Thermoelastodynamics in Transversely Isotropic Media With Scalar Potential Functions1

2013 ◽  
Vol 81 (2) ◽  
Author(s):  
Morteza Eskandari-Ghadi ◽  
Mohammad Rahimian ◽  
Stein Sture ◽  
Maysam Forati
Keyword(s):  
Heat Equation ◽  
Potential Function ◽  
Convex Domain ◽  
Scalar Potential ◽  
Transversely Isotropic ◽  
Potential Functions ◽  
Newtonian Potential ◽  
Existence Of A Solution ◽  
Axis Of Symmetry ◽  
Special Case

A complete set of potential functions consisting of three scalar functions is presented for coupled displacement-temperature equations of motion and heat equation for an arbitrary x3-convex domain containing a linear thermoelastic transversely isotropic material, where the x3-axis is parallel to the axis of symmetry of the material. The proof of the completeness theorem is based on a retarded logarithmic potential function, retarded Newtonian potential function, repeated wave equation, the extended Boggio's theorem for the transversely isotropic axially convex domain, and the existence of a solution for the heat equation. It is shown that the solution degenerates to a set of complete potential functions for elastodynamics and elastostatics under certain conditions. In a special case, the number of potential functions is reduced to one, and the required conditions are discussed. Another special case involves the rotationally symmetric configuration with respect to the axis of symmetry of the material.

scholarly journals A note on the uniqueness of 2D elastostatic problems formulated by different types of potential functions

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 201-210
Author(s):  
José Luis Morales Guerrero ◽  
Manuel Cánovas Vidal ◽  
José Andrés Moreno Nicolás ◽  
Francisco Alhama López
Keyword(s):  
Boundary Conditions ◽  
Potential Function ◽  
Vector Potential ◽  
Numerical Scheme ◽  
Scalar Potential ◽  
Three Dimensional ◽  
Potential Functions ◽  
Network Method ◽  
Different Types ◽  
Physical Boundary

Abstract New additional conditions required for the uniqueness of the 2D elastostatic problems formulated in terms of potential functions for the derived Papkovich-Neuber representations, are studied. Two cases are considered, each of them formulated by the scalar potential function plus one of the rectangular non-zero components of the vector potential function. For these formulations, in addition to the original (physical) boundary conditions, two new additional conditions are required. In addition, for the complete Papkovich-Neuber formulation, expressed by the scalar potential plus two components of the vector potential, the additional conditions established previously for the three-dimensional case in z-convex domain can be applied. To show the usefulness of these new conditions in a numerical scheme two applications are numerically solved by the network method for the three cases of potential formulations.

Analytical Solution of Coupled Thermoelastic Axisymmetric Transient Waves in a Transversely Isotropic Half-Space

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
M. Raoofian Naeeni ◽  
M. Eskandari-Ghadi ◽  
Alireza A. Ardalan ◽  
M. Rahimian ◽  
Y. Hayati
Keyword(s):  
Potential Function ◽  
Half Space ◽  
Equations Of Motion ◽  
Scalar Potential ◽  
Transversely Isotropic ◽  
Integral Transforms ◽  
Heaviside Step Function ◽  
Isotropic Materials ◽  
Coupled Equations ◽  
Degree Of Anisotropy

A half-space containing transversely isotropic thermoelastic material with a depth-wise axis of material symmetry is considered to be under the effects of axisymmetric transient surface thermal and forced excitations. With the use of a new scalar potential function, the coupled equations of motion and energy equation are uncoupled, and the governing equation for the potential function, is solved with the use of Hankel and Laplace integral transforms. As a result, the displacements and temperature are represented in the form of improper double integrals. The solutions are also investigated in detail for surface traction and thermal pulses varying with time as Heaviside step function. It is also shown that the derived solutions degenerate to the results given in the literature for isotropic materials. Some numerical evaluations for displacement and temperature functions for two different transversely isotropic materials with different degree of anisotropy are presented to portray the dependency of response on the thermal properties as well as the degree of anisotropy of the medium.

The derivation of the rotational potential function from atom–atom potentials. III. Borohydride compounds

1988 ◽  
Vol 66 (4) ◽  
pp. 791-793 ◽  
Author(s):  
David Smith
Keyword(s):  
Transition Temperature ◽  
Experimental Method ◽  
Potential Function ◽  
Ground Level ◽  
Potential Functions ◽  
The Difference ◽  
Level Degeneracy ◽  
Entropy Of Transition ◽  
Good Agreement

The rotational potential functions for the borohydride ion embedded in potassium and rubidium halides are derived from atom–atom potentials of the Buckingham (exp-6) type. The librational frequencies computed from the potential functions are in good agreement with the observed frequencies. The potential functions for rubidium and potassium borohydrides derived from the atom–atom potentials yield librational frequencies that are about 10% higher than the observed values. Since the entropy of transition for potassium and rubidium borohydrides is less than expected, there is a possibility that there is some ordering of the borohydride ions above the transition temperature. An experimental method is presented for studying the ordering of the borohydride ions based on the difference in the ground level degeneracy of a tetrahedral ion in ordered and disordered states.

Control of Multiple Mobile Agents Via Artificial Potential Functions and Random Motion

2007 ◽  
Author(s):  
Manish Kumar ◽  
Devendra P. Garg ◽  
Randy Zachery
Keyword(s):  
Potential Function ◽  
Mobile Agents ◽  
Formation Control ◽  
Cluster Formation ◽  
Limited Range ◽  
Random Motion ◽  
Potential Functions ◽  
Random Behavior ◽  
Artificial Potential Function ◽  
Multiple Mobile Agents

This paper investigates the effectiveness of designed random behavior in cooperative formation control of multiple mobile agents. A method based on artificial potential functions provides a framework for decentralized control of their formation. However, it implies heavy communication costs. The communication requirement can be replaced by onboard sensors. The onboard sensors have limited range and provide only local information, and may result in the formation of isolated clusters. This paper proposes to introduce a component representing random motion in the artificial potential function formulation of the formation control problem. The introduction of the random behavior component results in a better chance of global cluster formation. The paper uses an agent model that includes both position and orientation, and formulates the dynamic equations to incorporate that model in artificial potential function approach. The effectiveness of the proposed method is verified via extensive simulations performed on a group of mobile agents and leaders.

Reflection moveout approximations for P-waves in a moderately anisotropic homogeneous tilted transverse isotropy layer

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. C175-C185 ◽  
Author(s):  
Ivan Pšenčík ◽  
Véronique Farra
Keyword(s):  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
P Wave ◽  
Weak Anisotropy ◽  
P Waves ◽  
3D Space ◽  
Axis Of Symmetry ◽  
Relative Errors ◽  
Symmetry Tests ◽  
Ti Media

We have developed approximate nonhyperbolic P-wave moveout formulas applicable to weakly or moderately anisotropic media of arbitrary anisotropy symmetry and orientation. Instead of the commonly used Taylor expansion of the square of the reflection traveltime in terms of the square of the offset, we expand the square of the reflection traveltime in terms of weak-anisotropy (WA) parameters. No acoustic approximation is used. We specify the formulas designed for anisotropy of arbitrary symmetry for the transversely isotropic (TI) media with the axis of symmetry oriented arbitrarily in the 3D space. Resulting formulas depend on three P-wave WA parameters specifying the TI symmetry and two angles specifying the orientation of the axis of symmetry. Tests of the accuracy of the more accurate of the approximate formulas indicate that maximum relative errors do not exceed 0.3% or 2.5% for weak or moderate P-wave anisotropy, respectively.

An Analytical Solution for Transversely Isotropic Simply Supported Thick Rectangular Plates Using Displacement Potential Functions

2011 ◽  
Vol 46 (2) ◽  
pp. 121-142 ◽  
Author(s):  
M Nematzadeh ◽  
M Eskandari-Ghadi ◽  
B Navayi Neya
Keyword(s):  
Isotropic Material ◽  
Transversely Isotropic ◽  
Numerical Results ◽  
Potential Functions ◽  
Constant Thickness ◽  
Rectangular Plates ◽  
Displacement Potential ◽  
Simply Supported ◽  
Axial Forces ◽  
Internal Forces

Using a complete set of displacement potential functions, the exact solution of three-dimensional elasticity equations of a simply supported rectangular plates with constant thickness consisting of a transversely isotropic linearly elastic material subjected to an arbitrary static load is presented. The governing partial differential equations for the potential functions are solved through the use of the Fourier method, which results in exponential and trigonometric expression along the plate thickness and the other two lengths respectively. The displacements, stresses, and internal forces are determined through the potential functions at any point of the body. To prove the validity of this approach, the analytical solutions developed in this paper are degenerated for the simpler case of plates containing isotropic material and compared with the existing solution. In addition, the numerical results obtained from this study are compared with those reported in other researches for the isotropic material, where excellent agreement is achieved for both thin and thick plates. The results show that increasing the thickness ratios of the plate causes compressive axial forces and central shear forces inside the plate. Finally, the internal forces and displacement components are calculated numerically for several kinds of transversely isotropic materials with different anisotropies and are compared with a finite element (FE) solution obtained from the ANSYS software, where the high accuracy of the present method is demonstrated. The effects of the material anisotropy are clearly revealed in the numerical results presented.

scholarly journals An efficient wavefield inversion for transversely isotropic media with a vertical axis of symmetry

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. R195-R206 ◽  
Author(s):  
Chao Song ◽  
Tariq Alkhalifah
Keyword(s):  
High Resolution ◽  
Optimization Problem ◽  
Source Function ◽  
Transversely Isotropic ◽  
Vertical Axis ◽  
Trade Off ◽  
Transversely Isotropic Media ◽  
Highly Nonlinear ◽  
Isotropic Media ◽  
Axis Of Symmetry

Conventional full-waveform inversion (FWI) aims at retrieving a high-resolution velocity model directly from the wavefields measured at the sensor locations resulting in a highly nonlinear optimization problem. Due to the high nonlinearity of FWI (manifested in one form in the cycle-skipping problem), it is easy to fall into local minima. Considering that the earth is truly anisotropic, a multiparameter inversion imposes additional challenges in exacerbating the null-space problem and the parameter trade-off issue. We have formulated an optimization problem to reconstruct the wavefield in an efficient matter with background models by using an enhanced source function (which includes secondary sources) in combination with fitting the data. In this two-term optimization problem to fit the wavefield to the data and to the background wave equation, the inversion for the wavefield is linear. Because we keep the modeling operator stationary within each frequency, we only need one matrix inversion per frequency. The inversion for the anisotropic parameters is handled in a separate optimization using the wavefield and the enhanced source function. Because the velocity is the dominant parameter controlling the wave propagation, it is updated first. Thus, this reduces undesired updates for anisotropic parameters due to the velocity update leakage. We find the effectiveness of this approach in reducing parameter trade-off with a distinct Gaussian anomaly model. We find that in using the parameterization [Formula: see text], and [Formula: see text] to describe the transversely isotropic media with a vertical axis of symmetry model in the inversion, we end up with high resolution and minimal trade-off compared to conventional parameterizations for the anisotropic Marmousi model. Application on 2D real data also indicates the validity of our method.

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