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1.
Summary In this paper, the eigen-equations governing antiplane stress singularities in a bonded piezoelectric wedge are derived analytically.
Boundary conditions are set as various combinations of traction-free, clamped, electrically open and electrically closed ones.
Application of the Mellin transform to the stress/electric displacement function or displacement/electric potential function
and particular boundary and continuity conditions yields identical eigen-equations. All of the analytical results are tabulated.
It is found that the singularity orders of a bonded bimaterial piezoelectric wedge may be complex, as opposed to those of
the antiplane elastic bonded wedge, which are always real. For a single piezoelectric wedge, the eigen-equations are independent
of material constants, and the eigenvalues are all real, except in the case of the combination C–D. In this special case,
C–D, the real part of the complex eigenvalues is not dependent on material constants, while the imaginary part is.
Received 26 March 2002; accepted for publication 2 July 2002 相似文献
2.
《International Journal of Solids and Structures》2004,41(5-6):1625-1643
An analytical solution for the cylindrical bending vibrations of linear piezoelectric laminated plates is obtained by extending the Stroh formalism to the generalized plane strain vibrations of piezoelectric materials. The laminated plate consists of homogeneous elastic or piezoelectric laminae of arbitrary thickness and width. Fourier basis functions for the mechanical displacements and electric potential that identically satisfy the equations of motion and the charge equation of electrostatics are used to solve boundary value problems via the superposition principle. The coefficients in the infinite series solution are determined from the boundary conditions at the edges and continuity conditions at the interfaces between laminae, which are satisfied in the sense of Fourier series. The formulation admits different boundary conditions at the edges of the laminated piezoelectric composite plate. Results for laminated elastic plates with either distributed or segmented piezoelectric actuators are presented for different sets of boundary conditions at the edges. 相似文献
3.
I. V. Andrianov H. Topol D. Weichert 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(11):999-1007
In A fibre-reinforced 2D composite material with elastic fibres and viscoelastic, isotropic matrix is studied. Starting from
the solution of a reference-problem with elastic matrix material the elastic matrix parameters are substituted by their viscoelastic
correspondents in the Laplace domain. For simplification the time-dependent solution is approximated by using limiting value
theorems that give information about the time-dependent solution for t → 0 and t → ∞. Then the method of asymptotically equivalent functions is used and illustrated with examples of a steel fibre in a PMMA
matrix. The analytical solutions are compared with their numerical counterparts. In summary it can be stated that this paper
is a further contribution to the vast literature about the application of the correspondence principle to the solution of
special problems of the linear viscoelasticity. 相似文献
4.
V. S. Kirilyuk 《International Applied Mechanics》2008,44(2):150-157
The elastic stress state in a piezoelectric body with an arbitrarily oriented elliptic crack under mechanical and electric
loads is analyzed. The solution is obtained using triple Fourier transform and the Fourier-transformed Green’s function for
an unbounded piezoelastic body. Solving the problem for the case of a crack lying in the isotropy plane, for which there is
an exact solution, demonstrates that the approach is highly efficient. The distribution of the stress intensity factors along
the front of a crack in a piezoelectric body under uniform mechanical loading is analyzed numerically for different orientations
of the crack
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 39–48, February 2008. 相似文献
5.
Thermal stresses and shakedown in wheel/rail contact 总被引:1,自引:0,他引:1
Summary Sliding friction between railway wheels and rails results in considerable contact temperatures and gives rise to severe thermal
stresses at the surfaces of the wheels and rails. An approximate analytical solution is presented for a line contact model.
The increased bulk temperature of the wheel after a long period of constant operating conditions is also taken into account.
The thermal stresses have to be superimposed on the mechanical contact stresses. They reduce the elastic limit of the wheel
and rail, and yielding begins at lower mechanical loads. When residual stresses build up during the initial cycles of plastic
deformation, the structure can carry higher loads with a purely elastic response in subsequent load cycles. This phenomenon
is referred to as shakedown. Due to the distribution of temperature, the rail surface is generally subjected to higher stresses
than the wheel surface. This can cause structural changes in the rail material and hence rail damage.
Received 7 May 2002; accepted for publication 3 September 2002 相似文献
6.
《International Journal of Solids and Structures》2007,44(7-8):2509-2522
A mathematical model for the vibration of beams with piezoelectric inclusions is presented. The piezoelectric inclusion in a non-piezoelectric matrix (host beam) is analyzed as two inhomogeneous inclusion problems, elastic and dielectric, by using Eshelby’s equivalent inclusion method. The natural frequency of the beam is determined from the variational principle in Rayleigh quotient form, which is expressed as functions of the elastic strain energy and dielectric energy of the piezoelectric inclusion. The Euler–Bernoulli beam theory and Rayleigh–Ritz approximation technique are used in the present analysis. In addition, a parametric study is conducted to investigate the influence of the energies due to piezoelectric coupling on the natural frequency of the beam. 相似文献
7.
The solution of the Saint-Venant’s Problem for a slender compound piezoelectric beam presented in this paper generalizes the
recent solution by the authors and E. Harash (J. Appl. Mech. 11:1–10, 2007) for a homogeneous piezoelectric beam and the solution for a compound elastic beam developed by O. Rand and the first author
(Analytical Methods in Anisotropic Elasticity with Symbolic Computational Tools, Birkhauser, Boston, 2005). Justification for this approximation emerges from the St. Venant’s Principle. The stress, strain and (electrical) displacement
components (“solution hypothesis”) are presented as a set of initially assumed expressions involving twelve tip loading parameters,
six unknown weight coefficients, and three pairs of torsion/bending functions of two variables. Each pair of functions satisfies
the so-called coupled non-homogeneous Neumann problem (CNNP) in the cross-sectional domain. The work develops concepts of the torsion/bending functions, the torsional rigidity
and piezoelectric shear center, the tip coupling matrix, for a compound piezoelectric beam. Examples of exact and approximate
solutions for rectangular laminated beams made of transtropic materials are presented.
相似文献
8.
9.
Summary A piezoelectric layer bonded to the surface of an elastic structure is considered. The piezoelectric and the elastic layers
are infinite along the x-axis and have finite thickness in the y-direction. The polarization direction of the piezoelectric material is along the y-axis. By means of the method of singular integral equations, the solution in a Laplace transform plane is demonstrated. Laplace
inversion yields the results in the time domain. Numerical values of the crack tip fields under in-plane transient electromechanical
loading are obtained. The influence of layers thickness on stress and electric displacement intensity factors is investigated.
Received 16 March 2000; accepted for publication 16 August 2000 相似文献
10.
Transient response of an insulating crack between dissimilar piezoelectric layers under mechanical and electrical impacts 总被引:1,自引:0,他引:1
Summary The dynamic response of an interface crack between two dissimilar piezoelectric layers subjected to mechanical and electrical
impacts is investigated under the boundary condition of electrical insulation on the crack surface by using the integral transform
and the Cauchy singular integral equation methods. The dynamic stress intensity factors, the dynamic electrical displacement
intensity factor, and the dynamic energy release rate (DERR) are determined. The numerical calculation of the mode-I plane
problem indicates that the DERR is more liable to be the token of the crack growth when an electrical load is applied. The
dynamic response shows a significant dependence on the loading mode, the material combination parameters as well as the crack
configuration. Under a given loading mode and a specified crack configuration, the DERR of an interface crack between piezoelectric
media may be decreased or increased by adjusting the material combination parameters. It is also found that the intrinsic
mechanical-electrical coupling plays a more significant role in the dynamic fracture response of in-plane problems than that
in anti-plane problems.
Received 4 September 2001; accepted for publication 23 July 2002
The work was supported by the National Natural Science Foundation under Grant Number 19891180, the Fundamental Research Foundation
of Tsinghua University, and the Education Ministry of China. 相似文献
11.
The paper establishes the relationship between the solutions of the static contact problems of elasticity (no friction) for
an isotropic half-plane and problems of electroelasticity for a transversely isotropic piezoelectric half-plane with the boundary
perpendicular to the polarization axis. This allows finding the contact characteristics in the electroelastic case from the
known elastic solution, without the need to solve the electroelastic problem. The contact problems of electroelasticity for
different types of wedge-shaped punches (flat punch with rounded one or two edges, half-parabolic punch, and a periodic system
of punches) are solved as examples
Translated from Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 55–70, November 2008. 相似文献
12.
X.-F. Li 《Archive of Applied Mechanics (Ingenieur Archiv)》2003,72(10):745-758
Summary The dynamic problem of an impermeable crack of constant length 2a propagating along a piezoelectric ceramic strip is considered under the action of uniform anti-plane shear stress and uniform
electric field. The integral transform technique is employed to reduce the mixed-boundary-value problem to a singular integral
equation. For the case of a crack moving in the mid-plane, explicit analytic expressions for the electroelastic field and
the field intensity factors are obtained, while for an eccentric crack moving along a piezoelectric strip, numerical results
are determined via the Lobatto–Chebyshev collocation method for solving a resulting singular integral equation. The results
reveal that the electric-displacement intensity factor is independent of the crack velocity, while other field intensity factors
depend on the crack velocity when referred to the moving coordinate system. If the crack velocity vanishes, the present results
reduce to those for a stationary crack in a piezoelectric strip. In contrast to the results for a stationary crack, applied
stress gives rise to a singular electric field and applied electric field results in a singular stress for a moving crack
in a piezoelectric strip.
Received 14 August 2001; accepted for publication 24 September 2002
The author is indebted to the AAM Reviewers for their helpful suggestions for improving this paper. The work was supported
by the National Natural Science Foundation of China under Grant 70272043. 相似文献
13.
B. L. Wang Y. W. Mai Y. G. Sun 《Archive of Applied Mechanics (Ingenieur Archiv)》2003,73(5-6):434-447
Summary A piezoelectric material layer bonded to an elastic substrate is investigated. The piezoelectric layer contains an edge crack that is perpendicular to the surface of medium. The poling axis of the piezoelectric layer is parallel to its edge. The elastic layer can be an ideal insulator or an ideal conductor. The Fourier transform technique is used to reduce the problem to a solution of singular integral equations. Both impermeable crack and permeable crack assumptions are considered. Stress and electric displacement intensity factors are investigated for different dimensions of the medium. A double-edge cracked symmetric piezoelectric laminate under symmetric electro-mechanical load is also investigated.
BLW would like to thank the National Science Foundation of China (#10102004) and the City University of Hong Kong for the support of this work (DAG #7100219). YGS also thanks the Multidiscipline Scientific Research Foundation Project (HIT. MD 2001. 39) of the Harbin Institute of Technology and the SRF for ROCS, SEM. 相似文献
14.
V. S. Kirilyuk 《International Applied Mechanics》2008,44(3):320-330
The paper addresses a thermoelectroelastic problem for a piezoelectric body with an arbitrarily shaped plane crack in a plane
perpendicular to the polarization axis under a symmetric thermal load. A relationship between the intensity factors for stress
(SIF) and electric displacement (EDIF) in an infinite piezoceramic body with a crack under a thermal load and the SIF for
a purely elastic body with a crack of the same shape under a mechanical load is established. This makes it possible to find
the SIF and EDIF for an electroelastic material from the elastic solution without the need to solve specific problems of thermoelasticity.
The SIF and EDIF for a piezoceramic body with an elliptic crack and linear distribution of temperature over the crack surface
are found as an example
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 96–108, March 2008. 相似文献
15.
H. J. Ding H. M. Wang W. Q. Chen 《Archive of Applied Mechanics (Ingenieur Archiv)》2002,72(8):545-553
Summary The spherically symmetric dynamic thermoelastic problem for a special nonhomogeneous transversely isotropic elastic hollow
sphere is formulated by introduction of a dependent variable and separation of variables technique. The derived solution can
be degenerated into that for a homogeneous transversely isotropic hollow sphere, a nonhomogeneous isotropic hollow sphere
or a solid sphere. The present method, allow to avoid integral transforms, is suited for a hollow sphere of arbitrary thickness
subjected to arbitrary spherical symmetric thermal and mechanical loads, and is convenient in dealing with different boundary
conditions of dynamic thermoelasticity . The numerical calculation involved is easy to be performed and its results are also
presented.
Received 30 October 2001; accepted for publication 21 February 2002
The work was supported by the National Natural Science Foundation of China (No. 10172075 and No. 10002016) 相似文献
16.
Modified H-R mixed variational principle for magnetoelectroelastic bodies and state-vector equation 总被引:1,自引:0,他引:1
Based upon the Hellinger-Reissner (H-R) mixed variational principle for three-dimensional elastic bodies, the modified H-R mixed variational theorem for magnetoelectroelastic bodies was established. The state-vector equation of magnetoelectroelastic plates was derived from the proposed theorem by performing the variational operations. To lay a theoretical basis of the semi-analytical solution applied with the magnetoelectroelastic plates, the state-vector equation for the discrete element in plane was proposed through the use of the proposed principle. Finally, it is pointed out that the modified H-R mixed variational principle for pure elastic, single piezoelectric or single piezomagnetic bodies are the special cases of the present variational theorem. 相似文献
17.
Summary In this paper, we study a two-dimensional electroelastic problem of an infinite piezoelectric body with two circular piezoelectric
inhomogeneities, one of which contains a crack. We formulate the stress intensity factor (SIF) analytically and investigate
it numerically. The problem is solved based on Bueckner's principle, and is reduced to a problem of a singular integral equation
of the first kind with respect to the distribution function of screw dislocation. The effect of interaction between the two
inhomogeneities and the crack on the electroelastic field as well as the control of the SIF by electrical loads is investigated.
Received 18 April 2000; accepted for publication 24 October 2000 相似文献
18.
Stiffness relations for voltage-dependent contact mechanics of piezoelectric material are derived for an indenter of arbitrary planform under normal force, centrally or non-centrally applied, and electric charge distribution at the base. Relations between indentation depth, indentation force, electric potential and electric charge are explicitly given in terms of indenter's geometry and piezoelectric material constants. The analysis covers indenters with non-flat base approximated by a second-order surface; elliptic paraboloid is considered as an example. In the case of the elliptic non-flat planform, the derived stiffness relations are exact; otherwise, they are approximate and are shown to have good accuracy. The stiffness relations are given in elementary functions and are obtained by utilizing the recently established principle of correspondence between the piezoelectric and purely elastic problems. Besides contributing to extension of Hertzian mechanics to piezoelectric materials, these results are essential for quantitative interpretation of the scanning probe microscopy and piezoelectric nanoindentation data on piezoelectric, ferroelectric, and multiferroic materials. 相似文献
19.
压电层合板热屈曲问题的精确分析 总被引:8,自引:0,他引:8
本文在作者们以前工作的基础上导出了热压电介弹性稳定性问题的控制微分方程,提出了热压电层合板热屈曲问题的数学和学解法。由于最后所得特征值问题的复杂性,热屈曲临界必须数值求解。文中对不同压电材非压电材料层构成的层合板作了具体计算,考虑了压电性对屈曲温度的影响。 相似文献
20.
Summary This paper is concerned with a semi-infinite interfacial crack between two bonded dissimilar elastic strips with equal thickness.
Solutions for the complex stress intensity factor (SIF) and energy release rate (ERR) are obtained in closed form under in-plane
deformations. During the procedure, the mixed boundary-value problem is reduced by means of the conformal mapping technique
to the standard Riemann–Hilbert problem. In some limiting cases, the present solutions can cover the results found in literature.
Received 21 February 2002; accepted for publication 2 July 2002
X.-F Wu's work was supported in part by the Milton E. Mohr Research Fellowship (2001, 2002) of the Engineering College at
University of Nebraska-Lincoln. 相似文献