Fourier transform of fundamental solutions for the motion equations of two-component Biot’s media

2017 ◽  
Author(s):  
Lyudmila A. Alexeyeva ◽  
Ergali B. Kurmanov
Keyword(s):  
Fourier Transform ◽  
Fundamental Solutions ◽  
Motion Equations ◽  
Two Component

scholarly journals Generalized and Fundamental Solutions of Motion Equations of Two-Component Biot’s Medium

2020 ◽  
Author(s):  
Lyudmila Alexeyeva ◽  
Yergali Kurmanov
Keyword(s):  
Wave Propagation ◽  
Harmonic Oscillation ◽  
Delta Function ◽  
Fundamental Solutions ◽  
Generalized Functions ◽  
Integral Representations ◽  
Generalized Solutions ◽  
Motion Equations ◽  
Two Component ◽  
Water Saturated

Here processes of wave propagation in a two-component Biot’s medium are considered, which are generated by arbitrary forces actions. By using Fourier transformation of generalized functions, a fundamental solution, Green tensor, of motion equations of this medium has been constructed in a non-stationary case and in the case of stationary harmonic oscillation. These tensors describe the processes of wave propagation (in spaces of dimensions 1, 2, 3) under an action of power sources concentrated at coordinates origin, which are described by a singular delta-function. Based on them, generalized solutions of these equations are constructed under the action of various sources of periodic and non-stationary perturbations, which are described by both regular and singular generalized functions. For regular acting forces, integral representations of solutions are given that can be used to calculate the stress-strain state of a porous water-saturated medium.

A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier Transform

2011 ◽  
Vol 3 (5) ◽  
pp. 572-585 ◽  
Author(s):  
A. Tadeu ◽  
C. S. Chen ◽  
J. António ◽  
Nuno Simões
Keyword(s):  
Fourier Transform ◽  
Helmholtz Equation ◽  
Initial Conditions ◽  
Inverse Fourier Transform ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Static Response ◽  
Particular Solution ◽  
The Fourier Transform ◽  
Transfer Problems

AbstractFourier transform is applied to remove the time-dependent variable in the diffusion equation. Under non-harmonic initial conditions this gives rise to a non-homogeneous Helmholtz equation, which is solved by the method of fundamental solutions and the method of particular solutions. The particular solution of Helmholtz equation is available as shown in [4, 15]. The approximate solution in frequency domain is then inverted numerically using the inverse Fourier transform algorithm. Complex frequencies are used in order to avoid aliasing phenomena and to allow the computation of the static response. Two numerical examples are given to illustrate the effectiveness of the proposed approach for solving 2-D diffusion equations.

Study of a chlorite-smectite interstratified mineral by means of the Inter program

Clay Minerals ◽  
1988 ◽  
Vol 23 (4) ◽  
pp. 349-355 ◽  
Author(s):  
A. Ruiz-Amil ◽  
E. Vila ◽  
F. Aragón de la Cruz
Keyword(s):  
Fourier Transform ◽  
Function Method ◽  
Intensity Function ◽  
X Ray Diffraction ◽  
Diffraction Intensity ◽  
X Ray ◽  
Two Component ◽  
Hyogo Prefecture ◽  
Marked Tendency ◽  
Interstratified Mineral

AbstractA chlorite-smectite interstratified mineral in a pottery stone from Niwatorizawa mine, Izushi-Cho, Hyogo Prefecture (Japan), has been studied by means of Fourier transform methods, together with interlamellar sorption of ethylene glycol and glycerol. The calculations were carried out with the INTER program (using an Olivetti M-24 personal computer with MS-DOS operating system) which allows the analysis of two-component interstratified structures by two Fourier transform based methods: the X-ray diffraction intensity function method, and the interlayer distances distribution function method. The material studied contains a 1:1 chlorite-smectite interstratification and shows a marked tendency to alternation, i.e., the interstratification is almost regular.

Global well-posedness for the two-component Camassa–Holm equation with fractional dissipation

2019 ◽  
Vol 12 (04) ◽  
pp. 1950051
Author(s):  
Jingqun Wang ◽  
Jing Li ◽  
Lixin Tian
Keyword(s):  
Fourier Transform ◽  
Iterative Scheme ◽  
Dissipative Operator ◽  
Well Posedness ◽  
Holm Equation ◽  
Two Component ◽  
The Fourier Transform

In this paper, we investigate the two-component Camassa–Holm equation with fractional dissipation [Formula: see text] where [Formula: see text] denotes the fractional dissipative operator which is defined by the Fourier transform [Formula: see text]. We prove the local-posedness of this equation via the Littlewood–Paley theory and the suitable iterative scheme. Furthermore, under appropriate discussions, we give the global well-posedness of the above equation.

Fundamental Solutions and Fourier Transform

Distributions ◽  
2010 ◽  
pp. 271-285
Author(s):  
J. J. Duistermaat ◽  
J. A. C. Kolk
Keyword(s):  
Fourier Transform ◽  
Fundamental Solutions

In-Plane Free Vibration of Circular and Annular FG Disks

2019 ◽  
Vol 16 (06) ◽  
pp. 1840024 ◽  
Author(s):  
Y. Yang ◽  
K. P. Kou ◽  
C. C. Lam
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Integral Equation Method ◽  
Fundamental Solutions ◽  
Mode Shapes ◽  
Efficient Tool ◽  
Motion Equations ◽  
Linear Elastic ◽  
Parametric Studies ◽  
Linear Elastic Theory

The analysis of the in-plane free vibration of the circular and annular FG disks by a meshfree boundary-domain integral equation method is presented in this paper. The material properties of the disks are assumed to vary in the radial direction obeying an exponential law. Based on the two-dimensional linear elastic theory, the motion equations of the FG disks are derived by using the static fundamental solutions. Radial integration method as an efficient tool is adopted to treat the domain integrals which are raised due to the material inhomogeneous and inertial effects. The natural frequencies and associate mode shapes are calculated for the FG disks with combinations of free and clamped boundary conditions. Parametric studies are also conducted to study the effects of the material gradients, radius ratios and boundary conditions on the frequency of the FG disks.

Sign in / Sign up

Export Citation Format

Share Document