scholarly journals Self-equilibrated stresses in the system composed of a covering layer + spatially locally curved reinforcing layer + half-space

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 2179-2183
Author(s):  
Ramazan Tekercioglu
Keyword(s):  
Fourier Transform ◽  
Half Space ◽  
The Self ◽  
Normal Stresses ◽  
Normal Forces ◽  
Covering Layer ◽  
First Approximation ◽  
Double Fourier Transform ◽  
Curved Substrate ◽  
Reinforcing Layer

The system composed of a face covering layer + spatially locally curved substrate reinforcing layer + half-space is taken into consideration. It is presumed that this framework is compressed at infinity by uniformly distributed normal forces and it is required to establish the self-equilibrated normal stresses in that, caused by locally curved of the substrate reinforcing layer. The matching boundary and contact value problem is defined within the scope of 3-D geometrically non-linear exact equations. Formulated problem?s solution is introduced with the series form of small parameter which represents the degree of the aforesaid locally curving. These series? zeroth and first approximation are ascertained with the utilization of double Fourier transform. The original of values that are searching is ascertained numerically. Corresponding numerical outcomes about the self-equilibrated normal stress caused by this spatially local curving are presented and discussed.

Solution of Navier’s Equation in Cylindrical Curvilinear Coordinates

1978 ◽  
Vol 45 (4) ◽  
pp. 812-816 ◽  
Author(s):  
B. S. Berger ◽  
B. Alabi
Keyword(s):  
Fourier Transform ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Half Space ◽  
Coordinate Transformation ◽  
Numerical Results ◽  
Three Dimensions ◽  
Curvilinear Coordinates ◽  
Rectangular Region

A solution has been derived for the Navier equations in orthogonal cylindrical curvilinear coordinates in which the axial variable, X3, is suppressed through a Fourier transform. The necessary coordinate transformation may be found either analytically or numerically for given geometries. The finite-difference forms of the mapped Navier equations and boundary conditions are solved in a rectangular region in the curvilinear coordinaties. Numerical results are given for the half space with various surface shapes and boundary conditions in two and three dimensions.

An automatic means to discriminate between earthquakes and quarry blasts

1990 ◽  
Vol 80 (6B) ◽  
pp. 2143-2160
Author(s):  
Michael A. H. Hedlin ◽  
J. Bernard Minster ◽  
John A. Orcutt
Keyword(s):  
Fourier Transform ◽  
Spectral Features ◽  
Single Event ◽  
Vertical Array ◽  
Signal To Noise ◽  
Spectral Character ◽  
Frequency Pattern ◽  
Time Frequency ◽  
Cepstral Analysis ◽  
Double Fourier Transform

Abstract In this article we discuss our efforts to use the NORESS array to discriminate between regional earthquakes and ripple-fired quarry blasts (events that involve a number of subexplosions closely grouped in space and time). The method we describe is an extension of the time versus frequency “pattern-based” discriminant proposed by Hedlin et al. (1989b). At the heart of the discriminant is the observation that ripple-fired events tend to give rise to coda dominated by prominent spectral features that are independent of time and periodic in frequency. This spectral character is generally absent from the coda produced by earthquakes and “single-event” explosions. The discriminant originally proposed by Hedlin et al. (1989b) used data collected at 250 sec−1 by single sensors in the 1987 NRDC network in Kazakhstan, U.S.S.R. We have found that despite the relatively low digitization rate provide by the NORESS array (40 sec−1) we have had good success in our efforts to discriminate between earthquakes and quarry blasts by stacking all vertical array channels to improve signal-to-noise ratios. We describe our efforts to automate the method, so that visual pattern recognition is not required, and to make it less susceptible to spurious time-independent spectral features not originating at the source. In essence, we compute a Fourier transform of the time-frequency matrix and examine the power levels representing energy that is periodic in frequency and independent of time. Since a double Fourier transform is involved, our method can be considered as an extension of “cepstral” analysis (Tribolet, 1979). We have found, however, that our approach is superior since it is cognizant of the time independence of the spectral features of interest. We use earthquakes to define what cepstral power is to be expected in the absence of ripple firing and search for events that violate this limit. The assessment of the likelihood that ripple firing occurred at the source is made automatically by the computer and is based on the extent to which the limit is violated.

A Fast Method for Solving Contact Plasticity in a Half Space

2011 ◽  
Author(s):  
Zhanjiang Wang ◽  
Xiaoqing Jin ◽  
Shuangbiao Liu ◽  
Leon M. Keer ◽  
Jian Cao ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Residual Stresses ◽  
Fast Fourier Transform ◽  
Half Space ◽  
Three Dimensional ◽  
New Method ◽  
Fast Method ◽  
Discrete Convolution ◽  
Influence Coefficients ◽  
The One

This paper presents a new method of contact plasticity analysis based on Galerkin vectors to solve the eigenstresses due to eigenstrain. The influence coefficients relating eigenstrains to eigenstresses thus can be divided into four terms the one due to the eigenstrains in the full space, others due to the mirrored eigenstrains in the mirror half space. Each term can be solved fast and efficient by using the three-dimensional discrete convolution and fast Fourier transform (DC-FFT) or the three-dimensional discrete correlation and fast Fourier transform (DCR-FFT). The new method is used to analyze the contact plastic residual stresses in half space.

Bleustein-Gulyaev Waves in an Inhomogeneous Layered Piezoelectric Half-Space

2006 ◽  
Vol 306-308 ◽  
pp. 1223-1228
Author(s):  
Fei Peng ◽  
Hua Rui Liu
Keyword(s):  
Fourier Transform ◽  
Phase Velocity ◽  
Half Space ◽  
Electric Potential ◽  
Piezoelectric Layer ◽  
Field Equations ◽  
Transform Method ◽  
Coupled Field ◽  
Coupled Field Equations ◽  
The Fourier Transform

The propagation of Bleustein-Gulyaev (BG) waves in an inhomogeneous layered piezoelectric half-space is investigated in this paper. Application of the Fourier transform method and by solving the electromechanically coupled field equations, solutions to the mechanical displacement and electric potential are obtained for the piezoelectric layer and substrate, respectively. The phase velocity equations for BG waves are obtained for the surface electrically shorted case. When the layer and the substrate are homogenous, the dispersion equations are in agreement with the corresponding results. Numerical calculations are performed for the case that the layer and the substrate are identical LiNbO3 except that they are polarized in opposite directions. Effects of the inhomogeneities induced by either the layer or substrate are discussed in detail.

Synthesis, Characterization, and Flocculation Properties of Branched Polyacrylamide

2012 ◽  
Vol 476-478 ◽  
pp. 2311-2316 ◽  
Author(s):  
Wei Min Sun ◽  
Guang Cheng Zhang ◽  
He Lin Li ◽  
Dong Dong Li ◽  
Pei Pei Li ◽  
...  
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Fourier Transform ◽  
Water Soluble ◽  
The Self ◽  
Solution Polymerization ◽  
Solution Ph ◽  
Water And Wastewater Treatment ◽  
Water And Wastewater ◽  
Acrylamide Monomer ◽  
Clay Suspensions

A water soluble branched polyacrylamide has been synthesized through solution polymerization. The polymerization was initiated by potassium diperiodatocuprate, K5[Cu(HIO6)2](Cu(III)), in alkaline medium and capable of initiating the self condensation vinyl polymerization of acrylamide monomer. The polymer obtained was characterized using Fourier-transform infrared (FTIR) spectroscopy and nuclear magnetic resonance (NMR) spectroscopy. Its flocculation properties were evaluated with clay suspensions using standard jar tests. The concentration of monomers, concentration of initiators, reaction temperature and solution pH on the influence of intrinsic viscosity and flocculation properties of production were studied. The results demonstrate that the branched polymer can be used as a kind of novel flocculant in water and wastewater treatment.

Poisson’s integral formula via heat kernels

Analysis ◽  
2019 ◽  
Vol 39 (2) ◽  
pp. 59-64
Author(s):  
Yoichi Miyazaki
Keyword(s):  
Fourier Transform ◽  
Heat Kernel ◽  
Half Space ◽  
Unbounded Domain ◽  
Harmonic Functions ◽  
Integral Formula ◽  
Heat Kernels ◽  
Transform Method ◽  
Fourier Transform Method ◽  
The Fourier Transform

Abstract We give another proof of Poisson’s integral formula for harmonic functions in a ball or a half space by using heat kernels with Green’s formula. We wish to emphasize that this method works well even for a half space, which is an unbounded domain; the functions involved are integrable, since the heat kernel decays rapidly. This method needs no trick such as the subordination identity, which is indispensable when applying the Fourier transform method for a half space.

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