SCIENTIFIC ABSTRACT KAZAKEVICH, V.I. - KAZAKEVICH, V.V.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000721230005-1
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 83
• Document Creation Date: November 2, 2016
• Document Release Date: June 13, 2000
• Sequence Number: 5
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

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01 A
v,-,---- -v A V. 1. Chukh~~v., D. Shlenskiyl V. A. Z
SOUR'E: Byulieten' izobreteniy i tovarmykh znakov, no. 9, 1965, 81
'TOPIC ';BAGS: E.older, tensile test, test equipment
AbSFRACT: rntroCWces a so specimen maJe up
lder
T te sDecinren is des igned for
perties of ~c.,nt alnfi
ML~~ al pro
ttbe7su~face cf,-fhell rod i an :arjula:r--jvpov... cif . a.,deBtiz w,i
'~f 16~ iii '. - 1,
through which the
~older,flows, after heating of the sample. Ite rod an -~W6~'b34
'jgetheira
ASS-OCIATIM, llyctive gosv4L.Irstvennolgo komiteta po bboronnoy tekhnike SZ-Z-R
Fred-ar
ronrdttei fcr Def,?nse Technoic,--%, SSSR)
Card

Card 2/2
~A
IMM HISMOR,

XAZAKNVIGH, Y.M., Insh.; XONDRATYUK. A.P.0 Insh.
---Operatirg conditions of coupling transformers with the power system in
electric power plants. Ilek.sta. 29 no,.5:46-47 MY '58-
(MIRk 12:3)
(Electric power plants) (Blectric transformers)

-L 03083-67 EWT(M)/MP(j )/T-.4IJP( C) GD/1M
0 NR: AT6031600 SOURCE CODE: UR/0000/64/000/000/0185/0189
AUTHOR: Yer-ofeyev, B. V.; Shlyk,. V. Kazakevich, V.J.
Oro: non-e
TITLE: Similarity of the initiating action of salts of metals capable of assuming
several valencesp in autocatalvtic oxi-lation and polymerization. 1. Comparison of the
efficiency of carbo3qlates differing in the tqdrocarbon chain length
WURCE: GeterogwvWye reaktaii i reaktsionnMra sposobnostt (Heterogeneous reactions
and reactivity). Minskj lzd-ewo VysshWa shkolk., 1964p 185-189
TOPIC TAGS: chemical initiation, polymerization ratej autocatalytic oxidation, cobalt,
carbo:Nylate,, manganese stearate, lead, stearate., styrene, tetralin hydroperoxide., auto-
catalysis, chemical valence
ABSTRACT: A study has been made of the effect of carboiWlates of metals capable of
assuming several valences on the pn1=ArJz-n+i= rate nf --. the presence of
tetralin hydroperoxide. The experiments were canducted with Be eral coValt car-
boxylates (formiate, abetate,, butyrate, caprylate, and stearate), and with manganese
or bead stearates. The dependence of the polymerization rate on the hydroperoxide
Card 1/2

L 01083-67
ACC NR: AT6031600
and carboxylate concentratiam was studied. It was shown that the polymerization
rate of styrene, in the presence of bydroperoxide-carboyylate systems, depends both
on the nature of the metal and of the anion. The initiating efficiency of the
carbo.Vlates increased with tho hydrocarbon chain length, that of the metals In
creased in the order: coba3t< manganese < lead. Thus, the initiating action of
the carboxylates considered in polymerization is similar to that In au~ocatalytic
oxidation. A scheme is proposed which explains the initiating action of carboxylates
as a result of the substitution of hydroperoxide for acid radicals. Orig. art. has:
3 figares.
SUB OODE: 07/ SUBM DATE: 12Dec 64,/ ORIG REF: 007
Card 2/2 -flj-

GLADKIKH, %A.; KBACHATIWAN, S.A.; J%ZAKEVICftj V.V, , doktor tekhn.
nauk, prof., retsenzent; BODitA-"V.T.,7-d-ofior tekhn. nauk,
prof.* retsenzent; DANILOV, L.N., inzh., red.; DANILIN,
L.N., red.izd-va,- TIMOFEYE", N.V.p tekhn. red.
[Preventing and eliminating vibratioris In pumping units]
Preduprezbdonic i ustranenie kolebanii nagnetatellnykh usta-
novok. Moskva, Izd-vo "Mashinostroenie," 1964. 274 p.
(MIRA 17:4)

th:ulob V V. --oi-imoAlmat lntijii~&u 41 vii~-der
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Jn the fiva-papq-Ale amhor tActive-j ali '~j till o-mm"!
f0mut-1-for-th6 pCrW ithition bi IhO perWic SOlution
A for 'rbl. ry
ilk 'M
VA 5, 1 'S11
the vaiuk--z Obtafacd by fmajis of lfaphic'l! --na)"st;
van der N1, In he rather pipers the mabod is cucridut" w
tm t the +M itt 0, 1,34,M)-mv,
mattlevatical Reviews,

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Oa Appmlinsits IMMMUM I" OodUtM 1"Iffits
willi".Onp Devitt of Frwolmu,
I" Ito In Ft""it.) sth'11".1
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01,11-ill. Oil it %Of In lip 1". '10, 111111"A I.-I It,,
"I"I. 11"-wax $1.11 J.-I lot I'st $-I.,

systems and the sunid-1
1\-~57ns-Q-aCaT_nioda1q of cloc-kS.
SSSR. IN.S.) 74z 66;,-b(,B (1950). "Ru"".1"
with tort.-im
Multiply Villijo SySt MS aTiSC in conne
tv
have ch-am"Mijific's A 11 hyster'sis Thu gr1wr.'I t
a Snide fio~m, ill i;k- -
arisng with
an~ L-, CL
()PC VVIleling nf tile Ill Y
fl
t~,; 21 f4evltin.-ALAM61 1n`nl!ipjY,

USSR/Flathe=tica Speed Regulators Jan/FOb 51
Clocks, Recapements
"CoPtributio-A to the Theory of Trip Regulators (y
(Nis,cipements)," V. V. Kazakevich
"Avtomat i Telemekh" Vol XII, No 1, pp 41-60
Author applies the theory of manifold systems, as
developed by him (nDok Ak Wauk SSSR",Vol LXXIV,
1950), to Ana3,vsls of processep in escape-
'7MePtG; constructs multi-leaf phase surface of the
sistem and conducts quant investigation. Given
1e of the constr of multi-leaf pbase surface
18W,35
~*R/Y~athematics - Speed Regulators Jan/Fab 51
(Contd) -
or automatic regulation system in the case where
Coulomb friction is present in the sensitive-ele-
inent. Submitted 15 Dec 49; resubmitted 20 Jui 50
.1 -after revision.

z 14 A/ - -U. V.
SOLODOYNIKOV, V.V.; professor, doktor tekhatchaskikh nauk, redaktor;
AT2XRMAff. M.A., doktor takhnicheskikh nauk; BASHKIROT, D.A., kwAidat
tokhnichorki" nauk: 13ROMMG. P.V.. kandidait tekhnichaskikh nank:
VMWOV, A.A., kandIdat teklmicheakikh nauk, doteent; GOLIMPARB. L.S..
doktor takhatcheekikh nauk, profes'"or; XAZAX1VIq~$__V.V., doktor tokh-
nicheskikh nauk.- KWO'VSKIT. A.A., kan TUIST, 'GUwnTrTUTWwICikh nsuk,
dotsent; IXWR, A.Ta., ka-didat tekhnicheskikh nauk; LITOV, A.M.,
doler,or fiziko-matematicheakikh nauk; professor; MATRYBY, P.S.,
inzhener-, MARAYLOT, V.A., kandidat takhnicheakikh nauk; PBTRDT, B.N.;
PMOV,.V.V,, kandiclat takhnicheakikh nauk; POSPHLOV, G.S., kandidat
tekh&chssk-ikh nauk, doteent; TOPCHBYBV. Tu.I., inzhoner; ULANOV.
G.H.,.kandidat tekhnicheskikh nauk; KHRAMOT, A.V,, kandidat takhni-
cheekikh nauk;.TSTPK"Iff, Ya.Z..doktor W'thnicheakikh nauk, professor;
LOSSMVSKrY,.V.L., doktor tekhnicheskikh nauk, professor, retsenzent-,
TIKEIONOT, A.Ta., takhnicheskiy redaktor
(7undamentals of automatic control; theory] 0snovy avtomatichookogo
regalirovaniia; toorita. Koskva. Goo. nauchno-takhn. Izd-vo mashino-
stroit. lit-27, 1954. 111-6 P'O (MLRA 8:2)
1. Chlon-korrespondent AN SSSR (for Petrov, B.N.)
(Automatic control)

KAZA VICE, T.V. (Moskva).
..... ~ -.-, - ~!
Use of throttle devices for measuring fluid consumption at low
Reynolds numbers. Izv. All SSSR. Otd. takh. nauk. no.12:125-128
D, 155. (MIRA 9:3)
(Flovmaters)

KRZ-AKEVICti,
SUBJECT USSR/jUT�MT1CS/Differsntia1 equations CARD 1/1 PG - 150
AUTHOR XLZMVIC VOTO
TITLE On i=elatiorx 'between phase planes of Railoigh's equation and
van-der-Pblla equation.
PERIODICLL Dotlady Akad. Kauk~ j9-7-L 521-523 (1956)
reviewed 7/1956
Is is wall known, lay and 1(s) - df(s)/ds the Raileigh's differential
equation + o can be transfarsel to the van-,der-Pol's equation
14F(%) + a - 0. After a ahort general con'sideration.tke author shown by
the example f(i) . i~ ;3 th&% t1me oorrosponling A"i.plaaex show no visible
coincidenool e.g. the liatt oyalso have a -very different form,

KAZAM~.GJI jj -
_-, _ 1
- -- ~r
Characteristics of the excitation of vibrations in clocks. Dokl.As
SSGR 107 no.5:653-655 Ap 156. Ocm 9:8)
1. Predstavleno akademikom N.V. Bogolyubovym.
(Clocks mA watches--Vibration)

AUTHOR:
TITLE:
PERIODICAL:
ABSTRACT:
Card 1/2
SUBMITTED:
M I LAB LE
Card 2/2
Kazakevich, V. V.
2o-4-12/6o
On Surging in Compressors (u pompazhe v kompreoijorakh).
Doklady Akademii Nauk SSSR, 1957, Vol. 115, Vr 4, pp. 677-680
(USSR)
At first a short report is given on 6 relevant earlier vorka.
Thc presont paper investigates the character of the surging-
oscillations and a method for their suppression. The sYstem exam-
ined here contains a ventilatoro a sucking pipe and a pressing
pipe on whone outlet is a regulating resistance in form of a
throttle. The author assumes the followingi 1) The complicated
distributed acoustic system can be replaced by a system with one
degree of freedom. 2) Tile changes pressure in the oscillations
are small. Then the motions in the system oun be described by a
system of two first order differential equational
dQ,,/dt - (1/La)[F(Qo)-pj , dp/dt - (1/Ca) 1Q0 - Yj(p)]
In.this connection Tj(p) signifies the increase in the function:
T(QR); Ca- the acoustic mobility of the system, L.-the acoustic
mass, an-d F(Q.)_%j(Qo)-po applies. By eliminating'the time from
these equations the differentialmuation of the integral curves
is obtained,; dp/dQo. (No - 'Pi(p ) MQo)_P))La/Ca- After some
transformations expressions for the condition of the static prin-
Felyrrary 2-, 1-95-7
Library of 6ongress

103-2-919
AUTHOR: Rusevich, I. M.
TITLE: Conference on Automatic Control and Computation Engineerin,-,
(Soveshchaniye po avtomaticheskomu upravleniyu i vychislitel'noy
tekhnike)
PERIODICAL: Avtomatika i Telemekhanika, 1958, Vol- 19, 1Tr 2. pp. 191-194
(USSR)
ABSTRAM From March 5 - 8, 1957 the conference on automation and com-
putation engineering organized by the All Union Scientific
Engineering and Technical Society for Apparatus Building took
place. 900 delegates from the Institute of the AN USSR as
well as of the AN of the Unions' Republics, universities, re-
search institutes, designing offices and laboratories of the
various miniatries and authorities took part in it. 40 lec-
tures were held. The opening speech was delivered by 11. Ye.
Rakovskiy. The president of the organization committee of
this conference V. V. Solodovnikov (Central Scientific Re-
search Institito for Complex Automation - ToNIIKA) announced
Card 116 the tasks as well as the proCram of the conference. In the

Conference on Autxmtic Control and Computation Engineering
103-2-9/9
second part of his speech he defined the subject as well as
the characteristics of the content of technical cybernetics.
A. A. Lypunov indicated the Ale and the importance of cyber-
netics as scientific basis of a complex automation of pro-
duction. The following lectures were held orv,,,the theory and
the foundations of construction of control computors: V. V.
Kazakevich spoke on "Principles and circuits of optimuff-m7era-
t~ioncontrol methods". In a common lecture V. V. Solodovniko,
A. 11. Batkov, A. A. Bredis and P. S. lAatveyev (TsNIIKA) dealt,
with the "Present Stage of the Theory of Optimum Dynamic Sys-
tems Subjected to Arbitrary Effects". L. T. Kuzin showed the
use of the Z-transformation apparatus for the analysis and
synthesis of the automation systems Yrith numerical computa-
tion devices. A. M. Batkov spoke on the new way of using mo-
delling electronic plants (electronic simulation) for the
determination of the basic and statistical characteristics -
the correlation function and the dispersion of a non-stan-
dardized arbitrary magnitude at the output of the automation
system according to given characteristics of arbitrary effects
at the input. Yu. A. Shreyder spoke on the principles of con--
Card 2/6 struction of so-called "self-informing" control apparatus, the

103-2-9/9
Conference on Automatic Control and Co#utation Eng;Lneming
basic property of which is the capability to find the opti-
mum way of control by means of accumulated experiences in
operation. - V. I. Dikushin, Ilember of the Academy, (Scien-
tific Research and Experimental Institute for Machinino
Tools) spoke on the construction of systems for a preset
control of machine tools. The lecture of B. Z. Lyubimskiy9 S.
S. Kamynin and "W'. S. Shtarkman (Institute foi Mathematics
imeni Steklov All USSR) dealt with optimum information coJing
in automation and multistep automation schemes for production
processes. It. P. Shura-Bura (Institute for Mathematics imeni
Steklov Alf USSR) spoke on the possibility of using the means
of computation engineerinG for a transformation of any infor-
mations including those of automatic translation from one
language into the other. N. V. Korollkov, Ye. I. Mamonov and
Yu. I. Sharapov spoke on the achievements in the field of
quick, reliable, economical and small computor elements., On
the utilization of these elements in the circuits of coripu-
tors spoke V. A. Zimin and L. I. Gutenmakher. - V. I. llyzhov,
N. V. Trubnikov and A. K. Zavolokin, as well as Ye. It. Baska-
Card 3/6 kov spoke on the input and output devices of computors. Yu. S.

103-2-9/ 9
Conference on Automatic Control and C6zbm-L&tion Magneer-Ing
Valldenborg held a lecture on a specialized -mathematical ma-
chine of continuous operation for the solution of integral
equations of Fredholm and Volterra's first and second type,
aa they often occur in control problems. - Yu. V. Novikov
(IAT AIT USSR) spoke on the new computor created in the 1AT
AIT USSR (maZnetic correlograph) for the automatic computa-
tion of correlation functions. - 1. 11. Vitenberg spoke on the
modelling.clectronic apparatus for tho automatic finding of
a solution for a problem with a given system of equations. -
F. V. Mayorov and Ye. P. Zhidkov spoke on the mathematical
foundations of numerical differential analyzers (TsDa) as
well as on their use as control apparatus. - L. I. Gutenmakher
spoke on the prospects of usina informaticn- and statistical
machines of new design for control systems.
AVAILABLE: Library of Congress
Card 416

Conference on Automatio Control and Computation Engineering
103-2-9/9
The conference took place,in Moscow from March 5 1957-
A number of lectures dealt with examples from the field of
application of computation apparatus for the control of real
production objeets Yu. Ye. Yefroymovich (Central L&boratory
for Antomation)p V. Yu. Kaganov (Central Laboratory for Anto-
imation., A. B Chelyustkin (in AS MM) at;d P. N. Kopsy-Gora
spoke on the use of oomputation apparatuu flor the control of
basic objects Lu mataUurgy (furnacesp are fuftwes,, rolling
mills). D. T. Vaellyev and L. N. Fitener.spoke on compatators
fbr the detwmxtastion of the most mdtable sequence of cuts
in matelvorking industry. Up to 20 differentgaantities de-
Cerd 516 texmining the sequence of cuts can be introduced into the

Canference on Automatic Control and Computation Engineering
103-2-919
machine and when some of these ruLgaitudes are given the de-
mandedCoptimm parameter can be computed within 2 - 3 minates.
Y&. A. Detagurov reported on a mmerical system for the con-
trol of a machine tool. - The conference regards it necessary
to organize special groups within the TsNIIKA (Central Scienti-
fic Research Institute fbr Complex Automation), the NTI and KB
(Scientific Reaearch Institute and Construction Bureau), at
the whAstries as well as within the organization of the
AS USSR. These groups should be concer ed with the problems
of technica.1. cybernetics. It was decided to have-organized
an All-Union Conference fbr Cybernetics by the All-Union
Seientifie Rngine;wing and Teebnical Society for Apparatus
Building in collaboration with the AS USM.
-AVA-ILABLE: Library of Congress
1. Automation-Conference
ce-ra, 616 USCOM-DG-54858

PHASE I BOOK EXPLOITATION BOV3486
Kazakevich V. V.
Artokolebaniya (pompazh) v ventilyatomlih i kompressorakh (Self-excited
Oscillatinna 0)1lsaTion,7 in Ventilators and Compressors) Moscow, Mashgiz,
1959- 191 p. 61000 copies printed.
Sponsoring Agency: Nauchno-tekhnicheskoye ob8hchestvo priborostroitellnoy
prowlahlennosti.
13ech. Ed.: S. M. Lazarev.
PURPOSE: This monograph may be used by engineers and technicians, designers
and application engineers, scientific workers, and students of advanced
courses in the appropriate fields in schools of higher technical education.
COVERAGE. The theory developed in this book permits one to explain basic
phenomena occurring in self-excited oscillations, shows the causes for dif-
ferences in the character of oscillations in various types of fans, and evaluatei
the effect of Narious factors on the domain of oscillating regimes. This
Card V 6
Self-excited Oscillations (Cont.) SOV/3486
theory enables one to predict new phenomena. It shows in particular that
oscillations may take place not only in regimes corresponding to ascending
branches of the characteristic curves., but also in regimes corresponding
to the descending branches, which up till now were considered stable. The
book also shows a method of constructing(directly from the fart and system
characteristics)curves which characterize the oscillations. The new theory
also makes it possible to eliminate oscillationsby introducing a regulating
system with feedback, which affects the position of the throttle and dis-
tributor. Thege are 13 references: 3-1 Soviet, 1 English, and 1 German.
TABIZ OF CONTENTS:
Introduction
Ch. I. Equations of Motion of a Small-discharge Compressor and
5
Their Analysis 12
Derivation of the equations of motion 12
Reduction of-a system of two differential equations of the
first order to one equation of the second order 16
Condition for seif-excitation of oscillations and their
frequencies 20
Effect'of external conditions on oscillating characteristics 25
card 2/ 6

Self-excited Oscillations (Cont.) soV5486
Behavior of a system "on a small scale"(domains of self-excitation
and static stability) 32
Analytinal determination of the amplitude and period of
self-excited oscillations 35
Transformation of the equation of motion tt Rayleigh's form 39
Investigation of a system tion a large scale." Soit and hard ex-
citation of oscillations 45
Domains of stability and instability 68
Unstable operation on the descending branches of the compressor
characteristic 70
More complex cases of oscillation 74
Ch. Il. Method of Integrating the Oscillation Equation Directly From
the Fan and System Characteristics 83
Basis of the method 83
Determining the period of oscillations 89
Physical meaning of the phase plane 92
Investigation of oscillation in a specific system.
The effect on the character of oscillation brought about by a
change in position of the operating point on the fan characteristic 93
Card 3/6

,Self-excited Oscillations (Cont.)
SOV/3486
Determination of the period of oscillations 101
Effect of a change in the geometrical dimensions of the system
on the character of oscillation 102
Construction of curves showing pressure and discharge as
functions of time 117
More complex cases where pumping arises 122
Investigation of motions in a system where several points of
intersection between compressor and network ex-Ist 123
Ch. III. Oscillations in Systems With a Large-dtscharge Compressor 125
Derivation of equations of motion 125
Analysis of the equatioLs of motion 129
Conditions of soft and hard excitation of oscillations according
to Lyapunov 131
Oscillation in systems containing a throttling valve in the suction
11 "- 133
Derivation of equations of motion 133
Construction of the compressor characteristic 136
Phase plane of the system 14o
Derivation of the stability condition 142
Card 4/6
Ni i-,
U n-

Self-excited Oscillations (Cont.)
SOV/3486
Stability-of a system in which the air volume is located
at positions other than at the ends of the line 146
Investigation of motion in systems in the presence of bysteresis
and discontinuous compressor characteristics 149
Comparison of theoretical and experimental results 152
Determination of the frequency of oscillations as a function of
the geometrical dimensions of the system and number of
revolutions per minute 153
Determination of the limit of the domain of stability 161
Construction of the phase plane 163
Experimental investigations performed on axial %ompressors,
especially for checking theory 165
Methods of influencing oscillations 174
Regulation of the discharge throttle according to P's 177
Regulation of the discharge throttle accordling to 40 179
Regulation of the distributor according to p*d 180
Measurements required in conducting experiments 181
Card 5/6

Self-excited Oscillations (Cont.) sovi3486
Conclusions 182
Appendix. Mechanical Model of a System Representing a M 184
Bibliography 189
AVAILAME; Librea7 of Congress
AC/fal
card 6/6 5-27-6o

L., v
a "a A
9 t at- ! p. .
co. Ov -
-a 4
V., v
08S
14
12
Its
PI ... .........Lt-
------------

UZAKIVICH. V-V.
Theor7 of escapem9nt mechanisms with consideration of multiple-valued
characteristics. Avtom. upr. i vych. takh. no.2:167-220 159.
(YIRA 13:2)
(Time measurements)

XAZAMICH, V-V-; OSTROVSKIY,,G.M.
Mt7ing friction in a servomotor as a cause of self-,)scillations in
control units. Avtom. upr. i vych. tekh. no.2:296-317 '59.
(MRA 13:2)
(Servomochanisme)

soV/24-59-4-15/33
AUTHORS: Bodner, V.A. and Kazak8vick,_YA_YjL (Moscow)
TITLE: Ptability of CompressorWas Non-linear Elements in
Extended Systems
PERIODICAL: Izvestiya Akademii nauk SSSR, Otdeleniye telcbnicheskikh
nauk, Energetika I avtomatikaj 1959, Nr 4, pp 116-125 (USSR)
ABSTRACT: The compressor is one supplying compressed air to remote
points'through narrow pipes; the compressor is controlled
by the pressure prevailing at a fairly distant point.
The equations of motion (taken from Ref 1) are (1.1),
where u, p z-2d (i are, respectively, the speed ! /.
pressure and density, 4 Is the diameter of the pXpe,
a and m are coefficients representing viscous resistance
and y is the ratio of the specific heats. It is
assumed that the pipe (Figure 1) is loaded at the ends
by acoustic impedances Z 1 and Z 2 the boundary
conditions are then (1.2), where Pi and P2 are the
total pressures at the input and the output, respectively;
pol and P02 are the constant components of those
Card 1/5

JOV/24-19 4- 1 11
-line
Stability of Compressors as Non ar lements n X ended Systsms
pressures; Q I and Q 2 are flows (in volume terms)
and q 1 and q 2 are excess flows (again in' vol,,=e terms).
The equations are linearized (Ref 1) as (1-3 and (1.4),
with the symbols defined at the top of p 117; the
boundary conditions are put as (1-5). It is assumed that
h11 and h 21 are constant for the purposes of examining
the stability, though this is not so in unstable modes
(variation in OF/AQ 2 is used as a test for instability).
In the second section, the equations are solved usIng the
form given by Eqs_(2.1) and (2.2), which with (1-3) and
(1.4) give (2.3) for the Input pipe and (2.4) for the
output pipe; the corresponding solutions are (2.5) and
(2.6), where Z 11 and Z 22 are the wave impedances of
the pipes. Eq (2-7) gives the constants A and B ;
this system has a solution only if (2.8) is complied with.
The two equations derived from (2.8) are (2.9).
Card 2/5

SOV/24-5-9-4-15/33
Stability of Compressors as Non-linear Elements in Extended Systems
Then (2.8) is put as (2.10), with E 11 ` -E 121
In section 3, the compressor is assumed to be connected
to a pipe terminated by an impedance Z. 1, with an
impedance Zi at the input by the compressor (here
II= 0) . The substitutions at the top of p 119 are then
made, to give (3-1), which then splits up into Eqs (3.2)
and (3-3); these equations show that the natural
frequencies of the system depend only on the pipe and V
terminating Impedance and that there are two series of
frequencies given by Eq (3.4). First, the roots
corresponding to the + sign are consld~ered, with
( A