共查询到20条相似文献,搜索用时 31 毫秒
1.
Holm Altenbach Victor A. Eremeyev Leonid P. Lebedev Leonardo A. Rendón 《Archive of Applied Mechanics (Ingenieur Archiv)》2010,80(3):217-227
Acceleration waves in nonlinear thermoelastic micropolar media are considered. We establish the kinematic and dynamic compatibility
relations for a singular surface of order 2 in the media. An analogy to the Fresnel–Hadamard–Duhem theorem and an expression
for the acoustic tensor are derived. The condition for acceleration wave’s propagation is formulated as an algebraic spectral
problem. It is shown that the condition coincides with the strong ellipticity of equilibrium equations. As an example, a quadratic
form for the specific free energy is considered and the solutions of the corresponding spectral problem are presented. 相似文献
2.
Baljeet Singh 《Archive of Applied Mechanics (Ingenieur Archiv)》2006,75(8-9):513-520
The propagation of plane waves in a fibre-reinforced, anisotropic, generalized thermoelastic media is discussed. The governing
equations in x–y plane are solved to obtain a cubic equation in phase velocity. Three coupled waves, namely quasi-P, quasi-SV and quasi-thermal
waves are shown to exist. The propagation of Rayleigh waves in stress free thermally insulated and transversely isotropic
fibre-reinforced thermoelastic solid half-space is also investigated. The frequency equation is obtained for these waves.
The velocities of the plane waves are shown graphically with the angle of propagation. The numerical results are also compared
to those without thermal disturbances and anisotropy parameters. 相似文献
3.
Wang Zikun 《Acta Mechanica Sinica》1994,10(1):49-60
Using a method of potential functions introduced successively to integrate the field equations of three-dimensional problems
for transversely isotropic piezoelectric materials, we obtain the so-called general solution in which the displacement components
and electric potential functions are represented by a singular function satisfying some special partial differential equations
of 6th order. In order to analyse the mechanical-electric coupling behaviour of penny-shaped crack for above materials, another
form of the general solution is obtained under cylindrical coordinate system by introducing three quasi-harmonic functions
into the general equations obtained above. It is shown that both the two forms of the general solutions are complete. Furthermore,
the mechanical-electric coupling behaviour of penny-shaped crack in transversely isotropic piezoelectric media is analysed
under axisymmetric tensile loading case, and the crack-tip stress field and electric displacement field are obtained. The
results show that the stress and the electric displacement components near the crack tip have (r
−1/2) singularity.
The project supported by the Natural Science Foundation of Shaanxi Province, China 相似文献
4.
5.
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
6.
Zheng-Hua Qian Feng Jin Peng Li Sohichi Hirose 《International Journal of Solids and Structures》2010,47(25-26):3513-3518
In this paper, we analyze the propagation of Bleustein–Gulyaev waves in an unbounded piezoelectric half-space loaded with a viscous liquid layer of finite thickness within the linear elastic theories. Exact solutions of the phase velocity equations are obtained in the cases of both electrically open circuit and short circuit by solving the equilibrium equations of piezoelectric materials and the diffusion equation of viscous liquid. A PZT-5H/Glycerin system is selected to perform the numerical calculation. The results show that the mass density and the viscous coefficient have different effects on the propagation attenuation and phase velocity under different electrical boundary conditions. In particular, the penetration depth of the waves is of the same order as the wavelength in the case of electrically short circuit. These effects can be used to manipulate the behavior of the waves and have implications in the application of acoustic wave devices. 相似文献
7.
James R. Rice 《Journal of Elasticity》1988,20(2):131-142
The Eshelby tensor E has vanishing divergence in a homogeneous elastic material, whereas the invariance of the crack tip J integral suggests, in accord with known solutions, that the product rE will have a finite limit at the tip. Here r is distance from the tip. These considerations are shown to lead to two general integrals of the equations governing singular crack tip deformation fields. Some of their consequences are discussed for analysis of crack tip fields in linear and nonlinear materials. 相似文献
8.
纳米科技的快速发展使压电纳米结构在纳米机电系统中得到广泛应用,形成了诸如纳米压电电子学等新的研究方向.与传统的宏观压电材料相比,在纳米尺度下压电材料往往呈现出不同的力学特性,而造成这种差异的原因之一便是表面效应.本文基于Stroh公式、Barnett-Lothe积分矩阵及表面阻抗矩阵,研究计入表面效应的任意各向异性压电半空间中的表面波传播问题,导出了频散方程.针对横观各向同性压电材料,假设矢状平面平行于材料各向同性面,发现Rayleigh表面波和B-G波解耦,并得到各自的显式频散方程.结果表明,Rayleigh表面波的波速小于偏振方向垂直于表面的体波,而B-G波的波速小于偏振方向垂直于矢状平面的体波.以PZT-5H材料为例,用数值方法考察表面残余应力和电学边界条件对表面波频散特性的影响发现:表面残余应力只对第一阶Rayleigh波有明显的影响;电学开路情形的B-G波比电学闭路情形的B-G波传播快.本文工作可为纳米表面声波器件的设计或压电纳米结构的无损检测提供理论依据. 相似文献
9.
Michael Y. Shatalov Arthur G. Every Alfred S. Yenwong-Fai 《International Journal of Solids and Structures》2009,46(3-4):837-850
A study concerning the propagation of free non-axisymmetric waves in a homogeneous piezoelectric cylinder of transversely isotropic material with axial polarization is carried out on the basis of the linear theory of elasticity and linear electro-mechanical coupling. The solution of the three dimensional equations of motion and quasi-electrostatic equation is given in terms of seven mechanical and three electric potentials. The characteristic equations are obtained by the application of the mechanical and two types of electric boundary conditions at the surface of the piezoelectric cylinder. A novel method of displaying dispersion curves is described in the paper and the resulting dispersion curves are presented for propagating and evanescent waves for PZT-4 and PZT-7A piezoelectric ceramics for circumferential wave numbers m = 1, 2, and 3. It is observed that the dispersion curves are sensitive to the type of the imposed boundary conditions as well as to the measure of the electro-mechanical coupling of the material. 相似文献
10.
A. Montanaro 《Journal of Elasticity》1999,57(1):25-53
By extending the procedure of linearization for constrained elastic materials in the papers by Marlow and Chadwick et al., we set up a linearized theory of constrained materials with initial stress (not necessarily based on a nonlinear theory).
The conditions of propagation are characterized for small-displacement waves that may be either of discontinuity type of any
given order or, in the homogeneous case, plane progressive. We see that, just as in the unconstrained case, the laws of propagation
of discontinuity waves are the same as those of progressive waves. Waves are classified as mixed, kinematic, or ghost. Then we prove that the analogues of Truesdell"s two equivalence theorems on wave propagation in finite elasticity hold for
each type of wave.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
11.
Summary This paper deals with interaction problems of elliptical and ellipsoidal inclusions under bending, using singular integral
equations of the body force method. The problems are formulated as a system of singular integral equations with Cauchy-type
or logarithmic-type singularities, where unknown functions are densities of body forces distributed in the x,y and r,θ,z directions in infinite bodies having the same elastic constants as those of the matrix and inclusions. In order to satisfy
the boundary conditions along the elliptical and the ellipsoidal boundaries, the unknown functions are approximated by a linear
combination of fundamental density functions and polynomials. The present method is found to yield the exact solutions for
a single elliptical or spherical inclusion under a bending stress field. It yields rapidly converging numerical results for
interface stresses in the interaction of inclusions.
Received 9 September 1999; accepted for publication 15 January 2000 相似文献
12.
Wave fronts admitting discontinuities only in the derivatives of the dependent variables are by convention called ‘weak’ waves. For the special case of discontinuous first-order derivatives, the fronts are customarily called ‘acceleration’ waves. If the governing equations are quasi-linear, then the weak waves are necessarily characteristic surfaces. Sometimes, these surfaces are also referred to as ‘singular surfaces’ of order r ? 1, where r stands for the order of the first discontinuous derivatives. This latter approach is adopted in this paper and applied to governing equations which form a set of first-order quasi-linear hyperbolic equations. When these equations are written in terms of singular surface coordinates, simplification occurs upon differencing equations written on the front and rear sides of the surface: a set of algebraic (‘connection’) equations is generated for the discontinuities in the normal derivatives of the dependent variables across the surface. When a similar operation is performed on the governing equations written for second-order derivatives, a set of first-order differential (‘transport’) equations is generated. 相似文献
13.
Nonlinear characteristic boundary conditions based on nonlinear multidimensional characteristics are proposed for 2‐ and 3‐D compressible Navier–Stokes equations with/without scalar transport equations. This approach is consistent with the flow physics and transport properties. Based on the theory of characteristics, which is a rigorous mathematical technique, multidimensional flows can be decomposed into acoustic, entropy, and vorticity waves. Nonreflecting boundary conditions are derived by setting corresponding characteristic variables of incoming waves to zero and by partially damping the source terms of the incoming acoustic waves. In order to obtain the resulting optimal damping coefficient, analysis is performed for problems of pure acoustic plane wave propagation and arbitrary flows. The proposed boundary conditions are tested on two benchmark problems: cylindrical acoustic wave propagation and the wake flow behind a cylinder with strong periodic vortex convected out of the computational domain. This new approach substantially minimizes the spurious wave reflections of pressure, density, temperature, and velocity as well as vorticity from the artificial boundaries, where strong multidimensional flow effects exist. The numerical simulations yield accurate results, confirm the optimal damping coefficient obtained from analysis, and verify that the method substantially improves the 1‐D characteristics‐based nonreflecting boundary conditions for complex multidimensional flows. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
14.
A. Morro 《International Journal of Non》2012,47(9):1008-1013
A non-linear rate-type constitutive equation, established by Rajagopal, provides a generalization of the Maxwell fluid. This note embodies such a constitutive equation within the scheme of materials with internal variables thus allowing also for solids with both dissipative and thermoelastic mechanisms. The compatibility with the second law of thermodynamics, expressed by the Clausius–Duhem inequality, is examined and the restrictions on the evolution equations are determined. Next the propagation condition of discontinuity waves is derived, for shock waves and acceleration waves, by regarding the body as a definite conductor. Infinitesimal shock waves and acceleration waves show similar effects. The effective acoustic tensor proves to be the sum of a thermoelastic tensor and a tensor arising from the rate-type equation. 相似文献
15.
16.
The propagation of plane vertical transverse waves at an interface of a semi-infinite piezoelectric elastic medium under the
influence of the initial stresses is discussed. The free surface of the piezoelectric elastic medium is considered to be adjacent
to vacuum. We assumed that the piezoelectric material is anisotropic of the type of a transversely isotropic crystals (hexagonal
crystal structure, class 6 mm). For an incident of vertical transverse plane wave, four types (two for the displacement and
two for the electric potential) of reflected plane waves, called quasi-longitudinal (qP) and quasi-shear vertical (qSV) waves are shown to be exist. The relations governing the reflection coefficients of these reflected waves for various boundary
conditions (mixed-free-fixed) are derived. It has been shown analytically that reflected coefficients of (qP) and (qSV) waves depend upon the angle of incidence, the parameters of electric potential, the material constants of the medium as
well as the initial stresses presented in the medium. The numerical computations of reflection coefficients for different
values of initial stresses have been carried out by computer for aluminum nitride (AlN) as an example and the results are
given in the form of graphs. Finally, particular cases are considered in the absence of the initial stresses and the electric
potential. Some of earlier studies have been compared to the special cases and shown good agreement with them. 相似文献
17.
Isaac A. García Héctor Giacomini Maite Grau 《Journal of Dynamics and Differential Equations》2011,23(2):251-281
In this paper we study the maximum number of limit cycles that can bifurcate from a focus singular point p
0 of an analytic, autonomous differential system in the real plane under an analytic perturbation. We consider p
0 being a focus singular point of the following three types: non-degenerate, degenerate without characteristic directions and
nilpotent. In a neighborhood of p
0 the differential system can always be brought, by means of a change to (generalized) polar coordinates (r, θ), to an equation over a cylinder in which the singular point p
0 corresponds to a limit cycle γ
0. This equation over the cylinder always has an inverse integrating factor which is smooth and non-flat in r in a neighborhood of γ
0. We define the notion of vanishing multiplicity of the inverse integrating factor over γ
0. This vanishing multiplicity determines the maximum number of limit cycles that bifurcate from the singular point p
0 in the non-degenerate case and a lower bound for the cyclicity otherwise. Moreover, we prove the existence of an inverse
integrating factor in a neighborhood of many types of singular points, namely for the three types of focus considered in the
previous paragraph and for any isolated singular point with at least one non-zero eigenvalue. 相似文献
18.
Maria Luisa Tonon 《Journal of Elasticity》2002,69(1-3):15-39
This paper deals with the propagation of acceleration waves in constrained linear elastic materials, within the framework
of the so-called linearized finite theory of elasticity, as defined by Hoger and Johnson in [12, 13]. In this theory, the
constitutive equations are obtained by linearization of the corresponding finite constitutive equations with respect to the
displacement gradient and significantly differ from those of the classical linear theory of elasticity. First, following the
same procedure used for the constitutive equations, the amplitude condition for a general constraint is obtained. Explicit
results for the amplitude condition for incompressible and inextensible materials are also given and compared with those of
the classical linear theory of elasticity. In particular, it is shown that for the constraint of incompressibility the classical
linear elasticity provides an amplitude condition that, coincidently, is correct, while for the constraint of inextensibility
the disagreement is first order in the displacement gradient. Then, the propagation condition for the constraints of incompressibility
and inextensibility is studied. For incompressible materials the propagation condition is solved and explicit values for the
squares of the speeds of propagation are obtained. For inextensible materials the propagation condition is solved for plane
acceleration waves propagating into a homogeneously strained material. For both constraints, it is shown that the squares
of the speeds of propagation depend by terms that are first order in the displacement gradient, while in classical linear
elasticity they are constant.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
19.
20.
Anil K. Vashishth Vishakha Gupta 《International Journal of Solids and Structures》2009,46(20):3620-3632
Wave propagation in porous piezoelectric material (PPM), having crystal symmetry 6 mm, is studied analytically. Christoffel equation is derived for the propagation of plane harmonic waves in such a medium. The roots of this equation give four complex wave velocities which can propagate in such materials. The phase velocities of propagation and the attenuation quality factors of all these waves are described in terms of complex wave velocities. Phase velocities and attenuation of the waves in PPM depend on the phase direction. Numerical results are computed for the PPM BaTiO3. The variation of phase velocity and attenuation quality factor with phase direction, porosity and the wave frequency is studied. The effects of anisotropy and piezoelectric coupling are also studied. The phase velocities of two quasi dilatational waves and one quasi shear waves get affected due to piezoelectric coupling while that of type 2 quasi shear wave remain unaffected. The phase velocities of all the four waves show non-dispersive behavior after certain critical high frequency. The phase velocity of all waves decreases with porosity while attenuation of respective waves increases with porosity of the medium. The characteristic curves, including slowness curves, velocity curves, and the attenuation curves, are also studied in this paper. 相似文献