Mathematical and Computational Applications

2417 KiB

Open AccessArticle

On F-Monotone Operators and Generalized Strongly Nonlinear Variational Inequalities

by Ashok Ganguly and Kamal Wadhwa

Math. Comput. Appl. 1997, 2(3), 155-162; https://doi.org/10.3390/mca2030155 - 01 Dec 1997

Viewed by 1019

In this paper we develop the existence theory of generalized strongly nonlinear variational inequality problem involving F-monotone operator in the setting of reflexive Banach spaces and Hausdorff topological vector spaces separately. Our results include Dugundji’s and Granas’s variational inequality in reflexive Banach spaces [...] Read more.

In this paper we develop the existence theory of generalized strongly nonlinear variational inequality problem involving F-monotone operator in the setting of reflexive Banach spaces and Hausdorff topological vector spaces separately. Our results include Dugundji’s and Granas’s variational inequality in reflexive Banach spaces and Tan’s variational inequality in topological vector spaces. respectively. Full article

5790 KiB

Open AccessArticle

A Generalized Approach to Coupled Nonlinear Vibrations of Continuous Systems

by M. Pakdemirli and H. Boyacı

Math. Comput. Appl. 1997, 2(3), 141-154; https://doi.org/10.3390/mca2030141 - 01 Dec 1997

Cited by 4 | Viewed by 1059

Abstract

A mathematical model covering many practical vibration problems of continuous systems has been proposed. The equations of motion consist of two nonlinearly coupled partial differential equations. The quadratic and cubic nonlinearities as well as the linear part of the equations are represented by [...] Read more.

A mathematical model covering many practical vibration problems of continuous systems has been proposed. The equations of motion consist of two nonlinearly coupled partial differential equations. The quadratic and cubic nonlinearities as well as the linear part of the equations are represented by arbitrary operators. A perturbation approach (method of multiple time scales) has been applied directly to the partial differential equations. The responses as well as the amplitude and phase modulation equations are found for the case of primary resonances of the external excitation and one-to-one internal resonances between the natural frequencies of the equations. The coefficients of the amplitude and phase modulation equations are calculated in their most general form. Results are then applied to a nonlinear cable vibration problem having small sag-to span ratios. Full article

3322 KiB

Open AccessArticle

Investigation of NMR Relaxation Data Using Dipole Correlation Function

by Ş. Yılmaz and S. Bozdemir

Math. Comput. Appl. 1997, 2(3), 131-139; https://doi.org/10.3390/mca2030131 - 01 Dec 1997

Viewed by 1055

Abstract

In this work, the theories of the relaxation mechanism leading to the dipole-correlation function, playing an important role in the analysis of the spin-lattice and spin-spin relaxation times in magnetic rezonance, are investigated. An evaluation of these theories is made in the light [...] Read more.

In this work, the theories of the relaxation mechanism leading to the dipole-correlation function, playing an important role in the analysis of the spin-lattice and spin-spin relaxation times in magnetic rezonance, are investigated. An evaluation of these theories is made in the light of the experimental data. It is found that the spin-lattice relaxation data of the glassy medium, particularly, do not obey much the single dipole correlation function of the form exp(-t/τ), obtained from the classical Debye relaxation theory of the polar molecules. On the other hand, it is observed that the data can be represented by the non-exponential correlation function driven from the cooperative relaxation models based on the spin-defect interactions. Furthermore, it is shown that the spin-spin relaxation time, obtained from the dipole-correlation function representing the relaxation of the one-dimensional Ising spins with nearest neighbor interactions, is in complete agreement with the experimental observations. Full article

1643 KiB

Open AccessArticle

The Development of Euler Hyperbola in Heavy Bars

by Aydoğan Özdamar

Math. Comput. Appl. 1997, 2(3), 127-130; https://doi.org/10.3390/mca2030127 - 01 Dec 1997

Viewed by 1006

Abstract

Euler [1] discovered the critical buckling force of the bars under an axial load. Euler, however ignored bar's own weight in his calculations. He drew the line diagram of critical strength vs bars slenderness ratio, the so called Euler-Hyperbole. The goal of this [...] Read more.

Euler [1] discovered the critical buckling force of the bars under an axial load. Euler, however ignored bar's own weight in his calculations. He drew the line diagram of critical strength vs bars slenderness ratio, the so called Euler-Hyperbole. The goal of this paper is to extend Euler-Hyperbole to heavy bars. Furthermore, factors which have effects on critical buckling forces will be analysed. This study may lead to economical gain, since materials are fully utiliesed. Full article

3340 KiB

Open AccessArticle

An Investigation of Deep Drawing of Low Carbon Steel Sheets and Applications in Artificial Neural Networks

by Cevdet Meriç, N. Sinan Köksal and Bekir Karlık

Math. Comput. Appl. 1997, 2(3), 119-125; https://doi.org/10.3390/mca2030119 - 01 Dec 1997

Cited by 3 | Viewed by 1018

Abstract

In this study, the deep drawability of SAE 6114, being a low carbon steel, was investigated. The materials with thickness varying from 0.67 mm to 2 mm were subjected to tensile tests and then R (average vertical anisotropy coefficient) and n (stain hardening [...] Read more.

In this study, the deep drawability of SAE 6114, being a low carbon steel, was investigated. The materials with thickness varying from 0.67 mm to 2 mm were subjected to tensile tests and then R (average vertical anisotropy coefficient) and n (stain hardening exponent) values were determined. At the same time, h (the height of the cup) and F (the reaction force) values of the materials were found by subjecting them to Erichsen test A sheet with 2 mm thickness was cold rolled in 6 different deformation ratios and the tests were applied to it Results obtained from the tests were compared with each other and ANN application was performed for these results.
It was proved that, there was an ANN solution to obtain new values of % deformation rate and thickness properties of deep drawing of low carbon steel sheets which were found by experiment The obtained values satisfied our estimation. Full article

7289 KiB

Open AccessArticle

Numerical Simulation of a Gaseous Fueled (Methane) Combustor

by Mehmet Kopaç and Türkan Kopaç

Math. Comput. Appl. 1997, 2(3), 101-118; https://doi.org/10.3390/mca2030101 - 01 Dec 1997

Viewed by 1086

Abstract

In this study the combustion characteristics of the turbulent combustion of a gaseous fuel (methane) in a cylindrical combustion chamber were predicted numerically. For this reason; the equation of continuity, momentum, energy, chemical reaction rate, turbulent kinetic energy and turbulent kinetic energy dissipation [...] Read more.

In this study the combustion characteristics of the turbulent combustion of a gaseous fuel (methane) in a cylindrical combustion chamber were predicted numerically. For this reason; the equation of continuity, momentum, energy, chemical reaction rate, turbulent kinetic energy and turbulent kinetic energy dissipation rate equations were solved in polar coordinates using the K-ε turbulence model. The change of the axial velocity component, effective pressure, fuel mass fraction, mass fraction of the total combustion products, mass fraction of CO2, turbulent kinetic energy, turbulent kinetic energy dissipation rate and total enthalpy in the 3-dimensional turbulent polar region were predicted for different angle positions. The results were presented for θ = 72° for this study. The effect of fuel/air momentum was investigated on flow, heat and combustion characteristics. The chemical reaction rate was determined using the eddy-break up model. Full article

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Math. Comput. Appl., Volume 2, Issue 3 (December 1997) – 6 articles , Pages 101-162

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