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 共查询到19条相似文献,搜索用时 78 毫秒
1.
This study discusses wave propagation in perhaps the most general model of a poroelastic medium. The medium is considered as a viscoelastic, anisotropic and porous solid frame such that its pores of anisotropic permeability are filled with a viscous fluid. The anisotropy considered is of general type, and the attenuating waves in the medium are treated as the inhomogeneous waves. The complex slowness vector is resolved to define the phase velocity, homogeneous attenuation, inhomogeneous attenuation, and angle of attenuation for each of the four attenuating waves in the medium. A non-dimensional parameter measures the deviation of an inhomogeneous wave from its homogeneous version. An numerical model of a North-Sea sandstone is used to analyze the effects of the propagation direction, inhomogeneity parameter, frequency regime, anisotropy symmetry, anelasticity of the frame, and viscosity of the pore-fluid on the propagation characteristics of waves in such a medium.  相似文献   

2.
Based on the standard spaces of the physical presentation, both the quasi-static mechanical approximation and the quasi-static electromagnetic approximation of piezoelectric solids are studied here. The complete set of uncoupled elastic wave and electromagnetic wave equations are deduced. The results show that the number and propagation speed of elastic waves and electromagnetic waves in anisotropic piezoelectric solids are determined by both the subspaces of electromagnetically anisotropic media and ones of mechanically anisotropic media. Based on these laws, we discuss the propagation behaviour of elastic waves and electromagnetic waves in the piezoelectric material of class 6 mm.  相似文献   

3.
On condition that any perfectly plastic stress component near a singular point is nothing but the function of θ only, making use of equilibrium equations and Hill anisotropic yield condition, we derive the general analytical expressions of the anisotropic plastic stress field near a singular point in both the cases of anti-plane and in-plane strains. Applying these general analytical expressions to the concrete cracks and the plane-strain bodies with a singular point, the anisotropic plastic stress fields at the tips of Mode Ⅰ, Mode Ⅱ, Mode Ⅲ and mixed mode Ⅰ-Ⅱ cracks, and the limit loads of anisotropic plastic plane-strain bodies with a singular point are obtained.  相似文献   

4.
Fundamental theory presented in Part (Ⅰ) is used to analyze anisotropic plane stress problems. First we construct the generalized variational principle to enter Hamiltonian system and get Hamiltonian differential operator matrix, then we solve eigen problem; finally, we present the process of obtaining analytical solutions and semi-analytical solutions for anisotropic plane stress porblems on rectangular area.  相似文献   

5.
The paper studies the propagation of torsional surface waves in an initially stressed anisotropic poro-elastic layer over a semi-infinite heterogeneous half space with linearly varying rigidity and density due to irregularity at the interface. The irregularity is taken in the half space in the form of a rectangle. It is observed that torsional surface waves propagate in this assumed medium. In the absence of the irregularity, the velocity equation of the torsional surface wave is also obtained. For a layer over a homogeneous half space, the velocity of torsional surface waves coincides with that of the Love waves.  相似文献   

6.
Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams, the equations governing quasi-static and dynamical behavior of Timoshenko beams with damage were first derived. The quasi-static behavior of the viscoelastic Timoshenko beam under step loading was analyzed and the analytical solution was obtained in the Laplace transformation domain. The deflection and damage curves at different time were obtained by using the numerical inverse transform and the influences of material parameters on the quasi-static behavior of the beam were investigated in detail.  相似文献   

7.
From the Boltzmann‘ s constitutive law of viscoelastic materials and the linear theory of elastic materials with voids, a constitutive model of generalized force fields for viscoelastic solids with voids was given. By using the variational integral method, the convolution-type functional was given and the corresponding generalized variational principles and potential energy principle of viscoelastic solids with voids were presented. It can be shown that the variational principles correspond to the differential equations and theinitial and boundary conditions of viscoelastic body with voids. As an application, a generalized variational principle of viscoelastic Timoshenko beams with damage was obtained which corresponds to the differential equations of generalized motion and the initial and boundary conditions of beams. The variational principles provide a way for solving problems of viscoelastic solids with voids.  相似文献   

8.
The present study is carried out to investigate the transference of torsional surface waves in a heterogeneous anisotropic crust lying over a dry sandy half-space. The rigidities and densities as well as the initial stress are assumed varying as a function of depth in both the media. These variations are the product of the polynomial function of depth in degree n(n ∈ R) and the exponential function of depth. Following the theory of elastic waves, the mathematical model is established. Separation of variables is used to obtain the displacement in the layer and the half-space. Intrinsic boundary conditions are imposed to derive the dispersion equation. The inhomogeneity parameters associated with the rigidity, the density, and the initial stress of the medium are found to have substantial influence on the phase velocity of the torsional surface wave. The graphical presentations are drawn to exhibit the findings. The results thus obtained are significant for the investigation and characterization of torsional surface wave in the heterogeneous anisotropic layer.  相似文献   

9.
Reflection characteristics of longitudinal strain waves in a semi-infinite elastic rod con-nected to a viscoelastic stratum are investigated analytically.The three-dimensional viscoelasticity the-ory is applied to the stratum,and the Laplace transform with respect to time and the numerical inverseLaplace transform by means of Laguerre function are used.The time histories for the longitudinalstrain of an arbitrary point of the rod are presented.Two typical viscoelastic models are considered,one is the usual Maxwell-Voigt model,the other is whose relaxation function is given by a power law.The numerical results for the two models are presented and compared each other and also with previ-ously published results for the elastic stratum.  相似文献   

10.
We derive a Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom. From the formulation and using the Hamiltonian perturbation theory, we obtain effective Boussinesq equations that describe the motion of bidirectional long waves and unidirectional equations that are similar to the KdV equation for the case in which the bottom possesses short length scale. The computations for these results are performed in the framework of an asymptotic analysis of multiple scale operators.  相似文献   

11.
EIGEN THEORY OF VISCOELASTIC MECHANICS FOR ANISOTROPIC SOLIDS   总被引:4,自引:0,他引:4  
Anisotropic viscoelastic mechanics is studied under anisotropic subspace. It is proved that there also exist the eigen properties for viscoelastic medium. The modal Maxwell's equation, modal dynamical equation (or modal equilibrium equation) and modal compatibility equation are obtained. Based on them, a new theory of anisotropic viscoelastic mechanics is presented. The advantages of the theory are as follows: 1) the equations are all scalar, and independent of each other. The number of equations is equal to that of anisotropic subspaces, 2) no matter how complicated the anisotropy of solids may be, the form of the definite equation and the boundary condition are in common and explicit, 3) there is no distinction between the force method and the displacement method for statics, that is, the equilibrium equation and the compatibility equation are indistinguishable under the mechanical space, 4) each model equation has a definite physical meaning, for example, the modal equations of order one and order two express the volume change and shear deformation respectively for isotropic solids, 5) there also exist the potential functions which are similar to the stress functions of elastic mechanics for viscoelastic mechanics, but they are not man-made, 6) the final solution of stress or strain is given in the form of modal superimposition, which is suitable to the proximate calculation in engineering.  相似文献   

12.
Wave propagation in anisotropic dissipative bodies is considered through the form of inhomogeneous waves. The dissipativity of the body is characterized by a restriction of thermodynamic character on the viscoelastic tensor. As a consequence, the divergence of the usual (time-averaged) energy flux is proved to be negative. This in turn is shown to imply that the amplitude of the wave decays in the direction of the energy flux and the angle, subtended by the imaginary part of the wave vector and the energy flux, is acute. Moreover, the symmetry of the viscoelastic tensor and the positive definiteness of its real part imply that also the imaginary part of the wave vector subtends an acute angle with the energy flux. Such properties are shown to hold in both solids and fluids. Because of anisotropy, the angle subtended by the real and imaginary parts of the wave vector need not be acute, which means that the amplitude may increase in the direction of phase propagation.  相似文献   

13.
The Stroh formalism is employed to discuss the existence of transient surface waves on a viscoelastic anisotropic hall-space. The compatibility conditions, obtained using the integral formulation of Lothe and Barnett [13, 14], are examined on the basis of an asymptotic expansion of the viscoelastic kernel and a separation of space variables. Some previous results on elastic media are extended to viscoelasticity, exploiting the consequences of the second law of thermodynamics. It is found that all the allowed transient surface modes take the form of inhomogeneous plane waves whose amplitude exponentially decays along the propagation direction on the surface. Special solutions are derived explicitly for one-component surface waves where transient modes are admitted also in those cases in which stationary waves cannot occur. Mathematics Subject Classifications (2000) 74D05, 74J15.  相似文献   

14.
Homogeneous and two-layer half-spaces consisting of an anisotropic elastic, isotropic viscoelastic, or poroelastic material are considered. The Kelvin–Voigt model and the model with the Abel kernel are used as models of the viscoelastic material; the poroelastic material is studied within the framework of the model of the compressible Biot material. The case where the half-space contains a cavity is also considered. Propagation of surface waves is studied by the boundary element method. The numerical solution involves the method of collocations for a regularized boundary integral equation.  相似文献   

15.
A study is made of methods for solving linear viscoelastic problems on the basis of the Volterra concept — representation of irrational functions of integral operators as operator power series (analogues of Taylor series). It is pointed out that these series converge weakly. The results of development and substantiation of a new mathematical method for solution of the above problems are summarized. It is based on representing irrational functions of integral operators by operator continued fractions, which converge well. Solutions to certain linear viscoelastic problems for anisotropic bodies are given  相似文献   

16.
提出一种分析粘弹性结构自振特性的数值方法,通过弹性等效空间特征值问题及一个代数方程的求解,得出粘弹性结构的频率及振型。此外建立了薄板的粘弹性动力方程并给出相应的求解方法。文中做了数值验证。  相似文献   

17.
In this paper, we are interested in developing thermodynamically consistent constitutive equations for fiber-reinforced nonlinearly viscoelastic bodies, in particular for transversely isotropic nonlinearly viscoelastic solids, in isothermal processes. It follows from results in the theory of algebraic invariants that constitutive equations for such materials can be expressed in terms of functions of 18 independent invariants associated with deformation and fiber orientation: 10 of them are isotropic invariants and 8 of them are associated with the deformation and the orientation of the fiber. Among the 8 anisotropic invariants just 6 are related to the viscoelastic response. The terms in the Cauchy stress tensor associated to these 6 invariants are analyzed with respect to thermodynamical consistency, and we obtain restrictions for the corresponding constitutive coefficients. This framework is applied to viscoelastic potentials within the context of biomaterials.  相似文献   

18.
The integral equation method is presented for elastodynamic problems of inhomogeneous anisotropic bodies. Since fundamental solutions are not available for general inhomogeneous anisotropic media, we employ the fundamental solution for homogeneous elastostatics. The terms induced by material inhomogeneity and inertia force are regarded as body forces in elastostatics, and evaluated in the form of volume integrals. The scattering problems of elastic waves by inhomogeneous anisotropic inclusions are investigated for some test cases. Numerical results show the significant effects of inhomogeneity and anisotropy of materials on wave propagations.  相似文献   

19.
A new method is proposed to solve some problems of linear viscoelasticity for anisotropic bodies. The method uses a branching continued fraction to approximate an irrational multivariable function. Such an approach allows obtaining a linear operator as an approximation of a multivariable operator function. The deformation of a cracked composite body with a plastic matrix is analyzed as an example. Both composite components are assumed to exhibit viscoelastic properties  相似文献   

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