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ISSN 1449-5910  

 

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Total of 22 results found in site

10: Paper Source PDF document

Paper's Title:

Hyperbolic Models Arising in the Theory of Longitudinal Vibration of Elastic Bars

Author(s):

1I. Fedotov, 1J. Marais, 1,2M. Shatalov and 1H.M. Tenkam


1Department of Mathematics and Statistics,
Tshwane University of Technology
 Private Bag X6680, Pretoria 0001
South Africa.


fedotovi@tut.ac.za, julian.marais@gmail.com, djouosseutenkamhm@tut.ac.za.

 2Manufacturing and Materials
Council of Scientific and Industrial Research (CSIR)
P.O. Box 395, Pretoria, 0001
South Africa.
mshatlov@csir.co.za

 

Abstract:

In this paper a unified approach to the derivation of families of one
dimensional hyperbolic differential equations and boundary conditions describing
the longitudinal vibration of elastic bars is outlined. The longitudinal and
lateral displacements are expressed in the form of a power series expansion in
the lateral coordinate. Equations of motion and boundary conditions are derived
using Hamilton's variational principle. Most of the well known models in this
field fall within the frames of the proposed theory, including the classical
model, and the more elaborated models proposed by by Rayleigh, Love, Bishop,
Mindlin, Herrmann and McNiven. The exact solution is presented for the
Mindlin-Herrmann case in terms of Green functions. Finally, deductions regarding
the accuracy of the models are made by comparison with the exact
Pochhammer-Chree solution for an isotropic cylinder.



7: Paper Source PDF document

Paper's Title:

On The Rayleigh-Love Rod Accreting In Both Length And Cross-Sectional Area: Forced And Damped Vibrations

Author(s):

M.L.G. Lekalakala1, M. Shatalov2, I. Fedotov3, S.V. Joubert4

1Department of Mathematics, Vaal University of Technology, P.O. Box 1889, Secunda, 2302, South Africa.
E-mail1: glen@vut.ac.za 

2,3,4Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria, South Africa.

Abstract:

In this paper an elastic cylindrical rod that is subjected to forced and damped vibrations is considered. The rod is assumed to be isotropic. The applied external force of excitation is assumed to be harmonic, and the damping force is that of Kelvin-Voigt. The longitudinally vibrating rod is fixed at the left end and free at the other end. The rod is assumed to be accreting in length and cross-sectional area as it vibrates. The problem arising and the dynamics of the vibrating rod are described and investigated within the Rayleigh-Love theories of the rod. A partial differential equation describing the longitudinal displacement of the rod is formulated. The formulated partial differential equation, together with the corresponding boundary conditions as per the configuration of the rod, is solved numerically using the Galerkin-Kantorovich method. The frequency of vibration of the harmonic exciting force is kept constant in this investigation.

It is shown that in this periodically forced viscoelastic damped vibration, all the modes of vibration are subjected to the resonance behaviour within a proper time interval, depending on the length of the accreting rod.



3: Paper Source PDF document

Paper's Title:

Inequalities for Functions of Selfadjoint Operators on Hilbert Spaces:
a Survey of Recent Results

Author(s):

Sever S. Dragomir1,2

1Mathematics, College of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
2DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL: https://rgmia.org/dragomir 

Abstract:

The main aim of this survey is to present recent results concerning inequalities for continuous functions of selfadjoint operators on complex Hilbert spaces. It is intended for use by both researchers in various fields of Linear Operator Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.



1: Paper Source PDF document

Paper's Title:

Inequalities for the Čebyev Functional of Two Functions of Selfadjoint Operators in Hilbert Spaces

Author(s):

S. S. Dragomir

School of Engineering and Science
 Victoria University, PO 14428
 Melbourne City MC, Victoria 8001,
Australia

sever.dragomir@vu.edu.au
URL
: http://www.staff.vu.edu.au/RGMIA/dragomir/

Abstract:

Some recent inequalities for the Čebyev functional of two functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved functions and operators, are surveyed.



1: Paper Source PDF document

Paper's Title:

Ostrowski Type Inequalities for Lebesgue Integral: a Survey of Recent Results

Author(s):

Sever S. Dragomir1,2

1Mathematics, School of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
2DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL: http://rgmia.org/dragomir 

Abstract:

The main aim of this survey is to present recent results concerning Ostrowski type inequalities for the Lebesgue integral of various classes of complex and real-valued functions. The survey is intended for use by both researchers in various fields of Classical and Modern Analysis and Mathematical Inequalities and their Applications, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.


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