Dynamic anti-plane characteristic on an infinite piezoelectric medium with a movable rigid cylindrical inclusion

Scattering and dynamic stress concentrations of time harmonic SH-wave in an infinite elastic piezoelectric medium with a movable rigid cylindrical inclusion are studied in this paper with the help of complex variable and wave function expansion method. The relations that a movable rigid cylindrical inclusion depends on intensity of incident wave and electric field are revealed. The expressions of dynamic stress at the edge of the inclusion are obtained. Numerical calculations are made with different wave numbers and different piezoelectric characteristic parameters. The calculating results show that dynamic stress concentrations at the edge of the inclusion have linear dependence on the incident electric field. And dynamic analyses are very important for an infinite piezoelectric medium with a movable rigid cylindrical inclusion at larger piezoelectric characteristic parameters.

THE ELECTRO-ELASTIC FIELD OF THE INFINITE PIEZOELECTRIC MEDIUM WITH TWO PIEZOELECTRIC CIRCULAR CYLINDRICAL INCLUSIONS

The electro-elastic field of the infinite piezoelectric medium with two piezoelectric circular cylindrical inclusions is derived under the antiplane shear stresses and inplane electric fields.The analytical solution is obtained.The proposed method is based upon the use of conformal mapping and the theorem of analytic continuation.From the results obtained,it can be found that the electro-elastic field depends on the material constants of individual phases,the geometric parameters of the system and the applied antiplane shear stresses and electric fields at infinity.In addition,the specific cases when two circular cylindrical inclusions are tangent to each other and they are holes and/or rigid ones,are also studied in this paper.

Dynamic anti-plane interaction between an impermeable crack and a circular cavity in an infinite piezoelectric medium

Wave propagation in an infinite elastic piezoelectric medium with a circular cavity and an impermeable crack subjected to steady-state anti-plane shearing was studied based on Green's function and the crack-division technique.Theoretical solutions were derived for the whole elastic displacement and electric potential field in the interaction between the circular cavity and the impermeable crack.Expressions were obtained on the dynamic stress concentration factor(DSCF) at the cavity's edge,the dynamic stress intensity factor(DSIF) and the dynamic electric displacement intensity factor(DEDIF) at the crack tip.Numerical solutions were performed and plotted with different incident wave numbers,parameters of piezoelectric materials and geometries of the structure.Finally,some of the calculation results were compared with the case of dynamic anti-plane interaction of a permeable crack and a circular cavity in an infinite piezoelectric medium.This paper can provide a valuable reference for the design of piezoelectric actuators and sensors widely used in marine structures.

On Propagation of Rayleigh Type Surface Wave in a Micropolar Piezoelectric Medium

In the present paper, the governing equations of a linear transversely isotropic micropolar piezoelectric medium are specialized for x-z plane after using symmetry relations in constitutive coefficients. These equations are solved for the general surface wave solutions in the medium. Following radiation conditions in the half-space, the particular solutions are obtained, which satisfy the appropriate boundary conditions at the stress-free surface of the half-space. A secular equation for Rayleigh type surface wave is obtained. An iteration method is applied to compute the non-dimensional wave speed of the Rayleigh surface wave for specific material parameters. The effects of piezoelectricity, non-dimensional frequency and non-dimensional material constant, charge free surface and electrically shorted surface are shown graphically on the wave speed of Rayleigh wave.

A MIXED ELECTRIC BOUNDARY VALUE PROBLEM FOR AN ANTI-PLANE PIEZOELECTRIC CRACK

The analytical continuation method is adopted to solve a mixed electric boundary value problem for a piezoelectric medium under anti-plane deformation.The crack face is partly conductive and partly impermeable.The results show that the stress intensity factor is identical with the mode Ⅲ stress intensity factor independent of the conducting length.But the electric field and the electric displacement are dependent on the electric boundary conditions on the crack faces and are singular not only at the crack tips but also at the junctures between the impermeable part and conducting portions.

APPLICATION OF TREFFTZ BEM TO ANTI-PLANE PIEZOELECTRIC PROBLEM

Anti-plane electroelastic problems are studied by the Trefftz boundary element method （BEM） in this paper. The Trefftz BEM is based on a weighted residual formulation and indirect boundary approach. In particular the point-collocation and Galerkin techniques, in which the basic unknowns are the retained expansion coefficients in the system of complete equations, are considered. Furthermore, special Trefftz functions and auxiliary functions which satisfy exactly the specified boundary conditions along the slit boundaries are also used to derive a special purpose element with local defects. The path-independent integral is evaluated at the tip of a crack to determine the energy release rate for a mode Ⅲ fracture problem. In final, the accuracy and efficiency of the Trefftz boundary element method are illustrated by an example and the comparison is made with other methods.

TWO-DIMENSIONAL ELECTROELASTIC FUNDAMENTAL SOLUTIONS FOR GENERAL ANISOTROPIC PIEZOELECTRIC MEDIA

Explicit fomulas for 2-D electroelastic fundamental solutions in general anisotropic piezoelectric media subjected to a line force and a line charge are obtained by using the plane wave decomposition method and a subsequent application of the residue calculus. 'Anisotropic' means that any material symmetry restrictions are not assumed. 'Two dimensional' includes not only in-plane problems but also anti-plane problems and problems in which in-plane and anti-plane deformations couple each other. As a special case, the solutions for transversely isotropic piezoelectric media are given.

EXACT STATIC ANALYSIS OF A ROTATING PIEZOELECTRIC SPHERICAL SHELL

An exact analysis of a rotating piezoelectric spherical shell with arbitrary thickness is given. Three displacement functions are introduced to simplify the basic equations of a spherically isotropic, piezoelectric medium. By expanding the displacement functions as well as the electric potential in terms of spherical harmonics, the basic equations of equilibrium are converted to an uncoupled Euler type, second order ordinary differential equation and a coupled system of three second order ordinary differential equations. A general solution to the homogeneous equations of equilibrium is then derived. The static analysis of a rotating spherical shell is performed and the numerical example is presented. (Edited author abstract) 13 Refs.

The Static Solution for the Layered Piezoelectric Bounded Domain with Side Face Load by the Modified SBFEM

The static response of two-dimensional horizontal layered piezoelectric bounded domain with side face load was investigated.In this paper,the modified scaled boundary finite element method(SBFEM)is provided as an effective semi analytical methodology.The method is used to solve the static problem for the layered piezoelectric bounded domain.The scaling line definition extends the SBFEM to be more suitable for analyzing the multilayered piezoelectric bounded domain.It avoids the limitations of original SBFEM in modeling the horizontal layered bounded domain.The modified SBFEM governing equation with piezoelectric medium is derived by introducing Duality variable in the Hamilton system.This derivation technology makes the progress be concise.The novel displacement and electric governing equations of the modified SBFEM is given together by the first time.The node forces can be expressed as power exponent function with radial coordinate by introducing the auxiliary variable and using the eigenvalue decomposition.The novel modified SBFEM solution of layered bounded domain with piezoelectric medium is solved.The new power expansion function of layered piezoelectric medium with side face load is proposed.This technology significantly extends the application range of modified SBFEM.The novel treatment of side face load for the layered piezoelectric bounded domain is proposed.Numerical studies are conducted to demonstrate the accuracy of proposed technique in handling with the static problem of layered bounded domain with piezoelectric medium for side face load.The influence of the side face load type and depth are discussed in detail.

Non-local theory solution to two collinear limited-permeable mode-I cracks in a piezoelectric/piezomagnetic material plane

The non-local theory solution to two collinear limited-permeable mode-1 cracks in a piezoelectric/piezomagnetic medium was investigated by using the generalized Almansi＇s theorem and the Schmidt method in the present paper. The problem was for- mulated through Fourier transformation into two pairs of dual integral equations, in which the unknown variables are the dis- placement jumps across the crack surfaces. For solving the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Numerical examples were provided to show the effects of the crack length, the distance between the two collinear cracks, the lattice parameter, the electric permittivity and the magnetic permeability of the air inside the crack on the stress fields, the electric displacement fields and the magnetic flux fields near the crack tips in a piezoeleetric/piezomaguetic medium. Different from the classical solutions, the present solution exhibits no stress, electric displacement and magnetic flux singularities at the crack tips in a piezoelectric/piezomagnetic medium.