Mathematical and Computational Applications

244 KiB

Open AccessArticle

A Comparison between Active and Passive Vibration Control of Non-Linear Simple Pendulum. Part II: Longitudinal Tuned Absorber and Negative Gφ and Gφn Feedback

by M. Eissa and M. Sayed

Math. Comput. Appl. 2006, 11(2), 151-162; https://doi.org/10.3390/mca11020151 - 01 Aug 2006

Cited by 39 | Viewed by 1188

Abstract

In part I [1] we dealt with a tuned absorber, which can move in the transversally direction, where it is added to an externally excited pendulum. Active control is applied to the system via negative velocity feedback or its square or cubic value. [...] Read more.

In part I [1] we dealt with a tuned absorber, which can move in the transversally direction, where it is added to an externally excited pendulum. Active control is applied to the system via negative velocity feedback or its square or cubic value. The multiple time scale perturbation technique is applied throughout. An approximate solution is derived up to second order approximation. The stability of the system is investigated applying both frequency response equations and phase plane methods. The effects of the absorber on system behavior are studied numerically. Optimum working conditions of the system are obtained applying passive and active control methods. Both control methods are demonstrated numerically. In this paper, a tuned absorber, in the longitudinal direction, is added to an externally excited pendulum. Active control is applied to the system via negative acceleration feedback or via negative angular displacement or its square or cubic value. An approximate solution is derived up to the second order approximation for the system with absorber. The stability of the system is investigated applying both frequency response equations and phase plane methods. The effects of the absorber on system behavior are studied numerically. Optimum working conditions of the system are extracted when applying both passive and active control methods. Full article

262 KiB

Open AccessArticle

A Comparison between Active and Passive Vibration Control of Non-Linear Simple Pendulum. Part I: Transversally Tuned Absorber and Negative Gφn Feedback

by M. Eissa and M. Sayed

Math. Comput. Appl. 2006, 11(2), 137-149; https://doi.org/10.3390/mca11020137 - 01 Aug 2006

Cited by 39 | Viewed by 1386

Abstract

Vibrations and dynamic chaos should be controlled in structures and machines. The most famous method of vibration control is using absorbers or tuned dampers or neutralizers. The main aim is to improve the system behavior at different resonance conditions. Two main strategies are [...] Read more.

Vibrations and dynamic chaos should be controlled in structures and machines. The most famous method of vibration control is using absorbers or tuned dampers or neutralizers. The main aim is to improve the system behavior at different resonance conditions. Two main strategies are used. They are passive and active control methods. In this paper, a tuned absorber, in the transversally direction, is added to an externally excited pendulum, which is simulated by a second order non-linear differential equation having both quadratic and cubic non-linearties, subjected to harmonic excitation. The absorber is usually designed to control one frequency at primary resonance where system damage is probable. The quenching efficiency of the system is studied. Active control is applied to the system via negative velocity feedback or its square or cubic value. The multiple time scale perturbation technique is applied throughout. An approximate solution is derived up to the second order approximation. The stability of the system is investigated applying both frequency response equations and phase plane methods. The effects of the absorber on system behavior are studied numerically. Optimum working conditions of the system are extracted when applying both passive and active control methods. Full article

312 KiB

Open AccessArticle

On the Numerical Solution of the Incompressible Navier-Stokes Equations in Primitive Variables Using Grid Generation Techniques

by S. A. Salem

Math. Comput. Appl. 2006, 11(2), 127-136; https://doi.org/10.3390/mca11020127 - 01 Aug 2006

Cited by 5 | Viewed by 1089

Abstract

In this paper presents a new model procedure for the solution of the incompressible Navier-Stokes equations in primitive variables, using grid generation techniques. The time dependent momentum equations are solved explicitly for the velocity field using the explicit marching procedure, the continuity equation [...] Read more.

In this paper presents a new model procedure for the solution of the incompressible Navier-Stokes equations in primitive variables, using grid generation techniques. The time dependent momentum equations are solved explicitly for the velocity field using the explicit marching procedure, the continuity equation is implied at each grid point in the solution of pressure equation, while the SOR method is used for the Neumann problem for pressure. Results obtained for the model problem of driven flow in a square cavity demonstrate that the method yields accurate solutions. The results of the numerical computations in a driven cavity, which are presented for the history of the residues at several Reynolds numbers Re=100,1000,4000 and 5000 all the computed results are obtained without any artificial dissipation. This feature of the present procedure demonstrates its excellent convergence and stability characteristics. Numerically results obtained for the steady state static pressure in the driven cavity are presented for the first time at Re=4000 and 5000 using non-staggered grid. Full article

119 KiB

Open AccessArticle

Sensitivity Analysis of General Mixed Multivalued Mildly Nonlinear Variational Inequalities

by Hanif Salahuddin

Math. Comput. Appl. 2006, 11(2), 121-125; https://doi.org/10.3390/mca11020121 - 01 Aug 2006

Cited by 1 | Viewed by 950

Abstract

Dafermos [1] studied the sensitivity properties of solutions of a variational inequality with respect to a parameter y. In this paper, we extend this analysis for general mixed multivalued mildly nonlinear variational inequalities in the setting of Hilbert spaces. Full article

329 KiB

Open AccessArticle

A Classification Methodology for Color Textures Using Multispectral Random Field Mathematical Models

by Alireza Khotanzad, Jesse W. Bennett and Orlando J. Hernandez

Math. Comput. Appl. 2006, 11(2), 111-120; https://doi.org/10.3390/mca11020111 - 01 Aug 2006

Cited by 7 | Viewed by 1183

Abstract

A large number of texture classification approaches have been developed in the past but most of these studies target gray-level textures. In this paper, supervised classification of color textures is considered. Several different Multispectral Random Field models are used to characterize the texture. [...] Read more.

A large number of texture classification approaches have been developed in the past but most of these studies target gray-level textures. In this paper, supervised classification of color textures is considered. Several different Multispectral Random Field models are used to characterize the texture. The classifying features are based on the estimated parameters of these model and functions defined on them. The approach is tested on a database of sixteen different color textures. A near 100% classification accuracy is achieved. The advantage of utilizing color information is demonstrated by converting color textures to gray-level ones and classifying them using gray-level random field models. It is shown that color based classification is significantly more accurate than its gray-level counterpart. Full article

154 KiB

Open AccessArticle

Thermal Shock Problem for One Dimensional Generalized Thermoelastic Layered Composite Material

by A. A. El-Bary and H. M. Youssef

Math. Comput. Appl. 2006, 11(2), 103-110; https://doi.org/10.3390/mca11020103 - 01 Aug 2006

Cited by 8 | Viewed by 1085

Abstract

The dynamic treatment of one-dimensional generalized thermoelastic problem of heat conduction is made for a layered thin plate, which is exposed, to a uniform thermal shock. The basic equations are transformed by Laplace transform and solved by a direct method. The solution was [...] Read more.

The dynamic treatment of one-dimensional generalized thermoelastic problem of heat conduction is made for a layered thin plate, which is exposed, to a uniform thermal shock. The basic equations are transformed by Laplace transform and solved by a direct method. The solution was applied for a plate of sandwich structure. The inverses of Laplace transforms are obtained numerically. The temperature, the stress and the displacement distributions are represented in graphs, which show the coupled and the generalized cases. Full article

179 KiB

Open AccessArticle

Propagation of Cylindrical Shock Waves in a Non-Uniform Rotating Stellar Atmosphere under the Action of Monochromatic Radiation and Gravitation

by Shilpa Shinde

Math. Comput. Appl. 2006, 11(2), 95-102; https://doi.org/10.3390/mca11020095 - 01 Aug 2006

Cited by 4 | Viewed by 1042

Abstract

A self-similar, theoretical model of propagation of cylindrical shock wave in a magneto- gas dynamic rotating non-uniform atmosphere in the presence of monochromatic radiation and gravitation, is considered. The result discussed depends upon the variations of the flow variables behind the shock, which [...] Read more.

A self-similar, theoretical model of propagation of cylindrical shock wave in a magneto- gas dynamic rotating non-uniform atmosphere in the presence of monochromatic radiation and gravitation, is considered. The result discussed depends upon the variations of the flow variables behind the shock, which are displayed graphically. A special case is considered in presence and absence of gravitation along with rotation to observe the influence of gravitation. Full article

100 KiB

Open AccessArticle

Sobolev’s Method for Hammerstein Integral Equations

by A.A. El-Bary

Math. Comput. Appl. 2006, 11(2), 91-94; https://doi.org/10.3390/mca11020091 - 01 Aug 2006

Cited by 2 | Viewed by 1015

Abstract

Sobolev’s initial value method is used to solve the Hammerstain equation of the second kind. Full article

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Math. Comput. Appl., Volume 11, Issue 2 (August 2006) – 8 articles , Pages 91-162

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