Xue-Qian Fang

Dynamic stress and electric displacement around a nano-fiber in piezoelectric nanocomposites under electro-elastic waves

In piezoelectric nanocomposites, surface/interface stress and electric displacement have a great effect on the strength of structures. In this work, predicated on nanoscale size-effects, the dynamic stress along the interface of a cylindrical piezoelectric nano-fiber in piezoelectric nanocomposites under electro-elastic waves is studied. The surface/interface model of Gurtin and Murdoch is extended to the case of piezoelectric interface, and the coupling of stress and electric displacement is considered. By introducing a function, the governing equation in piezoelectric materials is decoupled. The displacement and electric potential are expressed by a wave function. The dynamic stress concentration around the nano-fiber is obtained. Through analysis, it is found that the coupling of stress and electric displacement at the surface/interface shows important effect on the dynamic stress and electric displacement around the nano-fiber. The surface/interface effect is also related to the frequency of electro-elastic waves, and the properties of the nano-fiber and the interface. To show the accuracy for certain given parameters, comparison is made with existing results.

Surface effect on size-dependent wave propagation in nanoplates via nonlocal elasticity

Within the framework of nonlocal elasticity, the surface layer model is proposed to investigate the wave propagation characteristics in a single-layered nanoplate. The general solutions of nonlocal governing equations are expressed using partial wave technique and the nonclassical boundary conditions are derived. The dispersion relation with the effects of surface and nonlocal small-scale is obtained, and the size-dependent dispersion behaviour is demonstrated. The impacts of surface elasticity, residual surface stress and nonlocal parameter on the dispersion curves of the lowest-order two modes are illustrated. Numerical examples reveal that both the surface effect and nonlocal small-scale effect can obviously decrease the magnitude of phase velocity, and the thinner nanoplate corresponds to the smaller wave velocity and the narrower frequency bandwidth.

Electro-mechanical coupling properties of piezoelectric nanocomposites with coated elliptical nano-fibers under anti-plane shear

Surfaces/interfaces in nanostructures play a significant role in deciding the electro-mechanical coupling properties of piezoelectric nanocomposites. A comprehensive electro-mechanical model of nano-size is developed to predict the effective coupling properties of piezoelectric nanocomposites with coated elliptical nano-fibers. The effects of surfaces/interfaces around the coating layer and the shape of the nano-fibers on the effective elastic modulus and piezoelectric coefficient are considered. Combining the generalized self-consistent method, the electro-elastic surface/interface model, and the mapping method, a closed-form solution of the effective electro-mechanical coupling properties is given. Through numerical calculations, it is found that the elastic modulus and dielectric constant increase with the semi-major axes, while piezoelectric constant expresses different behaviors. The interface effect on the effective electro-elastic moduli is also examined.

Dynamic stress from a circular hole in a functionally graded piezoelectric/piezomagnetic material subjected to shear waves

An analytical method is applied to investigate the scattering of magneto-electro-elastic waves and dynamic stress around a circular hole in a functionally graded piezoelectric/piezomagnetic material layer. Analytical solutions of the wave, electric and magnetic fields are expressed by employing a wave function expansion method. Analyses show that the piezoelectric and piezomagnetic properties greatly affect the dynamic stress in the region of the intermediate frequency, and the effect increases with increasing non-homogeneous parameter. The effects of the incident wave number and non-homogeneous parameter of the materials on the dynamic stress and electric field are also examined.

Interface energy effect on the dispersion relation of nano-sized cylindrical piezoelectric/piezomagnetic composites.

Interface between the constituents plays an important role in the non-destructive detection of smart piezoelectric/piezomagnetic devices. The propagation of SH waves in nano-sized cylindrically multiferroic composites consisting of a piezoelectric layer and a piezomagnetic central cylinder is investigated, and the size-dependent dispersion relation with interface effect is derived. The general solutions of decoupled governing equation in different regions are expressed by using Bessel functions, and the unknown coefficients are determined by satisfying the boundary conditions at the inner interface with negligible thickness and the outer surface of the structure. Through the numerical examples of dispersion relation, it is found that the interface around the nano-cylinder may remarkably reduce the phase velocity, depending on the combination of the value of thickness ratio and the surface condition. The interface shows different effect on the first and second modes of dispersion relation.

Scattering of Thermal Waves and Unsteady Effective Thermal Conductivity of Particular Composites with Functionally Graded Interface

In this study, thermal wave method is applied to investigate the unsteady effective thermal conductivity of particular composites with a functionally graded interface, and the analytical solution of the problem is obtained. The Fourier heat conduction law is applied to analyze the propagation of thermal waves in the particular composite. The scattering and refraction of thermal waves by a spherical particle with an inhomogeneous interface layer in the matrix are analyzed, and the results of the single scattering problem are applied to the composite medium. The wave fields in different material layers are expressed by employing spherical wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions of the layers. The theory of Waterman and Truell is applied to obtain the effective propagating wave number and the unsteady effective thermal conductivity of composites. Through the numerical examples, it is found that in different region of wave frequency, the effect of the thickness of the interface on the unsteady effective thermal conductivity of composites shows great difference. The effect of the thermal conductivity ratio of the particles and matrix on the unsteady effective thermal conductivity is closely related to the incident frequency of thermal waves. The variation of the interface properties between the particles and matrix also expresses great effect on the unsteady effective thermal conductivity of composites. Finally, comparison with the results obtained from other methods is made.

Dynamic stress concentration of a circular cutout buried in semi-infinite plates subjected to flexural waves

In this paper, based on the theory of elastic thin plates, applying the image method and the wave function expansion method, multiple scattering of elastic waves and dynamic stress concentration in semi-infinite plates with a circular cutout are investigated, and the general solutions of this problem are obtained. As an example, the numerical results of dynamic stress concentration factors are graphically presented and discussed. Numerical results show that the analytical results of scattered waves and dynamic stress in semi-infinite plates are different from those in infinite plates when the distance ratio b/a is comparatively small. In the region of low frequency and long wavelength, the maximum dynamic stress concentration factors occur on the illuminated side of scattered body with θ= π, but not on the side of cutout with θ=π/2. As the incidence frequency increases (the wavelength becomes short), the dynamic stress on the illuminated side of cutout becomes little, and the dynamic stress on the shadow side becomes great.

Surface effects on the scattering of compressional waves by a piezoelectric nano-cylinder

Based on the surface piezoelectricity model, surface effects on the scattering behaviors of plane compressional waves by an embedded piezoelectric cylinder with nanoscale radius are investigated. The existence of surface stresses and surface electric displacements exerting on the boundary conditions is taken into account through generalized Young-Laplace equations, and the potential function method is employed to derive the analytical expressions of wave fields and electric potential. For two typical incident frequencies, the influence of surface properties on the distribution of electroelastic fields around the cylinder is discussed in detail. In comparison with the results obtained from the classical continuum theories, it is found that the surface effects play a prominent role on the dynamic stress and electric field concentrations, especially under a high-frequency excitation.

Dynamic stress around two holes buried in a functionally graded piezoelectric material layer under electro-elastic waves

A theoretical method is presented to study the multiple scattering of electro-elastic waves resulting from two subsurface holes in a functionally graded piezoelectric material (FGPM) layer bonded to a homogeneous piezoelectric material, and the dynamic stress around the holes is also presented. The analytical solutions of wave fields are expressed by employing wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions at the surface and around the holes. The mechanical and electrical boundary conditions at the free surface of the structure are satisfied by using the image method. Analyses show that the piezoelectric property and the distance between the two holes express great effect on the dynamic stress around the holes, and the effect increases with the decrease of the thickness of FGPM layer. If the material properties of the homogeneous piezoelectric material are greater than those at the surface of the structure, the dynamic stress increases dramatically due to the piezoelectric property and the distance between the two holes. The angular distribution of electric displacement under different parameters is also presented. The accuracy and efficiency of the solving method are demonstrated by the comparison of selected results with the solutions obtained by using finite element software ANSYS.

Effective shear modulus of piezoelectric film embedded with square nano-fibers under anti-plane shear waves

For piezoelectric films, the surface/interface energy around the nano-fibers plays an important role in predicting the overall properties. Square nano-fibers are very popular in piezoelectric films. This paper presents the size-dependent dynamic effective elastic modulus of piezoelectric films under anti-plane shear waves. The average electro-elastic field resulting from the randomly distributed nano-fibers is solved by applying the effective field method. To express the coupling fields in the effective field, the mapping method and wave function expansion method are introduced. The closed-form solution of piezoelectrically stiffened shear modulus with respect to the shape and volume fraction of fibers and surface/interface properties is obtained. The interacting effect of surface/interface and square shape of nano-fibers is examined.