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Browsing Conference Publications by Author "Fedotov, I"

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Analysis of a new unidimensional model and lateral vibrations of 1-3 piezocomposite side scan sonar array

Author: Shatalov, MY ; Fedotov, I ; Wallis, JR ; Nicolaides, KE Date: Jan 2006 A novel unidimensional model of 1-3 piezocomposite ultrasonic transducers is presented. A new electromechanical model is the generalization of the Smith-Auld unidimentional model, which is formulated in terms of a variational approach. It ... Read more
Application of eigenfunction orthogonalities to vibration problems

Author: Fedotov, I ; Fedotova, T ; Shatalov, M ; Tenkam, HM Date: Jul 2009 The modelling of vibration problems is of great importance in engineering. A popular method of analysing such problems is the variational method. The simplest vibration model is represented using the example of a long rod. Two kinds of ... Read more
Combined Helmholtz Integral Equation - Fourier series formulation of acoustical radiation and scattering problems

Author: Fedotov, I ; Shatalov, M Date: Jul 2006 The Combined Helmholtz Integral Equation – Fourier series Formulation (CHIEFF) is based on representation of a velocity potential in terms of Fourier series and finding the Fourier coefficients of this expansion. The solution could be ... Read more
Comparison of classical and modern theories of longitudinal wave propagation in elastic rods

Author: Shatalov, M ; Fedotov, I ; Tenkam, HM ; Marais, J Date: Jul 2009 A unified approach to derivation of different families of differential equations describing the longitudinal vibration of elastic rods and based on the Hamilton variational principle is outlined. The simplest model of longitudinal vibration ... Read more
Comparison of classical and modern theories of longitudinal wave propagation in elastic rods

Author: Shatalov, M ; Fedotov, I ; Tenkam, HM ; Marais, J Date: Jan 2011 A unified approach to derivation of different families of differential equations describing the longitudinal vibration of elastic rods and based on the Hamilton variational principle is outlined. The simplest model of longitudinal vibration ... Read more
Dynamics and control of vibratory gyroscopes with special spherical symmetry

Author: Shatalov, M ; Fedotov, I ; Joubert, S Date: 2006 It was shown in 1985 by Acad. V. Zhuravlev that the angular rate of a pure vibrating mode excited in a vibratory gyroscope with spherical symmetry is proportional to an inertial angular rate of the gyroscope. The effect is three dimensional ... Read more
Exact solutions and numerical simulation of longitudinal vibration of the Rayleigh-Love rods with variable cross-sections

Author: Shatalov, M ; Fedotov, I Date: Sep 2012 Exact solutions of equations of longitudinal vibration of conical and exponential rod are analyzed for the Rayleigh-Love model. These solutions are used as reference results for checking accuracy of the method of lines. It is shown that the ... Read more
Gyroscopic effects in vibrating fluid-filled spheres subjected to inertial rotation

Author: Shatalov, MY ; Joubert, SV ; Coetzee, CE ; Fedotov, I Date: Jul 2007 In symmetric distributed structures subjected to vibration and an inertial rotation, the vibrating patterns turn in the direction of revolution at a rate proportional to the inertial angular rate. This effect has numerous applications in ... Read more
Novel approach to the Helmholtz integral equation solution by Fourier series expansion for acoustic radiation and scattering problems

Author: Shatalov, MY ; Fedotov, I ; Joubert, S Date: 2006 Conventional methods of solution of the Helmholtz integral equation consist in discretization of a radiating/scattering boundary on multiple boundary elements, assumption of a smooth distribution of the velocity potential on every element and ... Read more
Novel method of interpolation and extrapolation of functions by a linear initial value problem

Author: Shatalov, M ; Fedotov, I ; Joubert, SV Date: Sep 2008 A novel method of function approximation using an initial value, linear, ordinary differential equation (ODE) is presented. The main advantage of this method is to obtain the approximation expressions in a closed form. This technique can be ... Read more
Numerical computation of special functions with applications to physics

Author: Motsepe, K ; Fedotov, I ; Shatalov, M ; Joubert, SV Date: Sep 2008 Students of mathematical physics, engineering, natural and biological sciences sometimes need to use special functions that are not found in ordinary mathematical software. In this paper a simple universal numerical algorithm is developed to ... Read more
On dynamics and control of vibratory gyroscopes with special spherical symmetry

Author: Shatalov, M ; Fedotov, I ; Joubert, S Date: May 2006 It was shown in 1985 by Acad. V. Zhuravlev that the angular rate of a pure vibrating mode excited in a vibratory gyroscope with spherical symmetry is proportional to an inertial angular rate of the gyroscope. The effect is three dimensional ... Read more
On gyroscopic effects in vibrating and axially rotating solid and annular discs

Author: Joubert, SV ; Fedotov, I ; Pretorius, W ; Shatalov, MY Date: May 2007 “Bryan’s effect" - that is, the effect of a vibrating pattern’s precession in the direction of inertial rotation of a vibrating ring - was discovered by G. Bryan in 1890. This effect has several applications in navigational instruments, such ... Read more
On the resonant behavior of longitudinally vibrating accreting rods

Author: Shatalov, M ; Manzhirov, A ; Fedotov, I Date: Sep 2012 The theory of accreting structures is a new and fast developing branch of analytical mechanics basing on the theory of partial differential and integral equations. In the present paper the authors analyze qualitative properties of accreting ... Read more
Parametric identification of the model with one predator and two prey species

Author: Shatalov, M ; Greeff, JC ; Joubert, SV ; Fedotov, I Date: Sep 2008 In this paper a mathematical model describing the interaction of a lion population with that of the zebra and wildebeest populations is considered. The traditional method uses a model with known coefficients and a CAS numerical routine to ... Read more
Precession of elastic waves in vibrating isotropic spheres and transversely isotropic cylinders subjected to inertial rotation

Author: Joubert, S ; Shatalov, M ; Fedotov, I ; Voges, E Date: May 2006 It was found by G. Bryan in 1890 that vibrating pattern of a rotating ring follows to a direction of the inertial rotation of this ring with an angular rate of the vibrating pattern smaller than the inertial rate. In 1979 E. Loper and D. Lynch ... Read more
Rayleigh-Love model of longitudinal vibrations of conical and exponential rods: Exact solutions and numerical simulation by the method of lines

Author: Shatalov, M ; Schiesser, W ; Polyanin, A ; Fedotov, I Date: Jul 2011 New exact solutions of equations of longitudinal vibration of conical and exponential rod are obtained for the Rayleigh-Love model. These solutions are used as reference results for checking accuracy of the method of lines. It is shown that ... Read more
Resonant vibrations and acoustic radiation of rotating spherical structures.

Author: Shatalov, M ; Fedotov, I ; Joubert, S Date: Jul 2006 The generating equations of the problem are considered in terms of a system of three dimensional equations of linear elasticity considered in the spherical coordinates. It is known that in this case the exact solution of the problem could be ... Read more
Scattering of obliquely incident standing wave by a rotating transversely isotropic cylinder

Author: Shatalov, MY ; Fedotov, I ; Joubert, S Date: May 2006 It is known that vibrating patterns of an isotropic cylinder, subjected to inertial rotation over the symmetry axis, precess in the direction of rotation with a different angular rate. The proportionality coefficient, or the so-called Bryan ... Read more
Solution of heat equation with variable coefficient using derive

Author: Lebelo, RS ; Fedotov, I ; Shatalov, M Date: Sep 2008 In this paper, the method of approximating solutions of partial differential equations with variable coefficients is studied. This is done by considering heat flow through a one-dimensional model with variable cross-sections. Two cases are ... Read more

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