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.

scholarly journals Magnetic Fields Generated by a Mechanical Singularity in a Magnetized Anisotropic Half Plane

2010 ◽  
Vol 26 (2) ◽  
pp. 173-186
Author(s):  
C.-S. Yeh ◽  
C.-W. Ren
Keyword(s):  
Fourier Transform ◽  
Magnetic Fields ◽  
Exact Solutions ◽  
Closed Form ◽  
Linear Theory ◽  
Half Plane ◽  
Multidomain Structure ◽  
Soft Ferromagnetic ◽  
Single Force ◽  
The Fourier Transform

AbstractThe induced magnetic fields generated by a line mechanical singularity in a magnetized anisotropic half plane are considered in this paper. The linear theory for a soft ferromagnetic elastic with multidomain structure, which has been developed by Pao and Yeh [1] is adopted to investigate this problem. By applying the Fourier transform technique, the exact solutions for the generated magnetic inductions due to various mechanical singularities such as single force, a dipole, single couple and dislocation are obtained in a closed form. The distributions of the generated inductions on the surface are shown graphically.

Exact Analysis of Dynamic Sliding Indentation at any Constant Speed on an Orthotropic or Transversely Isotropic Half-Space

2002 ◽  
Vol 69 (3) ◽  
pp. 340-345 ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Plane Strain ◽  
Half Space ◽  
Contact Zone ◽  
Transversely Isotropic ◽  
Exact Formula ◽  
Constant Speed ◽  
Displacement Fields ◽  
Rigid Indentor

A plane-strain study of steady sliding by a smooth rigid indentor at any constant speed on a class of orthotropic or transversely isotropic half-spaces is performed. Exact solutions for the full displacement fields are constructed, and applied to the case of the generic parabolic indentor. The closed-form results obtained confirm previous observations that physically acceptable solutions arise for sliding speeds below the Rayleigh speed, for a single critical transonic speed, and for all supersonic speeds. Continuity of contact zone traction is lost for the latter two cases. Calculations for five representative materials indicate that contact zone width achieves minimum values at high, but not critical, subsonic sliding speeds. A key feature of the analysis is the factorization that gives, despite anisotropy, solution expressions that are rather simple in form. In particular, a compact function of the Rayleigh-type emerges that leads to a simple exact formula for the Rayleigh speed itself.

A note on holomorphic functions and the Fourier-Laplace transform

2017 ◽  
Vol 120 (2) ◽  
pp. 225 ◽  
Author(s):  
Marcus Carlsson ◽  
Jens Wittsten
Keyword(s):  
Fourier Transform ◽  
Laplace Transform ◽  
Half Plane ◽  
Classical Problem ◽  
Holomorphic Functions ◽  
Function Spaces ◽  
Classical Function ◽  
Upper Half Plane ◽  
The Fourier Transform ◽  
Half Axis

We revisit the classical problem of when a given function, which is analytic in the upper half plane $\mathbb{C} _+$, can be written as the Fourier transform of a function or distribution with support on a half axis $(-\infty ,b]$, $b\in \mathbb{R} $. We derive slight improvements of the classical Paley-Wiener-Schwartz Theorem, as well as softer conditions for verifying membership in classical function spaces such as $H^p(\mathbb{C} _+)$.

Fourier transforms related to ζ(s)

2021 ◽  
pp. 1-17
Author(s):  
Pablo A. Panzone
Keyword(s):  
Fourier Transform ◽  
Zeta Function ◽  
Closed Form ◽  
Dirichlet Series ◽  
Riemann Zeta Function ◽  
Fourier Transforms ◽  
Riemann Zeta ◽  
The Fourier Transform

Abstract Using some formulas of S. Ramanujan, we compute in closed form the Fourier transform of functions related to Riemann zeta function $\zeta (s)=\sum \nolimits _{n=1}^{\infty } {1}/{n^{s}}$ and other Dirichlet series.

scholarly journals The Effect of Defects in Piezoelectric Composite Half-Planes with Surface Electrodes

2020 ◽  
Vol 4 (2) ◽  
pp. 43
Author(s):  
Jacob Aboudi
Keyword(s):  
Fourier Transform ◽  
Boundary Value Problem ◽  
Half Plane ◽  
Iterative Procedure ◽  
Boundary Value ◽  
Piezoelectric Composite ◽  
Rectangular Region ◽  
Surface Electrodes ◽  
The Fourier Transform ◽  
Electromechanical Field

An analysis for the prediction of the electromechanical field in composite piezoelectric half-planes with attached surface electrode is presented. The composite half-planes are composed of distinct constituents and may include internal defects in various locations. The solution is carried out in a sufficiently large rectangular region, the boundary conditions of which are obtained from the corresponding solution of a homogeneous piezoelectric half-plane. This is followed by the application of the discrete Fourier transform at the domain of which a boundary-value problem is formulated. The solution of this boundary-value problem, followed by the inversion of the Fourier transform, provides, in conjunction with an iterative procedure, the electromechanical field at any point of the rectangular region. Applications are given for a piezoelectric half-plane with defects in the form of a cavity and of short and semi-infinite cracks as well as of a periodically bilayered composite with a crack in one of its layers.

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.

scholarly journals Strain Sensitivity Enhancement of Broadband Ultrasonic Signals in Plates Using Spectral Phase Filtering

2021 ◽  
Vol 11 (6) ◽  
pp. 2582
Author(s):  
Lucas M. Martinho ◽  
Alan C. Kubrusly ◽  
Nicolás Pérez ◽  
Jean Pierre von der Weid
Keyword(s):  
Fourier Transform ◽  
Guided Waves ◽  
Strain Level ◽  
Energy Concentration ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
The Fourier Transform ◽  
Short Time ◽  
Sensitivity Gain

The focused signal obtained by the time-reversal or the cross-correlation techniques of ultrasonic guided waves in plates changes when the medium is subject to strain, which can be used to monitor the medium strain level. In this paper, the sensitivity to strain of cross-correlated signals is enhanced by a post-processing filtering procedure aiming to preserve only strain-sensitive spectrum components. Two different strategies were adopted, based on the phase of either the Fourier transform or the short-time Fourier transform. Both use prior knowledge of the system impulse response at some strain level. The technique was evaluated in an aluminum plate, effectively providing up to twice higher sensitivity to strain. The sensitivity increase depends on a phase threshold parameter used in the filtering process. Its performance was assessed based on the sensitivity gain, the loss of energy concentration capability, and the value of the foreknown strain. Signals synthesized with the time–frequency representation, through the short-time Fourier transform, provided a better tradeoff between sensitivity gain and loss of energy concentration.

Determination of starch crystallinity with the Fourier-transform terahertz spectrometer

2021 ◽  
Vol 262 ◽  
pp. 117928
Author(s):  
Shusaku Nakajima ◽  
Shuhei Horiuchi ◽  
Akifumi Ikehata ◽  
Yuichi Ogawa
Keyword(s):  
Fourier Transform ◽  
The Fourier Transform ◽  
Starch Crystallinity
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