共查询到20条相似文献,搜索用时 994 毫秒
1.
The article is concerned with the mechanical responses of anisotropic multi-layered medium under harmonic moving load. An analytical solution for two-dimensional anisotropic multi-layered medium subjected to harmonic moving load is devoted via Spectral Element Method (SEM), while the anisotropic property is approximated as transverse isotropy. Starting with the constitutive equations of transversely isotropic body and the governing equations of motion based on the loading properties. The analytical spectral elements in the wavenumber domain are obtained according to the principle of wave superposition and Fourier transformation. Then, the spectral global stiffness matrix of the multi-layered medium is derived by assembling the nodded stiffness matrices of all layers depended on the different interlayer conditions between the adjacent layers, i.e. sliding and bonded. The corresponding analytical solutions are achieved by taking the Fourier series and Inverse Fast Fourier Transform (IFFT) algorithm. Finally, some examples are given to validate the accuracy of the proposed analytical solution, and to demonstrate the impact of both anisotropy, top layer thickness, interlayer conditions, and loading properties (velocity and natural frequency) on the mechanical response of the multi-layered medium. 相似文献
2.
Response of a ground subjected to dynamic sources is a classical problem in many fields. This paper develops a transversely isotropic (TI) half-space ground model which considers the alternating distribution of different media: a TI elastic surface layer, a TI poroelastic interlayer and a TI elastic half-space from top to bottom. The model can consider soils with different properties and the existence of groundwater. Dynamic responses of the model subjected to a buried moving source are investigated. General solutions to the TI poroelastic interlayer in the wavenumber domain are derived by Fourier transform and a potential function method in a Cartesian coordinate system. The layered system with different media is solved adopting an ‘adapted stiffness matrix method’ for a buried source scenario. Dynamic responses in the time-spatial domain are obtained by inverse fast Fourier transform (iFFT) and numerical integration. The performance of the method in this study is first tested by comparison with existing research, and the influences of the existence of pore water in the interlayer, transverse isotropy, and source features are comprehensively investigated. The effect of pore water is more significant for a TI ground compared with isotropic ground, and the model in this study cannot be simplified by an ‘equivalent’ layered TI elastic model. Peak values of displacement and pore pressure exist with increasing source speed. Source speeds corresponding to them are related to the wave speeds of the medium and affected by transverse isotropy. 相似文献
3.
This paper presents an analytical research on the dynamic interaction problem between a pre-stressed plate and a transversely isotropic multilayered half-plane subjected to a moving load. The pre-stressed plate is governed by the Kirchhoff plate theory, and the transversely isotropic multilayered half-plane is solved by the analytical layer-element method. Combining the frictionless contact and displacement compatibility conditions between the plate and the soil, the contact stress and the deflection of plate in the Fourier transform domain are derived. With the aid of the inverse Fourier transform, the actual solutions can be further achieved. Numerical examples are given to illustrate the influence of load speed, the rigidity of plate, the axial force applied on the plate and the stratified character of the soil. 相似文献
4.
The time-dependent system of partial differential equations of the second order describing the electric wave propagation in
vertically inhomogeneous electrically and magnetically biaxial anisotropic media is considered. A new analytical method for
solving an initial value problem for this system is the main object of the paper. This method consists in the following: the
initial value problem is written in terms of Fourier images with respect to lateral space variables, then the resulting problem
is reduced to an operator integral equation. After that the operator integral equation is solved by the method of successive
approximations. Finally, a solution of the original initial value problem is found by the inverse Fourier transform. 相似文献
5.
Dynamic Green's function plays an important role in the study of various wave radiation, scattering and soil-structure interaction problems. However, little research has been done on the response of transversely isotropic saturated layered media. In this paper, the 3D dynamic responses of a multi-layered transversely isotropic saturated half-space subjected to concentrated forces and pore pressure are investigated. First, utilizing Fourier expansion in circumferential direction accompanied by Hankel integral transform in radial direction, the wave equations for transversely isotropic saturated medium in cylindrical coordinate system are solved. Next, with the aid of the exact dynamic stiffness matrix for in-plane and out-of-plane motions, the solutions for multi-layered transversely isotropic saturated half-space under concentrated forces and pore pressure are obtained by direct stiffness method. A FORTRAN computer code is developed to achieve numerical evaluation of the proposed method, and its accuracy is validated through comparison with existing solutions that are special cases of the more general problems addressed. In addition, selected numerical results for a homogeneous and a layered material model are performed to illustrate the effects of material anisotropy, load frequency, drainage condition and layering on the dynamic responses. The presented solutions form a complete set of Green's functions for concentrated forces (including horizontal load in x(y)-direction, vertical load in z-direction) as well as pore pressure, which lays the foundation for further exploring wave propagation of complex local site in a layered transversely isotropic saturated half-space by using the BEMs. 相似文献
6.
Valery G. Yakhno Handan Çerdik Yaslan Tatiana M. Yakhno 《Central European Journal of Mathematics》2012,10(1):188-203
A new method for computation of the fundamental solution of electrodynamics for general anisotropic nondispersive materials
is suggested. It consists of several steps: equations for each column of the fundamental matrix are reduced to a symmetric
hyperbolic system; using the Fourier transform with respect to space variables and matrix transformations, formulae for Fourier
images of the fundamental matrix columns are obtained; finally, the fundamental solution is computed by the inverse Fourier
transform. Applying the suggested approach, the fundamental solution components are computed in general anisotropic media.
Computational examples confirm robustness of the suggested method. 相似文献
7.
横观各向同性饱和地基的三维动力响应 总被引:5,自引:1,他引:4
首先引入位移函数,将直角坐标系下横观各向同性饱和土Biot波动方程转化为2个解耦的六阶和二阶控制方程;然后基于双重Fourier变换,求解了Biot波动方程,得到以土骨架位移和孔隙水压力为基本未知量的积分形式的一般解,并用一般解给出了饱和土总应力分量的表达式.在此基础上系统研究了横观各向同性饱和半空间体的稳态动力响应问题,考虑表面排水和不排水两种情况,得到了半空间体在任意分布的表面谐振荷载作用下,表面位移的稳态动力响应,文末给出了算例. 相似文献
8.
H. Çerdik Yaslan 《Applied Mathematical Modelling》2013,37(18-19):8409-8418
The fundamental solution (FS) of the time-dependent differential equations of anisotropic elasticity in 3D quasicrystals are studied in the paper. Equations of the time-dependent differential equations of anisotropic elasticity in 3D quasicrystals are written in the form of a symmetric hyperbolic system of the first order. Using the Fourier transform with respect to the space variables and matrix transformations we obtain explicit formulae for Fourier images of the FS columns; finally, the FS is computed by the inverse Fourier transform. As a computational example applying the suggested approach FS components are computed for icosahedral QCs. 相似文献
9.
Jianguo Wang 《中国科学A辑(英文版)》1999,42(12):1323-1331
A state space formulation is established for the nonaxisymmetric space problem of transversely isotropic piezoelectric media
in a system of cylindrical coordinate by introducing the state vector. Using the Hankel transform and the Fourier series,
the state vector equations are transformed into ordinary differential equations. By the use of the matrix methods, the analytical
solutions of a single piezoelectric layer are presented in the form of the product of initial state variables and transfer
matrix. The applications of state vector solutions are discussed. An analytical solution for a semiinfinite piezoelectric
medium subjected to the vertical point forceP
z, horizontal point forceP
x along x-direction and point electric charge Q at the origin of the surface is presented. According to the continuity conditions
at the interfaces, the general solution formulation forN-layered transversely isotropic piezoelectric media is given.
Project supported by the National Natural Science Foundation of China (Grant No. 59648001). 相似文献
10.
11.
《Journal of Applied Mathematics and Mechanics》2007,71(1):20-29
For problems of the mechanics of an anisotropic inhomogeneous continuum, theorems are given concerning the uninterrupted symmetrical and antisymmetrical analytical continuation of the solution through the plane part of the boundary surface of the medium. Theorems are given for two types of mechanics problem; in the first of these both symmetrical and antisymmetrical continuations of the solution are allowed, while in the second only symmetrical continuation of the solution is allowed. Problems of the first type include problems which are reduced to linear thermoelastic dynamic differential equations of motion of an inhomogeneous anisotropic medium possessing a plane of elastic symmetry, to linear thermoelastic dynamic differential equations of motion of an inhomogeneous Cosserat medium, to non-linear differential equations describing the static elastoplastic stress state of a plate, etc. The second type includes problems which are reduced to non-linear differential equations describing geometrically non-linear strains of shells, to Navier–Stokes equations, etc. These theorems extend the principle of mirror reflection (the Riemann–Schwartz principle of symmetry) to linear and non-linear equations of continuum mechanics. The uninterrupted continuation of the solutions is used to solve problems of the equilibrium state of bodies of complex shape. 相似文献
12.
横观各向同性电磁弹性介质中裂纹对SH波的散射 总被引:2,自引:0,他引:2
研究横观各向同性电磁弹性介质中裂纹和反平面剪切波之间的相互作用.根据电磁弹性介质的平衡运动微分方程、电位移和磁感应强度微分方程,得到SH波传播的控制场方程.引入线性变换,将控制场方程简化为Helmholtz方程和两个Laplace方程A·D2通过Fourier变换,并采用非电磁渗透型裂面边界条件,得到了柯西奇异积分方程组.利用Chebyshev多项式求解积分方程,得到应力场、电场和磁场以及动应力强度因子的表达,并给出了数值算例. 相似文献
13.
《Journal of Computational and Applied Mathematics》2005,175(1):77-86
In this paper, wavelets are used in solving, by the method of moments, a modified version of the thin-wire electric field integral equation, in frequency domain. The time domain electromagnetic quantities, are obtained by using the inverse discrete fast Fourier transform. The retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation. The discretized model generated by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix which have to be solved for each frequency of the Fourier spectrum of the time domain impressed source. Therefore, orthogonal wavelet-like basis transform is used to sparsify the moment matrix. In particular, dyadic and M-band wavelet transforms have been adopted, so generating different sparse matrix structures. This leads to an efficient solution in solving the resulting sparse matrix equation. Moreover, a wavelet preconditioner is used to accelerate the convergence rate of the iterative solver employed. These numerical features are used in analyzing the transient behavior of a lightning protection system. In particular, the transient performance of the earth termination system of a lightning protection system or of the earth electrode of an electric power substation, during its operation is focused. The numerical results, obtained by running a complex structure, are discussed and the features of the used method are underlined. 相似文献
14.
15.
Gregory S. Chirikjian Alexander B. Kyatkin 《Journal of Fourier Analysis and Applications》2000,6(6):583-606
In this article we develop analytical and computational tools arising from harmonic analysis on the motion group of three-dimensional
Euclidean space. We demonstrate these tools in the context of applications in robotics and polymer science. To this end, we
review the theory of unitary representations of the motion group of three dimensional Euclidean space. The matrix elements
of the irreducible unitary representations are calculated and the Fourier transform of functions on the motion group is defined.
New symmetry and operational properties of the Fourier transform are derived. A technique for the solution of convolution
equations arising in robotics is presented and the corresponding regularized problem is solved explicity for particular functions.
A partial differential equation from polymer science is shown to be solvable using the operational properties of the Euclidean-group
Fourier transform. 相似文献
16.
A solution of the problem of the diffraction of unsteady elastic waves by a thin strip-like delaminated rigid inclusion in an unbounded elastic medium under conditions of planer strain is proposed. We have in mind an inclusion, one side of which is completely bonded with the medium while, the other side is delaminated and conditions of smooth contact are satisfied on it. The method of solution is based on the use of discontinuous solutions of the Lamé equations of motion under conditions of planer strain, which have been constructed earlier in the space of Laplace transforms. As a result, the problem reduces to solving a system of three singular integral equations for the transforms of the unknown discontinuities. The inverse transforms are found by a numerical method, based on the replacement of a Mellin integral by a Fourier series. 相似文献
17.
A. V. Baev 《Computational Mathematics and Mathematical Physics》2018,58(4):537-547
A two-dimensional inverse scattering problem in a layered acoustic medium occupying a half-plane is considered. Data is the scattered wavefield from a surface point source measured on the boundary of the half-plane. On the basis of the Radon transform, an algorithm is constructed that recovers the velocity and the acoustic impedance of the medium from the scattering data. An analytical solution is presented for an inverse scattering problem, and several inverse scattering problems are solved numerically. 相似文献
18.
19.
Meltem Altunkaynak 《Mathematical Methods in the Applied Sciences》2019,42(7):2324-2333
In this paper, the three‐dimensional initial value problem for elastic system in inhomogeneous orthotropic media is considered and an analytical method is studied to solve this problem. The system is written in terms of Fourier images of displacements with respect to lateral variables. The resulting problem is reduced to integral equations of the Volterra type, whose solution is obtained by the method of successive approximations. Finally, using the real Paley‐Wiener theorem, it is shown that the solution of the initial value problem can be found by the inverse Fourier transform. 相似文献
20.
Ya. M. Grigorenko 《Journal of Mathematical Sciences》2009,162(2):187-204
Some approaches to solving nonlinear boundary-value problems of the theory of flexible shells described by ordinary and partial
differential equations are presented. One-dimensional problems for a system of anisotropic shells of rotation in the subcritical
and supercritical regions of deformation, as well as two-dimensional problems for shells of canonical and noncanonical forms,
are considered. The solution of nonlinear problems is performed on the basis of numerical and numerical-analytic methods with
the use of discrete orthogonalization and Fourier discrete series. 相似文献