CONTENTS                

VOLUME  2,     issue 1

 S.B. Karavashkin and O.N. Karavashkina. THE BASIC PRINCIPLES OF OUR JOURNAL

Published on 24.12.2001

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  S.B. Karavashkin and O.N. Karavashkina. THEORETICAL SUBSTANTIATION AND EXPERIMENTAL CORROBORATION OF EXISTENCE OF TRANSVERSAL ACOUSTIC WAVE IN GAS

Published on 24.12.2001

In this paper we will consider the results of the experiment carried out in order to reveal and investigate prematurely the properties of transverse wave in gas medium. We will present the theoretical substantiation that such wave can exist in gas medium, where the property to transmit the transverse deformation is absent. This effect is possible when the sources of longitudinal oscillations oscillate in antiphase. We will prove theoretically and corroborate experimentally that as a result of this superposition, there forms a wave having all properties of the wave process in free space. The transversal acoustic wave has its near and far fields and typical properties inherent in them. The result of such superposition can be considered as the independent wave process in the far field, since its properties basically differ from the typical properties of the interference that bases, as is known, on the principle of oscillation superposition. A stable signal phase delay is experimentally ascertained in this field, as well as the presence of the polarisation plane and disappearance of the signal inversion typical for the near field and interference.

Keywords: Wave physics; Acoustics; Acoustic waves production and propagation; Technique of transversal acoustic waves production; Polarisation method of the acoustic waves investigation

Classification by MSC 2000: 76-05; 76-99.

Classification by PASC 2001: 43.20.+g; 43.38.+n; 43.58.+z; 43.90.+v; 43.20.Hq; 43.20.Tb; 46.25.Cc; 46.40.Cd

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S.B. Karavashkin and O.N. Karavashkina. SOME FEATURES OF VIBRATIONS IN HOMOGENEOUS 1D RESISTANT ELASTIC LINE WITH LUMPED PARAMETERS

Published on 28.12.2001

In this paper we consider the effect of the resistance on the vibration processes in a semi-infinite elastic line with lumped and with distributed parameters. Particularly, we will see that for the given type of a line, the progressive pattern of vibrations remains also at the overcritical frequencies, and the phase delay is always less than the value, corresponding to the first Brillouin zone. When comparing the obtained results with the experimental data on the phase velocity of ultrasonic wave in the carbonic acid gas, we see that taking into consideration the resistance, we can essentially refine the conventional models and promote their better correspondence to the experimental data.

Keywords: Wave physics; Many-body theory; Complex resonance systems; ODE systems

Classification by MSC 2000: 30E25; 70E55; 70J35; 70J60; 70K40; 70F40

Classification by PASC 2001: 02.60.Lj; 05.10.-a; 05.45.-a; 45.30.+s; 46.15.-x; 46.25.Cc; 46.40.-f; 46.40.Fr

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 S.B. Karavashkin and O.N. Karavashkina. OSCILLATION PATTERN FEATURES IN MISMATCHED FINITE ELECTRIC LADDER FILTERS

Published on 01.01.2002

Basing on the original relationship of the Dynamical ElectroMechanical Analogy DEMA and original exact analytical solutions for a lumped mechanical elastic line as an analogue, it is studied, how the load resistance effects on the amplitude-frequency and phase-frequency characteristics of mismatched finite ladder filters. It is shown that in filters of such type the indicated characteristics have a brightly expressed resonance form and essentially transform at the lower and medial regions of the pass band, changing insufficiently near the cutoff frequency. It disables the conventional method to define the total phase delay and the ladder filter transmission coefficient and requires to find the exact analytical solutions by the presented method. The obtained calculation regularities well agree with the experimental results for similar-parameters ladder filters. The obtained results can be extended to essentially more complicated ladder-filter circuits.

Keywords: Circuit theory; Ladder filters; Electromechanical analogy; Filters under mismatched load

Classification by MSC 2000: 30E25; 93A30; 93C05; 94C05

Classification by PASC 2001: 84.30.Vn; 84.40.Az

Full text in Postscript

Respond to the review by Dr J.O. Scanlan, Chief Editor of International Journal of Circuit Theory and Applications

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S.B. Karavashkin and O.N. Karavashkina. ON COMPLEX RESONANCE VIBRATION SYSTEMS CALCULATION

Published on 05.01.2002

Published in the MIS-RT, issue 30-1 (2003)

Basing on exact analytical solutions obtained for semi-finite elastic lines with resonance subsystems having the form of linear elastic lines with rigidly connected end elements, we will analyse the vibration pattern in systems having such structure. We will find that between the first boundary frequency for the system as a whole and that for the subsystem, the resonance peaks arise, and their number is equal to the integer part of [(n – 1)/2] , where n is the number of subsystem elements. These resonance peaks arise at the bound between the aperiodical and complex aperiodical vibration regimes. This last regime is inherent namely in elastic systems having resonance subsystems and impossible in simple elastic lines. We will explain the reasons of resonance peaks bifurcation. We will show that the phenomenon of negative measure of subsystems inertia arising in such type of lines agrees with the conservation laws. So we will corroborate and substantiate Professor Skudrzyk’s concept.

We will obtain a good qualitative agreement of our theoretical results with Professor Skudrzyk’s experimental results.

Keywords: Many-body theory; Wave physics; Complex resonance systems; ODE.

Classification by MSC 2000: 34A34; 34C15; 37N05; 37N15; 70E55; 70K30; 70K40; 70K75; 70J40; 74H45.

Classification by PASC 2001: 02.60.Lj; 46.25.Cc; 46.15.-x; 46.40.Fr

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 S.B. Karavashkin and O.N. Karavashkina. EXACT ANALYTICAL SOLUTIONS FOR AN IDEAL ELASTIC INFINITE LINE WITH ONE HETEROGENEITY TRANSITION

Published on 17.02.2002

Keywords: Mathematical physics; Wave physics; Nonlinear dynamics; ODE; Many-body theory; Heterogeneous elastic lines; Finite deformation; Oscillation theory; Dynamical systems

Classification by MSC 2000: 34A34; 34C15; 37N05; 37N15; 70E55; 70K30; 70K40; 70K75; 70J40; 74H45.

Classification by PASC 2001: 02.60.Lj; 46.25.Cc; 46.15.-x; 46.40.Fr

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S.B. Karavashkin and O.N. Karavashkina. SOME FEATURES OF FORCED VIBRATIONS MODELLING FOR 1D HOMOGENEOUS ELASTIC LUMPED LINES

Published on 26.02.2002

We will survey the conventional methods to calculate the systems that model vibrant 1D elastic lumped lines, in comparison with the new non-matrix method to yield the exact analytical solutions for such systems. We will consider the features arising when the external force affects an interior element of such system. We will analyse the conditions of the limiting process to the related distributed lines and derive the conditions at which a lumped line can be modelled by a distributed line.

Keywords: Mathematical physics; Wave physics; Theory of many-body systems; ODE systems; Finite deformation; Oscillation theory; Dynamical systems

Classification by MSC 2000: 34A34, 34C15, 37N05, 37N15, 70E55, 70J40, 70K30, 70K40, 70K75, 74H45.

Classification by PASC 2001: 02.60.Lj; 05.45.-a; 45.05.+x; 45.10.-b; 45.20.-d; 45.20.Dd; 45.30.+s; 45.50.-j; 45.50.Jf; 46.15.-x; 46.25.Cc; 46.40.-f; 46.40.Cd; 46.40.Ff; 46.50.+a; 46.70.-p; 46.70.Lk

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S.B. Karavashkin and O.N. Karavashkina, BEND IN ELASTIC LUMPED LINE AND ITS EFFECT ON VIBRATION PATTERN

We prove that the bend in an elastic line does not effect on the solution pattern only, if the longitudinal and transversal stiffnesses of a line were equal. Basing on the proved theorem, we consider some models typical for the applications, particularly, models of a semi-finite elastic bended line, a homogeneous closed-loop elastic line and an elastic line having inequal longitudinal and transversal stiffness coefficients. We show that in the lines obeying the theorem conditions, with the remaining general solution, the vibration processes features are conditioned by the regularities of the co-ordinate system transformation. In case of inequal stiffness coefficients in the bend region, the complex dynamical thrusts and vibration break-downs take place, and the vibration amplitude grows. In the bend region the resonance peaks arise; their frequencies do not coincide for the wave process longitudinal and transversal components. This last leads to the fact that in one and the same elastic line, with an invariable angle of external force inclination, dependently on frequency, the longitudinal, transversal or inclined waves can propagate along the line. With it, the wave inclination does not coincide with the external force inclination, as it takes place in the lines having equal stiffness coefficients. As the examples we will consider some aspects of these models application to the geophysical problems.

Keywords: Mathematical physics; Wave physics; Theory of many-body systems; ODE systems; Dynamics; Heterogeneous dynamical systems; Elastic bended systems; Nonlinear vibration systems; Wave propagation in nonlinear media; Geophysics; Tectonics; Seismology

Classification by MSC 2000: 34A34, 34C15, 37N05, 37N15, 70E55, 70J40, 70K30, 70K40, 70K75, 74H45.

Classification by PASC 2001: 02.60.Lj; 05.45.-a; 45.05.+x; 45.10.-b; 45.20.-d; 45.20.Dd; 45.30.+s; 45.50.-j; 45.50.Jf; 46.15.-x; 46.25.Cc; 46.40.-f; 46.40.Cd; 46.40.Ff; 46.50.+a; 46.70.-p; 46.70.Lk

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 S.B. Karavashkin and O.N. Karavashkina. ON COMPLEX FUNCTIONS ANALYTICITY

Published on 28.03.2002

We analyse here the conventional definitions of analyticity and differentiability of functions of complex variable. We reveal the possibility to extend the conditions of analyticity and differentiability to the functions implementing the non-conformal mapping. On this basis we formulate more general definitions of analyticity and differentiability covering those conventional. We present some examples of such functions. By the example of a horizontal belt on a plane Z mapped non-conformally onto a crater-like harmonic vortex, we study the pattern of trajectory variation of a body motion in such field in case of a field power function varying in time. We present the technique to solve the problems of such type with the help of dynamical functions of complex variable implementing the analytical non-conformal mapping.

Keywords: Analytical functions;  Theory of complex variable; Dynamical non-conformal mapping; Quasi-conformal mapping; Body trajectory

Classification by MSC: 30C62; 30C75; 30C99; 30G30; 32A30; 93A30

Classification by PASC 2001: 02.90.+p; 05.45.-a; 05.45.Ac; 05.45.Jc; 47.32.-y; 47.32.Cc

Full text in Postscript