SCIENTIFIC ABSTRACT SKURIDIN, G.A. - SKURIDIN, G.A.

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• Sequence Number: 15
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

,5 ;< ~, R) p I t~l J! G - F1 -
USSR/Geophysics - Seismology FD-2586
Card 1/1 Pub. 44 16119
Author : Skuridin, G. A.
Title : Concerning Yu. V. Riznichenkols article "Determination of the
fields of intensity of seismic waves (ibid, No 1, 1954)
Periodical : Izv. AN SSSR, Ser. geofiz, Jul-Aug 55, 391-392
Abstract : Yu. V. Riznicheako proposed a method for determining the fields of
intensity (more accurately, the energy density) of seismic waves
(longitudingal or transverse) within the medium, if one knows the
field of intensity on a certain surface R, at which is given the
Viso-called 'dynamic' hodograph represented by the set of functions
tr = t(xr, Yr, zr) and Er B(Xrl Yr, zd, where E is the intensity
of the waves and t is the time field; he reduces this problem to
the integration of a first-order differential equation relative to
E for given boundary condition E/R = Er. The writer of this note
states that Yu. V. Reznichenko, according to his faulty derivation
of his formulas, is apparently unaware of the classical work of
N. A. Umov (Izbr. uch. (Colleted Works), Moscow-Leningrad, 1954,
pp 161-163).
Institution
Submitted

~SIR/Geo'phys'ics Wave diffraction FD-1701--
Card 1/1 : Pub. 45-1/12
Author : Skuridin, G. A.
Title : Approximate solution to the problem of the diffraction of plane elastic
wave relative to the aperture
Periodical : Izv. AN SSSR, Ser. geofiz., 3-16 Jan-Yeb 1955
Abstract : The author derives an approximate solution to the problem of the dif-
fraction of a plane elastic longitudinal veve relative to the aperture
by means of the Huyghens-K1rcbhoff principle for the equations of elas-
ticity. The formulas obtained permit one to give a quantitative anal-
ysis of the diffraction field. The coMutations are illustrated by
numerous graphs. The author ackawledges N. V. Zvolinskiy for his pos-
ing of the subject, L. P. Zayteev for directing the work of cowuta-
tion, and the laboratory assist4ate M. A. Kuzmetsov, B. V. Ushakova,
and N. N. Limache". Fifteen references (6.g. I. S. Bernzon, "Certain
problems of the kinematics of propmption of diffracted seismic vaves,"
Trudy Geofiz. in-ta M SM, No 9 (136), 195o; m. x. Fridman, "Diffrac-
tion of plane elastic wave relative to semi-infinite rectilinear rigidly
divided slit," Uch. zap. tau, ser. rat., No U4, 17, 1949).
Institution : Geophysics Institute, Academy of Sciences LESSR
Submitted : February 13, 1954

SKURIDIII,G.A.
Concerning IU.V.Risnichenkols article "Determining fields of
intensity of seismic waves." Izv.AN SSSR. Ser.geofiz. no.4:
391-392 JI-Ag'55- (MIRA 8:10)
(Seismology)

SOV/124- 58-4 -44q8
Trar,slat;on from: Referati%-nyy zhurnal, Mekhanika, 1958, Nr4. p 118(USSR)
AUTHOR: , Skuridin, G.A.
TITLE- Approximate Solution of the Problem of the Diffraction of a Plane
Longitudinal Elastic Wave in Relation to a Horizontal Fault
(Priblizhennoye resheniye zadachi difraktsii ploskoy uprugoy
prodot'noy voIny otnositell no gorizontal'nogo sbrosa)
PERIODICAL: Tr. In-ta geofiz. AN GruzSSR, 1955, Vol 14, pp 79-90
ABSTRACT: Or. the basis of the integral relationship submitted by V. D~
Kupradze [Granichnyye zadachi teorli kolebaniy i integral'nyye
uravneniya (Boundary Problems of the Theory of Vibrations and
Integral Equations). 1950] for the solution of the problem of the
diffraction of a plane longitudinal elastic wave in relation to a
horizontal fault, the author offers an approximate solution to
the problems of the diffraction of elastic waves in a manner
analogous to the method of Kirchhoff as applied to optics and
acoustics. It is assumed that the value of the displacement
vector v on the "illuminated" section of the surface S coin-
cides with the value of the descending wave on the unilluminated
Card 1/2 section. The author further accepts the so-called "principle of

SOV/124 -58 4 4498
Approximate Solution of the Problem (cont. )
the isolated element" in accordance with which the descending longitudinal
wave is reflected from the rectilinear boundary at each point in the same
manner as if it were reflected from a small element of the plane surface
intersect.ing the given point. In the author's opinion, the method de-,eloped
is , generalization of the Huygens principle applied to the system of wa-.e
equat 'ons which describe the propagation of longitudinal ands trans%erse
wa-,es. With the help of the stationary- phase method a study is made of the
wa-. es spreading over wide wave areas.
E, Ye. Khachiyan
2. Mlathemat,~L--s
Card 2,12

~ "/, ./ ,, ?~ ,/ 1 ~%r,-4
1 , I
KARP M 0,A.G.; SKURIDIN.G.A.
Contemporary problems of space flight. Vest.Aff SSSR 25 no.9:19-30
S 155. (MLRA 8:12)
(Space flight)

ZVOLINSKIY, N.V.; SKURIDIN, G,A.
As7mptotic solution of dynamic problems on the theory of elasticity.
IzT.AN SSSR.Ser.geofiz.no.2:134-143 7 156. (HIMA 9:7)
J.Akademiya nauk SSSR, Geofizichaskiy institut.
(Blasticity) (Waves)

J~~ ~1-1~1--;~,~,
Jumps in discontinuous solutions of dynamic equations in the theory of
elasticity. Izv.AN SSSR Ber.geofiz.no.6:625-633 Je 156. (MiaA 9:9)
i.Akademi7a nauk SSSR, Geofizicheskiy institut.
(Elasticity) (Geophysics)

45
AUTHOR: Skuridin, G. A.
------------

TITLE: -
On the theory of elastic wave scattering on curvilinear
boundary. (K teoril rasseyaniya uprugikh voln na
krivolineynoy granitse).
PERIODICAL: Izvestiya Akademli Nauk, Seriya Geofizicheskaya, 1957,
No.2, pp. 161-183 (U.S.S.R.)
ABSTRACT: An expanded version of a paper read on July 3, 1956 at
the 3rd All Union Mathematical Conference. An
approximate solution of the problem of elastic wave
scattering along a curvilinear boundary, calculated by
on the basis of Kirchhoff's law Is described.
Analytical expressions are worked out for the displace-
ment of longitudinal and transverse reflected waves and
it is shown that the reflection of a plane elastic wave
-from a curvilinear boundary produces a longitudinal and
f 1/2
Card 1/4 .
a transverse wave with a divergence function o
45
TITLE:
Card 2/4
On the theory of elastic wave scattering on curvilinear
boundary. (K teoril rassehaniya uprugikh voln na
krivolineynoy granitse).
An analysis is given of the main wave produced during
the incidence of a transverse wave on a rigid curvili-
near boundary and It is shown that In this case the
formation of several main waves is Possible. Scattering
indicatrices are given of longitudinal and transverse
waves and also graphs illustrating the character of
weakening Of these waves along the R beam. The intro-
ductory paragraph summarizes briefly work of other
authors on this subject. The problem itself is formula-
ted and solved for the incidence of a plane longitudinal
wave in para.l. The solution for the Incidence of a
plane transverse wave is arrived at In para.2, while In
para-3 an approximate evaluation is-given of the inte-
grals, and in para.4 the main wave is analyzed. The
diffracted field in the wave zone during the Incidence of
a plane longitudinal or transverse wave on a curvilinear
boundary can be expressed by eqs.J16), (17) (1p6166-167),
(23), (24) (P.168) and (72) (P-17 ; two reflected waves'
are obtained, but these are no longer plane, due to the
curvilinear nature of the boundary.

45
TITLE:
PRESENTED BY:
SUBMITTED:
AVAILABLE:
Card 4/4
On the theory of elastic wave scattering
boundary. (K teorli rasseyaniya uprugikh
krivolineynoy granitse).
7/20/56
Library of Congress
on curvilinear
voln na

30-8-5/37
Rockets and Artificial Satellites for the Investigation of the Higher Atmosphere
tude of 120 km and 2 even 160 km). In White Sands also 91 rockets
of the type Aero-B were launched which reached altitudes of up
to 80 km. The "Aero-V - rocket carried the record at that time
and it reached 288 km. It was followed by the "Viking".with 253
km and the great event was% the two-stage-Vampyre-rooket (com-
posed of a V-2 and a "Corporal"). It reached 400 km on February
24, 1949. A short time after, the first 3-sta~e rocket was built
(discharge fiom the BBC-basis in Florida) which for the first
time reached an altitlide of 1200 km. Sounding of the atmosphere
by means of rockets was carried out in various ~_-ountries. In the
Soviet-Union too, rockets are used for research-purposes. Both
American and British constructors built their measuring inatru-
ments into the head of the rockets, whereas the Soviet scientists
dew2oped an other methodt the case contining the measuring in-
struments is automatically disengaged from the rocket and para-
chuted. Among the numerous projects of artificial satellites
there is one particularly interesting, i.e. the so called "Van-
guard"-project (USA). The 3-atage-rocket which is to convey the
satellite on its way, is constructed in such a way that the first
Card 2/3 two are guidable, whereas the third one stabilizes its position

U
26-12-2/49
AUTHORS: Skurid G.A., and Kurnosova, L.V., Candidates of Physico-
Mathematical Sciences
TITLE: Scientific Research by Means of Artificial Satellites of the
Earth (Nauchnyye issledovaniya pri pomoshchi iskusstvennykh
sputnikov zemli)

PERIODICAL: Priroda, 1957,pNo 12, pp 7-14 (USSR)
ABSTRACT: The article deals with the problem of inquiring into the
phenomena beyond the atmosphere by using artificial earth
satellites. The idea to build satellites originates from the
Russian scientist K.E. Tsiolkovskiy who years ago suggested
sending them into the space by means of rockets. The two
satellites recently launched by Soviet scientists -are the
first of a series of new research devices which in all prob-
ability will soon be commonly used for the study of the
phenomena in the universe and for solving problems of space
flight. According to the authors, Soviet scientists have de-
veloped a method of calculating the length of the operational
capability of a satellite and also the changes in the orbit's
parameters during the time of flight. The satellites will be
Card 1/5 able to collect important data on the characteristics of the

26-12-2/49
Scientific Research by Means of Artificial Satellites of the Earth
atmosphere at altitudes of up to 1,700 km, to measure the full
intensity of cosmic rays and to register ultraviolet and X-
rays emitted by the sun. The two satellites are equipped with
instruments for the study of the short wave part of the solar
spectrum (Figure 2 explains the arrangement of apparatus re-
gistering ultraviolet and X-rays of the sun) which enables the
investigation of various layers of the sun's atmosphere.
Cosmic rays will be observed with apparatus as shown by Figures
3 and 4, collecting the necessary material for determining
nuclear showers of low intensity. Other devices will enable
to register variations of cosmic rays of different kinds (last-
ing 24 hours, 27 days etc) which will be obtained at different
points of the globe almost simultaneously. Vital data are also
expected on the influence of the sun's activity on the intens-
ity of cosmic radiation. A further object of research is the
structure of the atmosphere. The most important problem of
physics of the atmosphere is to what extent its composition
depends on the altitude, as reliable data exist only up to
heights of 100 km. The satellites are also registering the
Card 2/5 corpuscular radiation of the sun, which is of vital importance

26-12-2/49
Scientific Research by Means of Artificial Satellites of the Earth
in the ionization of upper layers of the atmosphere, in the
formation of polar lights and in geomagnetic disturbances.
The study of the structure of the earth's magnetic field in
regions above the strongly ionized layers of the upper atmo-
sphere can probably answer the question of the earth's magnetic
field and why it changes in the course of time. Micropart-
icles of interplanetar substances moving about'at high alt-
itudes will be registered when touching the rocket's hull or
special membranes as shown by Figure 6. The 2nd artificial
satellite, which was launched on November 3, 1957, is described
as follows. Its orbit has the shape of an elipse whose re-
motest point from the earth is approximately 1,700 km away.
During 24 hours it circles the earth about 14 times. It
carries, beside scientific equipment, 2 radio transmitters
operating on frequencies of 40,002 and 20,005 megacycles re-
spectively, electric batteries and an airtight cabin with a
dog for experimental purposes. Contrary to the arrangement in
the first satellite, "Sputnik No 2" carries all the equipment
in the front part of the rocket's last stage. Only the radio-
metric measuring device is attached to the hull of the rocket.
Card 3/5 The total weight of the equipment, dog and electric batteries

26-12-2/49
3cientific Research by Means of Artificial Satellites of the Darth
included, is 508-5 kg. Figure I shows the devices for invest-
igating the sun's radiations as carried by "Sputnik No 211,
Figure 2 the dog in the airtight cabin before being placed in
the satellite. The cabin holds food for the dog, an air con-
ditioning system (for regeneration and temperature control),
instruments for registering pulse, respiration, blood pressure,
for taking electro-cardiograms and a series of sensitive cells
for measuring temperatures and pressure in the c6bin. A radio-
telemetric equipment enables the transmission of all measure-
ments to the earth at regular intervals according to a pre-
arranged plan. The dog's cabin and ball-shaped container are
made of aluminum alloys. Their surface is polished and
specially finished to attain a certain coefficient of radiation
and to absorb solar radiation. Figure 3 shows the equipment
for registering cosmic rays, Figure 4 the arrangement of the
containers holding the satellite's equipment, Figure 5 a dia-
gram showing the same arrangement.
There are 7 photos, 4 diagrams and 2 references, all of which
Card 4/5 are Slavic (Russian).

26-12-2/49
Scientific Research by Means of Artificial Satellites of the Earth
ASSOCIATION: Institute of Geophysics imeni O.Yu.SWdta of the AN, USSR
(Moskva) (Institut fiziki zemli imeni O.Yu. Shmidt Akademii
nauk SSSR (Moskva)
Institute of Physics imeni P.N. Lebedev of the AN, U3SR
(Moskva) (Fizicheskiy institut imeni P.N. Lebedeva Akademii
nauk SSSR (Moskva)
AVAILABLE: Library of Congress
Card 5/5

~A U Of A-! C, A
AUTHORS: Skuridin) G. A. and Gvozdev, A. A.
49-58-2-1/18
TITLE: On Boundary Conditions for Jumps in Discontinuous
Solutions of the Dynamical Equations of Elasticity
Theory. (0 krayevykh usloviyakh dlya skachkov razryv-
nykh resher--.-iy dinamicheskikh uravneniy teorii
uprugosti.)
PERIODICAL: Tzvestiya Akademii Nauk SSSR, Seriya Geofizicheskaya,
1958, Nr. 2, pp. 145-156. (USSR)
ABSTRACT: At the present time asymptotic representations are
important in many bran:!hes of mathematics and
theoretical physics. In Refs. 2-7 the application
of the asymptotic method to the solution of dynamical
problems in elasticity theory was indicated, and the
fundamental equations for ju-uLps in discontinuous
solutions of the equations, both for homogeneous and
for inhomogeneous media, %iere obtained. However,
for the further development of the asymptotic method
it is essential to formulate the basic boundary
Card 1/13 conditions for jumps in discontinuous solutions.

49-58-2-1/18
0--n Bour-,dary Conditions for J--,imps in D-.1-continuous Solutions of
the Dynamical Equations of Elast-city. Theory.
This makes it possible tc solve problems immediately
for jumps in displacemerr~~; and velocities, without
reference to -the solution of Lame's ;ysterr, of equations.
The passage to the limitin_q relations in these
equations naust be accompanied by a similar transition
in the boundary conditions (Ref-2). Such a
transition is absent from Refs. 4 and 5. For
simplicity the authors corsider the two-dimensional
case -Ath t-,io-dimensional boundaries and plane
boundaries of separation; but -,;~-thin The limits of
applicability of "the -principle of the isolated
element", the ions renain true for curvilinear
boundaries (qef.8). The authors begin by discussing
the transformation of the fundamental equations of
Card 2113 motion in an inhomogeneous elastic medium:

On, -BoundLiy Condition.,z; for, j1--p.3 in L-~uwus 2~olution-z of
t h e Dy n,- u i i ca 1 -', q:j a t il c n F- 7) -1--j~;'icit y "Theory~

u
L X d-i ir u 2 F,
1 X-i X2~;
-A
2v + dili u- +
-6y yay

P,
L-w + Z div +
- +
-
c

L ",
-Z~)Y: Y Z"4y Z;4 z
%vhe re s lal-I:c-S 1~ r:--,t 0 r

7
------ IT'
P
t
Card 3/13

CYn. c,-,nd a ry -ondi tion E
-nz cf
the Dyna I" I i(-- al Cf IJ i-
'-d
+ 2
Further, let
2 2
+
+
(Eq. 8
+
2
If the Is introduc-ed by t-7-,e
Card 4/13 rel-ation

4' 9 -3, 2 - 2- 1 /1 C.
C.n 31oundary Conditions, for in Discol-l-tir:'LO-u-c -'01-ationf-:
the Dynamical E'quations of E, 1-:i st i - c iT-il e o ry
d d
dsi cl-ri
denotes difIC--rentiation alon- a- nay)a d P
dsi
and Q, are def ined by
P
2
2
d-,
2 2
(L,,
then, the evations f~~r t-h-e t--mp in the
Clard 5/13 displacement -,re--to--r S, T Z!

On .3oundary Condituions~ for Dij~-,L-S j F1,
the Dynamical EquaLions o'L
C.
dP
2-Z- +
d-7 + 2~i
d-_q (Eq.10)
2- u c2. n
d-F,
respectively for aud trarsverse V-..-aves~
After solving ,~-he authors go on
deducle the bo-mOlary case C-F,
reflection of S ft,_:~ bou.2adary -.f a
half-spacce. It is supposed thatU on the boundaryy
of the half-space tllil;:~re fal'_s a longitudinal elasti,-_
wave whose wave-fron' `_-b=~ ha"'-.s-,,a,e (X, 7~
is defined b,-.,7 tne eVati,_n
Card 6/13 (X, Y. t) 0 (Eq. 28)

f j.
by
i)---not- L)" u (uo
1.,z~ n. t- Lon- 1 2, -L! L3Y
v nd
LI, (u
ThE- ve c G 1~ C~ Li f o rm
77 30
iC-

C~n .-o1 oi- -or s -c
- -

1(~ 11 t he I, d

C_ Lw _L

U_
I
'

1/18

Dn Eou dal-j "Jonditioll-Z c) -,- -,
U
i'n Di
sco- d.r.. cu,! solU4-~nn-- c"
~-u _u
tile Dynamical Eq:uati ons of -J~l a~~-ticity ' 21--eory.
1 2
---o 0
-X,
ly X
y

2
Y=o 0- 1

1
0~2 6y
0
y
y

-0 1 2
X y tx C,
*
V
O
2
Y= -
1 2 I
+

Oy 'Y
y
for the r!~-L'I,--,cted v..,ave o 1~ e
equations it i--~ 3n-- the bound:.ry y 0
Card 9/13 v,-e have

C-
On ConJJ--'L-Iio--nc for "T
anc,
;.j C) 1---c sp Onndi-n L., -,.-L So r*,, eire (I f C
ct a
71 n
!oil c ~.ILL~cec"-
he case o-~'
t
(Frie dri ohs Li: I I n d z; E; o n r a
di re ct wa
Sp a c o
by U~,i4n-- -ch e di --.,o ct .l;a -,,,e Font v.,
Imo-imn from outvith the f--narmev,-Orik- L-f
uhe as-YrqL-to-IL-! ...,-:,,Thlht~-~- L-i 'his pa-Der x-.he
obtuaiira. 'U'lle
free and fi-,--ed of an, elas--c-
- J. ul 11
on vh. ich a t.--.- a---r-Ls ve rse -..va ve i~- inc.'-dent Fo- a -f-Lxed
boundary the 'L oil eypress ions --,'c)r -1.1le J1.11 S -1,

4
0n -13oundal-i Condi-t-ionz for
the Dynamical of ElazIL-icitul
the displacement vector of
bound- i-
y 0 are

u (2) y
2 ) Y=o
i:c cr X q cl,
UN
(2) y
v2 1 y=o A

;J:,:

I/is
On 3oundc-,.i-j 'onditui on s for J,~=~Ds 1)-~
ka
the Dynamical ---~iqu at ions of L~'l a z-,i ci,
12 'l
i,'her, the boundaa~-j ds fr-e the rl'orres;-, or ln~;~
are:

(2) y
u
Y=O 2
'3\

2
t) y
v(2)
2
y=o

;y
(-j c

On -Doundaar-j Conditions for tiumns
Uhe Dynamical Equations o-f Elas-tici-y
Lhere are 4 fiLures and 13 references,
of which
are En,--lish and 10 Russian.-
L~,
ASSO'CIATIONI: Academy of Sciences of the USSR; Institute of Eaith
P'1-.ysir,s. (Akademiya nauk SSSR; Institut fiziki
Zemli.)
SUBLIITTED: April 22,
S 1957.
AVAIIABJE: Library of Congress.
Card 13/13

16(l) FILASS I BOOK ZXPWITATION sov/266o
Vooooyu%rqy natematichaskiy slyeid. 3rdo Moscow, 1956
Trudy. t. 4t Kratkoye, soderzhanLya sektsionnykh dokladov. Doklady
Inostrannykh uchonykh (Transactions of the 3rd All-Union Mathema-
tical Conference In Moscow,. vol. 4: Summary or Sectional Reports.
Rot) rte or PoreIgn Scientists) Moscow, Izd-vo AN SSSR, 19~9.
*
..7
p. 2,200 capita printed.
Sponsoring Agency: Akademiya nauk SSSR. Mat*matlcheskly lnntttut.

Todh. 9d.s . O.K. Sheychanka; aditartal Board- A.A. Abramov, V.0.
bolty4nakly A M Vasillrev, B.V. Medvedev, A.D. Myshk1s, S.M.
l-
X
Yu
V
Prokhorov
A
ikov
Mik
kl
: 9d
O
t
;
P
jR
)
.
.
.
.
o
s
e
.
oa
n
,
, X.
.
,
p
y
ltybnjk". P. L. Ullyanov, V.A. Uapenskiyj N.C. Chatayev, 0. Ye.
Shilov, and A.I. ShIrshov.
PUMM32i This bolok in Intended for mathematicians and physicists.
COVIRAOR: The book to Volume ry or the Transactions or the Third All-
The
Union Mathematical Conferencep held In June and July 1956.
_,
"Is __ -Th ri 's
in parts, 0 rot part contains aum-
O"Its or the papers presented by Soviet scientists at the Can-
forence that were not Included In the first two volumes. The
second part contains tht text of reports submitted to the editor
by non-Sovitt scientists. In those cases when the non-SovLet act-
antiat did not submit a copy of his paper to the editor, the title
or the paper Is cited ands Ir the paper was printed in a previous
Tolumeo reference to zoade to the appropriate volune. The papers,
both Soviet and non-Soviet, cover various topics In number theory,
algebror dirforentiaL and Integral equations~ function theoryp
functional analysis, probability theory, topology, mathematical
problems of' mechanics and physicoo computational mathe%.&tICS,
mathematical logic and the foundations of mathemattesp and the
history of mathematics.
%alto v,-O "t* I md) V.S. Buldyrev (I,*n1ne;rsdLZX,
Quantita-
t IT51-iliof the nonstiE onary dtfrraction of waves from
spherical and cylindrical regions 120
FomeranchUk__.X_YA_-4Xoscow). The turning to zero of ronor-
Iiilixed charges in theories with point interaction 120
Numer, TU.B. (tfavosibirsk). PLve-dimensional optics 120
Pur Xoscow). On the theory of the reflection
. M 1."t
&$tic rrom a curvilinear boundary 122
q _434oscow). Relativistic mechanics and
St!
r-y-es of continuous media 122
,Lodzh 1',n.L.Sh. (Stalinabad). Singular functions or quan-
. I:"
I." r3, 1H n-di-mensional pseudo-Euclidean space 124
card 23/34

AUTHOR: Skuridin, G. A. SOV/49-59-1-1/23
TITI3: Duhamells Principle and Asymptotic Solutions of
Dynamic Equations in the Theory of Elasticity. I.
(Printsip Dyuamelya i asimptoticheskiye resheniya
dinamicheskikh uravneniy teorii uprugosti. I)
PERIODICAL: Izvestiya Akademii Nauk SSSR1 Seriya Geofizicheskaya,
1959, Nr 1, pp 3-10 (USSR)
ABSTRACT: The asymptotic (ray) method has been applied in the.
study of propagation of elastic waves in uniform and
non-u-niform isotropic media by many workers (Refs 1-7).
The present paper uses Kline's method (Refs 8,9) to
solve asymptotically equations of the theory of
elasticity on the basis of Duhamel's principle. Kline's
results,obtained for one-hyj?erbolic equation,are applied
to a system of dynamic equations of the theory of
elasticity. It is shown that,if there is a system of
finite discontinuities in the pulse solution, then
solutions of dynamic equations may be represented in
the form of series in reciprocal powers of iw, where
w is the angular frequency. A harmonic source of
Card 1/2 vibrations is assumed in this analysis. The constants

SOV/49-59-1-1/23
Duhamel's Principle and Asymptotic Solutions of Dynamic Equations
in the Theory of Elasticity. 1. -.0
which appear in the series mentioned above are "jumps"
of the pulse solution and "jumps" of its derivatives
with respect to time. At w -:ooa the series obtained
for the components of the displacement vector become
asymptotic. The region of convergence of the;series
is not discussed. The paper is entirely theoretical.
There are 13 references, 7 of which are Soviet, 5.English,
1 German.
ASSOCIATION: Akadeiaiya nauk SSSR,,Institut fiziki Zemli
(Ac. Sc., USSR, Institute of Earth Physics)
SUEMITTED: August 20, 1957
Card 2/2

8/049/59/000/03/001/019
AUTHOR - Skuridin, G. A.
TITIE; Duhamel's Principle and the Asymptotic Solutions of
Dynamic Equations of the Theory of Elasticity. II
\-V
PERIODICAL: Izvestiya Akademii nauk SSSR, Seriya geofizicheskaya,
1959, Nr 3, pp 337-343 (USSR)
ABSTRACT: The first part of this work was published in this
jcurnal, Nr 1, 1959, where it was shown that Duhamel's
integral can be used to solve equations of the theory of
elasticity. In Part I Duhamel's integral was used to
find an. asymptotic expansion (Eq 1) for a harmonic
eource of -vibrations f(t) = exp(-.iwt). In order to
apply Eq (1) to practioal cases2 solution of the system
of Eqs (3), which express motion in a heter neous
elastic medium, must be fo-und (Eqs 4-7). Ors an example,
a homogeneous isotropic elastic medium is considered. In
Card 1/2 this case the system of Eqs (8) is derived where the

S/049/59/000/03/001/019
Duhamel's Principle and the Asymptotic Solutions of Dynamic Equations
of the Theory of Elasticity. II
region D is divided by a di ontinuity on the surface
0 into two regions D 9;"Zd D2 (Fig 1). If
Eqs (8) are applied to eack reglon separately, formulae
(12) to (14) a.Te found for Di. , By combining them with
the eq!aivaient formulae for D 11 Eq (20) can be derived
which determines the compone;~ u of Eq (1). The other
two coniponents -, and w a-T~e foland similarly. Thus the
integral (21) is obtained which in the case of longitudinal
and transverse waves can be written as Eqs (22). The
paper is entirely theoretical. There is 1 figure and
4 Soviet references.
ASSOCIATION: Akademiya nauk SSSR, Tastitut fiziki Zemli
(Ac. Sc. USSR. Institute of Physics of the Bart
SUBMITMiD: August 20, 1957
Card 2/2
,W.

0. '? 0 0 0 67891
v (7) 8/020/60/130/06/019/059
AUTHORS: Skuridin, G. A 9 S - B013/BO07
TITLE: An Approximate Solution of a Problem Concerning the Notion of a
Conductive PlasmaNy
PERIODICAL: Doklady Akads-mii nauk SSSR, 1960, Vol 130, Nr 6, pp 1248 - 1251
(USSR)
ABSTRACT: Several authors developed a new method for the asymptotic inte-
gration of linear partial differential equations of the hyper-
bolic type and by using this method they determined asymptotic
solutions for the equations of acoustics and for laxwell equa-
tions. Other authors solved the dynamic problems of the elas-
ticity theory by means of this method. The general idea of this
general method, discussed in the present paperg in a linear
hyperbolic differential equation ke.g. in a wave equation) is
based upon the following: The endeavor is made approximatively
to satisfy the initial equations by special selection of the
functions w1hioh means the solutions are sought in the form
II(x9y9z9t~ - A(Xgypz)exp fitik, - ~ (X'y'ZF0 if (J-_* 00.
Thus, one obtains the known relationa grad2 1/c2 and
Card 1/3 2(grad A grad fl + A L'i 0, where � (xPY9 Z) denotes the eikonal

67891
An Approximate Solution of a Problem Concerning the S/020/60/1,,;o/o6/oi9/059
Motion of a Conductive Plasma B013/3007
of the wave and A(X,Y,Z) the amplitude of the oscillation. The
compression shock of the unsteady wave front and the amplitude
of "geometric approximation" are found to be identical. The
physical interpretation of the asymptotic method in quaallinear
and linear equations isp howeverp no longer so easy, However,
also in this case several problems may be formally solved by
this method. The authors of thepresent paper integrate the e-
quation of plasma oacillationa'yby means of thin method: they
investigate the motion of K~~__aePin a medium with the finite
conductivity 0. The medium is here assumed to satisfy the equa-
tion of staU P - Q8 1. The corresponding system of
equations of ma;Matof"gas-dynamiceVin the onedimensional case is
explicitly writton down..The problem is reduced to the determina-
tion of the unknown quantities P, Q9 R, and u (velocity of the
gas) in a sufficiently general form, which means that these
equations are to contain-arbitrary functions which are then de-
termined from the initial- &nd boundary conditions. The calcu-
lative solution of this problem is followed step by step. For
Card 2/3 the determination of 0 and u (where 9 - (ink), one obtains tw~z

'07891
An Approximate Solution of a Problem Concerning the 5/020/60/130/06/019/059
Motion of a Conductive Plasma BO13/BOO7
arbitrary functions T(t) and F(G) and an arbitrary constant B.
The authors then investigate the case F(0) = PQ with P - const