SCIENTIFIC ABSTRACT FR:BOLOTIN, V.V. TO:BELOTSERKOVSKIY, D.Y.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000204400018-6
• Release Decision: RIP
• Original Classification: U
• Document Page Count: 6
• Document Creation Date: November 2, 2016
• Sequence Number: 18
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTR

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ACCESSION NR: AP404208? S/2881/83/000/020/005T/006?
AUTHOR: Bolotin, V. V. ~Protesaor, doctor)
{ fiITLE: Sationary`~distributiars of probabilities in the statistical dynaxnios of elastic
systems
SOURCE: AN LatSSR. Inetitut avtomatiki i mekhaniki. Voprnsy* dinamikl i prochnosti,
no. 10, 1963, 67-6?
i
TOPIC TAGS: oscillation, elastic system, statistical dynamios, stationary probability
distribution, Markov process, attenuation factor
ABSTRACT: The author notes that for the solution of problems involving the oscillations
of mechanical systems under the influence of stationary ratxlom forces, along with the
correlation and spectral, theories, methods based on the theory of multi-dimensional
Markov processes have been employed: Of particular interest, in the author's view, are
the stationary distributions of the parameters. These distributions provide a probabilistic
description of the behavior of the elastic system in time intervals rather large in com-'
parison with the relaxatiar time. The Maxwell - $olt$mann distributiar, widely used in
;statistical physics and in the theory of Brownian anotion, is an example of swell-studied
-,stationary distribution corresponding to certain special tapes of multi-dimensional Markav

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processes. The present article is devoted to a discussion of the constraints which must
be imposed on the properties of an elastic system and an the properties of a random load
in order that the stationary distribution of the dynamic variables of the system be dos-
cribed by a Maxwell -Boltzmann distribution. Some information from the theory of
multi-dimensional Markov processes is introduced, aAd the limitations are discussed
under which the time variation in the probability density is described by the Fokker -
Planck - Kolmogorov equation. This equation is introduced and solved, and it is shown
that if the generalized forces are "white noise", then the joint evolution of generalized
coordinates and generalized velocities represents amulti-dimensional continuous
Markov process, described by such an equation. The author notes, however, that the
equation derived in the text ~ ,.
d~ + (1)
9 ~9ti ~ Qz~ ..., qr 9~ ~ 9s�1 � �, 9.) ~' -- ~., 9a __.._
aa~ aqa
i ,
tea ' ,
rrr
aa1 Pa d~a
i
~,, ~ -. -

w
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~' permits a solution in a closed form In onl a few
stationary distributions are discussod, and the c ng~ ~ ~ ~~ For this rea8on,
Maxwell -Boltzmann distribotlon ie realized. The mechanical sen Yid under which We
� introduced is also conaiderecl, with special attenti~ to ~ '~ ~ the limitations
demonstrates that the t~anditiop ~ case r > 1. The author
Qa
is not overly restrictive, sad that the requirement for ~
factors ~ ~ibr ~~e wrrtial attenuation
generally own a conrst~. eis of greater coneequeace. This ~ ent cos
xPe ntai data regarding the damping forces is mechanic ye~ ems.
On the other hand, the condition
c~6 a cSQ~, (3)
impose$ eXtremely severe limitations on the properties of�the external for
problem is considered in some detail in the article. The ~s� This
. aaalyeis of a p~acular o8ee ,., a linear Paper concludes with an
forces, with an anaiysia of the followLng~et~ with statistically ~ePeadent ge~ueralized
sY of equations:
I
,~
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~, AceESSrort lvR: AP4a4zos~
~ ~~ ... . .
,, .. .._
j ~ ;qe '~' Zlaq� '~' Pawa7x ~' C~�(t) (u ~ 1 ~ 2, .. ~
~' - ~' j' ` (4j
.!, ,, where ire th� partial frequencies of the natural (eigenj oscillati
~ ~ Planck - Kolmogorov equation is presented in ire pro r fo ons� The Fokker -
~, solution is sought in the form of a aauesian dietrtbttti a� ~ rm ~ and the stationary .
Orig, art. has: 30 formulas and 4 fi r �~, 2 ��~ ~
gu ea.
ASSOCIATION: Institut avtomatild i mekhaniki AN LatS~
and Mechanics, AN Lat~j
(in+~titute fox Automation
:~
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ACCRSSION NRs AP4018426 ~.., ......,.. W ...~_..~......-._� 8~0179~64J00%Ol/0061,~0068 .
-~
~~~.,f .
~.!AVTBOxt Bolotin~ V. Y. (Yosoow) '
sta.
- .TITLES On bending of plates which are oaapoeed of a large nuwsber of lgrra
~t~lb i
!~.~
;.;~3 iSOURCTt AN 8858. I=v. Otd. tekh. sank. liskhanika i mashinostroyeniy~e, no. 1,
;~~, ;81.88
;~f l'e ~
"'�~k ~TOk'IC TAGSs stress analysis, bending, strasa,~aaltilayer plate, Evros analysis,
~~
`'`~~ elastic plate bending, plate bending
:_~.
~~- I
}.~~? ,ABSTRACT: A theory of elastic plates oamposad of alternating "hard" and "soft"
~.~,layers was presented in a work by V. V. Bolotia (K teorii aloistykh Alit. Isv. AY
.SSSR, OTN, Mekhanika i Maahinoatroyeniye, 1983, No. 3) as a natural generalisation
~Y:;~~, of the well knoavn theo of tril ~
ry ayer plates with a Sept filler. xn the present
~k~' article there is an examination oP the limiting vase of this theory built on the ~~
;supposition that there is a rather large number of plates. Differential equations
~~ 'and natural boundary ooaditiona are set up which correspond to same squinlent three
,~..,
~` dimensional problem. The error is estimated which i� oaunsotsd with transitiion to a'
~x.
~~`~' three dimensional problem. ~ example ie given of a solution to the problean off' '~~~""
~~> +bendi of a late which ie rsot
ag p angular in plan, loadod by � uniformly distributed
~~. ..
~~y~F ...
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ACCESSION NRs AP4043525 S/0258/64/OarF/oo3/0516/O~z4
AUT~iORS s Bolot,in~vHV'.._,-Y!,.- . (Mascox)f Maskalenko, ~. N. (Moscox)
TITT.Es Deflection of two layer plates connected xith elastic rode
SOURCES Inzhenorz~r*y zhurnal, v. 4, no. 3, 1964, 516-524
TOPIC TAGS: elastic plate, middle surface deflection, torsion, shear, deformation]
elasticity modulus, Poisson coeffici9nt, str�as tensor, potential. enemy, trans-
v�rse component, variational principle
AB:Ti~ACT: The deflection of a system consisting of two al.nstic plAtes connoctad
with rods {sea Pig. 1 on tho Enclosure) wus stud~.edg constdez~ing middle surfACe
def~.ection, plus the torsions shear' at~d doformrat~.on of the connecting rode, The
thickness hd, elasticity modulus E~ ,and goissonfs c0�ff3.cie~nt /~ for each
plate are assumed to be constant. Th� deflection off' a point on the plate u~,v~ ,
w~is defined by ~~- ._._`__� aWa ~---: ~- a~n . ._ . _. ,~_ -,
u
ua ~ a ~ ~ r3x ' ~~ na' ~ ~_" ~~ t~s rctta~ w~ {K .~ 1,t1 . ~
`_
,The com/ponents of the deformation and stress tensors are defined explicitly, and
Card /4
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an expression is introduced for tl~o paton~t;ial energy etorod ~~urin~; t}~e ~a1.aGo
deflection. It is further assumed that plate separation distance H is such
greater than ham. The forces geners ted in the rode are divided into langitudinAi.
and transverse components and an equivalent pot;entia~. anorgy expr�seion is ~rritten
for the rod deformation. Lagrange's variational principle is then cased to deter-�
mine the governing equation for plate and rod deflections and then reduced to a
simpler form corresponding to ho>nogen�ous rode, uniformly distributed between the
`two plates. The potential functions Sand ~ art then written in terns oP polar
~ooordinat�$ r, ~, and exp~reeeione derived for w and � under a conoentrated load or
a'..~T~ ~) `� S d9c S 4 ~~'�~ ee~ ~~ In ~rod- o,
~ ~` 0 r,
q,. fir, 8) `~ `-. ~ ~ dgoS 9 ~rr,ao~ [~' In g ~- 4x"' (! -!- In ~) rrdr~,~
' u r, � ,
f'" 8 ~~ _ v+~ q~+ ~ ~..~ r -{- r~. - rs cos - u .
~/~ 1 ..ter a W~J.~y. V. ~. ~� - ~. r. � -
Cord ~
- -__ _.. ~..,._. _ ~_ _..._._~.....~_...~_~~.._. _._.._._.._..~_,._....__._._ __...,. ~...._.I
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+i
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j.ACCESSION NR; AR40422^3
S/ 0124 / 84 / OOOI 008 /A OZO/A 020
'SOURCE: Ref. ah, Mekhanilia, Abs. 8A115
I
AUTNOA: Belotin, V, V.
TITLT;: Stationary distributions of probabilities in the statistical dynamics of
elastic systems
CITED SOURCE: Sb. Vopr, dinamiki i prochnosti. Vy~p. 10. Alga, AN LatvSSR,
1983, 57.87
TOPIC TAGS: probability, elastic system, statistical dynamics, elastic my,atem
;statistical dynamics
I
1TRANSLATION~ A description of the solution of the Fokker-Planck equa4ion
;fear elastic systems, under the action of random ~-correlated perturbation. It
considers both a system with finite number of degrees of ~~�eedorn, snd also a
system approximately reduced to such a means of intcodurtion of ~~pa~~si~,~ir~
card ~ 1/ 2
^++��.~.

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1.3~~ ht3-~-t?~t)
Translation from Refctratlvnyy zh~.It�n~l, ate*al! lrljl+;+a . +~~i ^+; }~ �,'i -"�+`~rtt
AUTHOR Belotserkov~k::,y~. , L 1
TITLE� Working Condltcoris ul tl~e Crush t~~; arlci 'rI�anspol�+ Dt l~;a r?I~lt::t
of .a C:opp~~�-are C,.,UrIC:t'lltr8l.IOII 1\llll ~iJ~la~-:ya tlud~~ ~ iiI�c)t)li ~~~.~-
transpot�tnc~rn otde E,`I;'; rnc:cltloruct~ic~y obas~tlt~tei'n+,~ ! :hr~!