvable differential equations of the Sturm-Liouville type. There are two important parameters in the reduced equations. One describes the radial variations of the translational inertia and fiexural rigidity with the consideration of the effect of Poisson＇s ratio. The other reflects the comprehensive effect of the rotatory inertia and shear deformation. The Heun-type equations, recently well-known in physics, are introduced here to solve the flexural free vibration of circular plates analytically, and two basic differential formulae for the local Heun-type functions are discovered for the first time, which will be of great value in enriching the theory of Heun-type differential equations.

Novel mode-coupling vibrations of AlN thin film bulk acoustic resonator operating with thickness-extensional mode

The dispersion curves of bulk waves propagating in both AlN and ZnO film bulk acoustic resonators(FBARs)are presented to illustrate the mode flip of the thickness-extensional(TE)and 2nd thickness-shear(TSh2)modes.The frequency spectrum quantitative prediction(FSQP)method is used to solve the frequency spectra for predicting the coupling strength among the eigen-modes in AlN and ZnO FBARs.The results elaborate that the flip of the TE and TSh2 branches results in novel self-coupling vibration between the small-wavenumber TE and large-wavenumber TE modes,which has never been observed in the ZnO FBAR.Besides,the mode flip leads to the change in the relative positions of the frequency spectral curves about the TE cut-off frequency.The obtained frequency spectra can be used to predict the mode-coupling behaviors of the vibration modes in the AlN FBAR.The conclusions drawn from the results can help to distinguish the desirable operation modes of the AlN FBAR with very weak coupling strength from all vibration modes.

On asymmetric bending of functionally graded solid circular plates

Based on the three-dimensional elasticity equations, this paper studies the elastic bending response of a transversely isotropic functionally graded solid circular plate subject to transverse biharmonic forces applied on its top surface. The material prop- erties can continuously and arbitrarily vary along the thickness direction. By virtue of the generalized England＇s method, the problem can be solved by determining the expres- sions of four analytic functions. Expanding the transverse loarl in Fourier series along the circumferential direction eases the theoretical construction of the four analytic functions for a series of important biharmonic loads. Certain boundary conditions are then used to determine the unknown constants that are involved in the four constructed analytic functions. Numerical examples are presented to validate the proposed method. Then, we scrutinize the asymmetric bending behavior of a transversely isotropic functionally graded solid circular plate with different geometric and material parameters.

Three-dimensional elastostatic solutions for transversely isotropic functionally graded material plates containing elastic inclusion

Based on the generalized England-Spencer plate theory, the equilibrium of a transversely isotropic functionally graded plate containing an elastic inclusion is studied. The general solutions of the governing equations are expressed by four analytic functions α（ζ）, β（ζ）, φ（ζ）, and ψ（ζ） when no transverse forces are acting on the surfaces of the plate. Axisymmetric problems of a functionally graded circular plate and an infinite func- tionally graded plate containing a circular hole subject to loads applied on the cylindrical boundaries of the plate are firstly investigated. On this basis, the three-dimensional （3D） elasticity solutions are then obtained for a functionally graded infinite plate containing an elastic circular inclusion. When the material is degenerated into the homogeneous one, the present elasticity solutions are exactly the same as the ones obtained based on the plane stress elasticity, thus validating the present analysis in a certain sense.

Editorial: Thermal Stresses

Thermomechanical properties of materials have significant influences on the normal operation and service life of devices and structures.It is therefore of crucial importance to analyze their thermomechanical responses in numerous application areas such as mechanical engineering,civil engineering,electronic technology,and machine manufacturing.Demands on thermomechanical analyses or thermal stress analysis of materials and structures subject to various thermal loads are growing with the expanding of novel materials(e.g.,graphene,phononic crystals),new technologies(e.g.,three-dimensional printing,transfer printing),and new devices(e.g.,flexible electronics,stretchable electronics).In the last few decades,thermal stress analyses have attracted much attention from academia and industry with not only Journal of Thermal Stresses for publishing novel and cutting edge researches,but also series of International Congress on Thermal Stresses to exchange ideas and extend further collaborations for scientists and engineers who are involved in the field of thermal stresses.

Editorial: Mechanics of soft materials, structures and systems

The concept of soft matter was first introduced by P. G. de Gennes in his acceptance speech for the No-bel Physics Prize in 1991. In mechanics community, however, people usually prefer using soft material in-stead of soft matter to describe the material whose en-ergy associated with thermal motion is comparative to the interaction energy. Unlike in the conventional con-densed matter, entropy plays an important and even de-terminative role in soft materials.

Statics of FGM circular plate with magneto-electro-elastic coupling:axisymmetric solutions and their relations with those for corresponding rectangular beam

This paper investigates the static behavior of a functionally graded circular plate made of magneto-electro-elastic（MEE） materials under tension and bending.The analysis is directly based on the three-dimensional governing equations for magnetoelectro-elasticity, with the boundary conditions on the upper and lower surfaces satisfied exactly and those on the cylindrical surface satisfied approximately（in the Saint Venant sense）. The analytical solutions, derived with a direct displacement method, are valid for any functionally graded material（FGM） with its properties varying independently in a continuous manner along the thickness direction. For homogeneous materials, these solutions are degenerated to the ones available in the literature. Interesting relations are also found between the solutions for a functionally graded magneto-electro-elastic（FGMEE） circular plate and those for an FGMEE rectangular beam, and even those for a functionally graded elastic beam when only the elastic displacements are considered. The beam solutions are also derived using a direct displacement method. Numerical examples are presented to verify the present analytical solutions, show the effects of material heterogeneity and multi-field coupling, and indicate the correspondence between the plate solutions and beam solutions.

Editorial:Mechanics of intelligent materials and structures

Recently, intelligent or smart materials and structures have been received more and more attention due to their distinguished multi-field coupling properties and wide applications in aerospace, automobiles, civil structures, medical devices, information storage, energy harvesting and so on. It is of academic challenge to fully understand the complex multi-field coupling behaviors of various smart materials and structures, and of engineering sig- nificance to enhance the performance and reliability of these materials and structures in industrial applications. The papers in the special topic of Mechanics of Intelligent Materials and Structures focus on the understanding of the electromechanical, magneto-elastic, and magneto-rheological coupling behav- iors and properties of smart materials and structures for applications in vibration control, resonators, and various functional devices.

Interaction energy of interface dislocation loops in piezoelectric bi-crystals

Interface dislocations may dramatically change the electric properties, such as polarization, of the piezoelectric crystals. In this paper, we study the linear interactions of two interface dislocation loops with arbitrary shape in generally anisotropic piezoelectric bi-crystals. A simple formula for calculating the interaction energy of the interface dislocation loops is derived and given by a double line integral along two closed dislocation curves. Particularly, interactions between two straight segments of the interface dislocations are solved analytically, which can be applied to approximate any curved loop so that an analytical solution can be also achieved. Numerical results show the influence of the bi-crystal interface as well as the material orientation on the interaction of interface dislocation loops.

Bending Analysis of Circular Piezoelectric Semiconductor Plates Incorporating Flexoelectricity

Based on the three-dimensional(3D)basic equations of piezoelectric semiconductors(PSs),we establish a two-dimensional(2D)deformation-polarization-carrier coupling bending model for PS structures,taking flexoelectricity into consideration.The analytical solutions to classical flexure of a clamped circular PS thin plate are derived.With the derived analytical model,we numerically investigate the distributions of electromechanical fields and the concentration of electrons in the circular PS thin plate under an upward concentrated force.The effect of flexoelectricity on the multi-field coupling responses of the circular PS plate is studied.The obtained results provide theoretical guidance for the design of novel PS devices.

内含弹性介质功能梯度压电球壳的径向振动调控

针对内含弹性介质的功能梯度压电球壳的径向振动问题,利用变量替换技术,求得了解析解.该解适用于材料参数沿厚度按幂律变化且密度的梯度指标可与其它物理量的梯度指标不同的功能梯度压电球壳,克服了以往分析中所有材料参数梯度指标均假设为相等的局限.数值结果表明,功能梯度压电球壳的径向振动特性可利用材料参数梯度指标、内部弹性介质的刚度以及内外径比进行有效调控.

Electromechanical Fields Near a Circular PN Junction Between Two Piezoelectric Semiconductors

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.

WAVES IN PRE-STRETCHED INCOMPRESSIBLE SOFT ELECTROACTIVE CYLINDERS:EXACT SOLUTION

This paper studies wave propagation in a soft electroactive cylinder with an under- lying finite deformation in the presence of an electric biasing field. Based on a recently proposed nonlinear framework for electroelastieity and the associated linear incremental theory, the basic equations governing the axisymmetric wave motion in the cylinder, which is subjected to homo- geneous pre-stretches and pre-existing axial electric displacement, are presented when the elec- troactive material is isotropic and incompressible. Exact wave solution is then derived in terms of （modified） Bessel functions. For a prototype model of nonlinear electroactive material, illus- trative numerical results are given. It is shown that the effect of pre-stretch and electric biasing field could be significant on the wave propagation characteristics.

Electrical Response of a Multiferroic Composite Semiconductor Fiber Under a Local Magnetic Field

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.