VOLUME 2, issue 1 



Published on 24.12.2001 



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: 7605;
7699. 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 Full text: / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15 / 16 / 

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 semiinfinite 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;
Manybody theory; Complex resonance systems; ODE 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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text: / 17 / 18 / 19 / 20 / 21 / 22 / 23 / 24 / 25 / 26 / 27 / 28 / 29 / 30 / 31 / 32 / 33 / 34 / 



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 amplitudefrequency and phasefrequency 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
similarparameters ladder filters. The obtained results can be extended to essentially
more complicated ladderfilter 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 

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

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

Published on 05.01.2002 

Published in the MISRT, issue 301 (2003) 

Basing on exact analytical solutions
obtained for semifinite 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:
Manybody 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 

We will present some results of study of an infinite 1D elastic lumped line with one section of heterogeneity. We yielded these results, using the original nonmatrix method to find exact analytical solutions for an infinite system of differential equations. We will present few features important for practical use, caused by the transition of an elastic line section to the antiphase damping regime. We will show the conditions of solutions transformation, when transiting to the models related to this basic, as well as to the related elastic distributed line. The results of this study can be extended to the rotary vibrations of elastic lumped or distributed lines, as well as with the help of original dynamical electromechanical analogy (DEMA) they can be applied to the calculation of electrical filters. Keywords: Mathematical physics; Wave physics; Nonlinear dynamics; ODE; Manybody 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 nonmatrix 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 manybody 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 

Published on 05.03.2002 

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 semifinite elastic bended line, a homogeneous closedloop 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 coordinate system transformation. In case of inequal stiffness coefficients in the bend region, the complex dynamical thrusts and vibration breakdowns 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 manybody 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 nonconformal 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 nonconformally onto a craterlike 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 nonconformal mapping. Keywords: Analytical functions; Theory of complex variable; Dynamical nonconformal mapping; Quasiconformal mapping; Body trajectory Classification
by MSC: 30C62; 30C75 Classification
by PASC 2001: 02.90.+p 

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