Complete Solution of the Linear Magnetoelasticity and the Magnetic Fields in a Magnetized Elastic Half-Space

1995 ◽  
Vol 62 (4) ◽  
pp. 930-934 ◽  
Author(s):  
Huang Ke-Fu ◽  
Wang Min-Zhong
Keyword(s):  
Magnetic Fields ◽  
General Solution ◽  
Closed Form ◽  
Half Space ◽  
Complete Solution ◽  
Three Dimensional ◽  
Phenomenological Theory ◽  
Elastic Half Space ◽  
Linearized Theory ◽  
Single Force

In this paper, a general solution of the equations in the linearized theory of magnetoe-lasticity, which was developed by Pao and Yeh (1973) on the basis of Brown’s phenomenological theory of magnetoelasticity (1966), is obtained. As in some applications, the magnetic fields caused by the mechanical singularities in a magnetized elastic half-space are considered. Using the general solution and the Mindlin state of the elastic half-space (1936), the exact three-dimensional solutions for the generated magnetic fields due to various mechanical singularities, such as a single force and a doublet, are obtained in closed form.

Guided Surface Waves on an Elastic Half Space

1971 ◽  
Vol 38 (4) ◽  
pp. 899-905 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Body Wave ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Rigid Barrier ◽  
Wave Disturbances

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

Contact Stress Analysis of a Layered Transversely Isotropic Half-Space

1992 ◽  
Vol 114 (2) ◽  
pp. 253-261 ◽  
Author(s):  
C. H. Kuo ◽  
L. M. Keer
Keyword(s):  
Half Space ◽  
Mixed Boundary ◽  
Contact Region ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Stress Components ◽  
Contact Failure

The three-dimensional problem of contact between a spherical indenter and a multi-layered structure bonded to an elastic half-space is investigated. The layers and half-space are assumed to be composed of transversely isotropic materials. By the use of Hankel transforms, the mixed boundary value problem is reduced to an integral equation, which is solved numerically to determine the contact stresses and contact region. The interior displacement and stress fields in both the layer and half-space can be calculated from the inverse Hankel transform used with the solved contact stresses prescribed over the contact region. The stress components, which may be related to the contact failure of coatings, are discussed for various coating thicknesses.

Transient Thermoelastic Stress Fields in a Half-Space

2002 ◽  
Vol 125 (1) ◽  
pp. 33-43 ◽  
Author(s):  
Shuangbiao Liu ◽  
Qian Wang
Keyword(s):  
Stress Field ◽  
Half Space ◽  
Frictional Heating ◽  
Three Dimensional ◽  
Thermoelastic Stress ◽  
Parabolic Type ◽  
Elastic Half Space ◽  
Transform Method ◽  
Rough Surface Contact ◽  
Thermoelastic Stress Field

Computing the thermoelastic stress field of a material subjected to frictional heating is essential for component failure prevention and life prediction. However, the analysis for three-dimensional thermoelastic stress field for tribological problems is not well developed. Furthermore, the pressure distribution due to rough surface contact is irregular; hence the frictional heating can hardly be described by an analytical expression. This paper presents a novel set of frequency-domain expressions (frequency response functions) of the thermoelastic stress field of a uniformly moving three-dimensional elastic half-space subjected to arbitrary transient frictional heating, where the velocity of the half-space, its magnitude and direction, can be an arbitrary function of time. General formulas are expressed in the form of time integrals, and important expressions for constant velocities are given for the transient-instantaneous, transient-continuous, and steady-state cases. The thermoelastic stress field inside a translating half-space with constant velocities are illustrated and discussed by using the discrete convolution and fast Fourier transform method when a parabolic type or an irregularly distributed heat source is applied.

The Transition Matrix Formalism for the Scattering of an Alluvium on an Elastic Half-Space

2007 ◽  
Author(s):  
Wen-I Liao ◽  
Tsung-Jen Teng ◽  
Shiang-Jung Wang
Keyword(s):  
Half Space ◽  
Transition Matrix ◽  
Plane Waves ◽  
Three Dimensional ◽  
Scattering Matrix ◽  
Elastic Half Space ◽  
Basis Functions ◽  
Matrix Formalism ◽  
T Matrix ◽  
Singular Wave

This paper develops the transition matrix formalism for scattering from an three-dimensional alluvium on an elastic half-space. Betti’s third identity is employed to establish orthogonality conditions among basis functions that are Lamb’s singular wave functions. The total displacements and associated tractions exterior and interior to the surface are expanded in a Rayleigh series. The boundary conditions are applied and the T-matrix is derived. A linear transformation is utilized to construct a set of orthogonal basis functions. The transformed T-matrix is related to the scattering matrix and it is shown that the scattering matrix is symmetric and unitary and that the T-matrix is symmetric. Typical numerical results obtained by incident plane waves for verification are presented.

scholarly journals Magneto-thermoelastic waves in a perfectly conducting elastic half-space in thermoelasticity III

2005 ◽  
Vol 2005 (20) ◽  
pp. 3303-3318
Author(s):  
S. K. Roychoudhuri ◽  
Nupur Bandyopadhyay
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Wave Front ◽  
Half Space ◽  
Temperature Stress ◽  
Elastic Half Space ◽  
Small Time ◽  
Dilatational Wave ◽  
Heat Transport Equation ◽  
Perturbed Magnetic Field

The propagation of magneto-thermoelastic disturbances in an elastic half-space caused by the application of a thermal shock on the stress-free bounding surface in contact with vacuum is investigated. The theory of thermoelasticity III proposed by Green and Naghdi is used to study the interaction between elastic, thermal, and magnetic fields. Small-time approximations of solutions for displacement, temperature, stress, perturbed magnetic fields both in the vacuum and in the half-space are derived. The solutions for displacement, temperature, stress, perturbed magnetic field in the solid consist of a dilatational wave front with attenuation depending on magneto-thermoelastic coupling and also consists of a part diffusive in nature due to the damping term present in the heat transport equation, while the perturbed field in vacuum represents a wave front without attenuation traveling with Alfv'en acoustic wave speed. Displacement and temperatures are continuous at the elastic wave front, while both the stress and the perturbed magnetic field in the half-space suffer finite jumps at this location. Numerical results for a copper-like material are presented.

Magnetic Fields Generated by a Mechanical Singularity in a Magnetized Elastic Half Plane

1989 ◽  
Vol 56 (1) ◽  
pp. 89-95 ◽  
Author(s):  
Chau-Shioung Yeh
Keyword(s):  
Fourier Transform ◽  
Magnetic Fields ◽  
Exact Solutions ◽  
Closed Form ◽  
Plane Strain ◽  
Half Plane ◽  
Elastic Solids ◽  
Soft Ferromagnetic ◽  
Single Force ◽  
The Fourier Transform

The induced magnetic fields generated by a line mechanical singularity in a magnetized elastic half plane are investigated in this paper. One version of linear theory for soft ferromagnetic elastic solids which has been developed by Pao and Yeh (1973) is adopted to analyze the plane strain problem undertaken. By applying the Fourier transform technique, the exact solutions for the generated magnetic inductions due to various mechanical singularities such as a single force, a dipole, and single couple are obtained in a closed form. The distributions of the generated inductions on the surface are shown with figures.

Closed-Form Solutions of the Elastic Half Space due to a Line Heat Source

2014 ◽  
Vol 638-640 ◽  
pp. 2082-2091
Author(s):  
John C.C. Lu ◽  
Feng Tsai Lin
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Half Space ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Line Heat Source ◽  
Closed Form Solutions ◽  
Line Sink ◽  
Vertical Displacements ◽  
Thermoelastic Response

Thermoelastic response due to a line heat source is analog to poroelastic reaction caused by a fluid line sink. In this study, the strata are modeled as a thermoelastic or poroelastic half space bounded by horizontal surface in the mathematical model. Thermomechanics and poromechanics are applied on the formulation of basic governing equations, and an analogy is drawn to show the similarity. Using Hankel transform technique and approaching symbolic integral through Mathematica, the closed-form solutions of the horizontal and vertical displacements due to a fluid line sink are obtained. The displacements produced by the line heat source are described through analog quantities between thermoelasticity and poroelasticity. The solutions can be applied to dewater operations and build waste repository.

Viscous-Elastic Half-Space Vibration Stimulated by High-Speed Moving Loads of Different Speeds

2012 ◽  
Vol 518-523 ◽  
pp. 3874-3877
Author(s):  
Tao Qian ◽  
Xiao Ping Shui ◽  
Yong Fa Zhang ◽  
Yong Gang Guo ◽  
Meng Ma
Keyword(s):  
Half Space ◽  
Coordinate Transformation ◽  
High Speed ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Moving Loads ◽  
Cylindrical Coordinates ◽  
Relative Coordinate ◽  
The Laplace Transform ◽  
Practical Security

A rule of response of an infinite viscous-elastic half-space stimulated by the moving loads of different speeds is outlined in this paper. In order to obtain a three-dimensional analytical solution of the Viscous-elastic half-space with the moving loads of different speeds, the Laplace transform and relative coordinate transformation in cylindrical coordinates are used. Then, the IFFT and relative coordinate transformation are used to solve two-dimensional infinite integration which can greatly improve the operational efficiency. The rules of responses of different velocities from the results by using the principle of dynamics and energy dissipation are also analyzed and induced in this paper, and obtain the incentives of displacement distortion by the super-Rayleigh wave velocity at surface. The results could be referred in improving the practical security in the project.

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