SCIENTIFIC ABSTRACT F.M. DIMENTBERG -

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• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000410410009-2
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 13, 2000
• Sequence Number: 9
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

24(o) PHASE I BOOK EXPLOITATION SOV/229q
Dimentberg, Fedor Menaslyevich
Izgibnyye kilebwaiya vrashchayu hchikhsya valov (Flexural
Vibrations
Whirling) of Rotating Shaft:) Moscow, Izd-vo AN SSSRI 1959. 246
p.
Mries: Problemy teorii mashin) MOO copies printed.
Sponsoring Agency: Akademiya nauk SSSR. Institut
maBhinovedeniya.
Ed.: S.V# Serensen, Academictah Ukrainian Academy of Sciences;
Ed. of Publishing House: A.S. Meleyev; Tech. Eds.: N.K. RuzIman,
and Ye, V. Makunih; Editorial Board of Series: I.I.
Artobolevskiy,
Academician (Resp. Ed.),'A.A.Blagonravov, Academician, N.G.
Bruye-
vich, Academician, V,I. Dikushin, Academici4a, S.V. Serensen,
Academician, Ukrainian Academy of Sciences, S.V. Pinegin, Doctor
of Technical Sciences, Professor, N.I. Levitskiy, Doctbr of
Techni-
cal Sciences, Professor, F.Me Dimentberg, Doctor of Technical
Sciences, A.Ye. Kobrinskiy, Doctor of Technical Sciences, N.P.
Rayevskiy, Candidate of.Technical Sciences, and A.P. Bessonov,
Candidate of Nchnical Sciences (Academic Secretary).
Card 1/7

Flexural Vibrations (Cont.)
SOV/2299
.PURPOSE: The book is intended for scientific and engineering
person-
nel of the machine-building industry and for stress analysts
and
designers of new types of machines.
COVERAGE: The book discusses natural frequencies of shafts, the
whirling3" critical speeds under various support conditions,
ef-
feet of the weight of the shaft itself and the vibrations of
its
supports, the unsteady passing of a shaft through critical
speeds,
influence of internal and external friction and the stabtlity
of
motion due to the action of friction. Problems of whirling,
meth-
ods of balancing, evaluation of stability between critical
speeds
and ptre'ngtkiii'long-time 'operation and often-repeated
starts are
analyzed. No personaliti6s are mentioned. There are 52
references:
31 Soviet, 12 English, 5 German, 2 Rumanian, 1 Czech and 1
Slovak.
TABLE OF CONTENTS:
Introduction
5
Ch. I. Some General Premises 15
1. Elements of the flexural vibration (whirling) of a rotating
shaft 15
Card 2/ 7

4) i /Yl r13 ~-i3 r) (---,
ARTOBOLEVSKIY. Ivan Ivanovich, skademik; ISVITSKIY, N.I.,
prof., doktor
tekhn.nsuk. otv.rea.; BLAGCKRAVOV, A.A., akademik, red.;
BRUYEVICH,
N.G., i3kademik, red.; DIKUSHIM, V.I., akademik, red..;
SEMSEN,
S.V., akademik, red.;. PIRGIN, S.V., prof., doktor
tekhn.nauki red.;
DIKRM- ERG, P.M., doktor tekhn.Aauk, red.; KOBRINM:IY,
A.Ye.,
-do-ktor-tekhn.nauk. red.; RAYEVSKIY, N.P.,
kand.taklm.nauk, red.;
BESSONOV, A.P., kand.takhn.nauk, red.; PERLYA, Z.N.,
red.izd-va
(deceased)
[Theory of mechanisms for reproduction of flat curves)
Teoriia
mekhanizmov dlia vosproizvedeniis plosicikh krivykh. Koskva,
12d-vo Akad.nauk SSSR, 1959. 253 P. (MIRA 12:8)
1. Aff USSR (for Sorenson).
(Drawing instruments)

DIKKNTBICRG, F.M..,doktor tekhn.nauk; LIUKS41N, V.S.,
kand.fiz.-mat.nauk-,
ta., kand.tekhn.nauk; OBHORSIIEV, I.H., prof., doktor
tekhn.nauk-, FLUZHNIKOV. 1.S., kand.fiz.-mat.nsuk;
UIIIAIISXIT, A.A.,
prof., doktor takhn.nauk; ACHERKAN, B.S., prof., dolitor
tekhn.nauk,
red.; VUUWVICII',- M.P., prof.. doktor tekhn.nauk. laureat
Laninskoy
premii. red.; KUDRTAVTSW, V.N., prof., doktor tekhra.nauk,
red.;
PONOMARIV, S.D., prof., doktor tekhn.nauk, laureat IseninBkoy
premiij
red.; prof.*, doktor takhn.nauk, red.; SHR S.V.'
akademilc, red.; RISHBTOV, D.H., prof., doktor takhn.nauk.
red.; GILID3N-
.,BERG, Hj., red.izd-va; SOKOLOVA, T.F., tekhn.red.
[Reference book for machinery designers in six volwisal
Spravochnik
mashinostroitalia; v shesti tomakh. Red.sovet: N.S.,Acherkan i
dr.
Izd.3., ispr. i dop. Moskva, Gos.nauelmo-tekhn.izd-vo
mashinostroit.
lit-ry. Vol.l. Pod red.N.S.Achorkanek. 1960. 592 p.. (MIRA
13-10)
1. AN USSR (for Serensen). . (blachinery-DeBign)

GUSAROV, A.A.; DIHMBIRG, F.K. -
Balancing of flexible rotor% with distributed and
concentrated
masses. Probl.proch.v mashinootr. :ao.6:5-37 6o.
(MIAA 13:9)
(Balancing of machinery)
(Rotors)

BANAKH, L.Ta.; DIMMBERG, F.N-* ZYINOGRODSKIY, 11J.
.Mll
Vibrations of a heavy shaft with distributed mass in
the presence
of a gap in one of the bearings. Probl,proch.v
mashinostr.
rLo.6:68-88 160. (MIRA 13:9)
(Shafting-Vibration)

VASILIYLPVA, R.V., inzh.; GUSAROV, A.A.,
kand.-tekhr,.nauk4--M3MITRW&.__
__j~.M., doktor telchn.naiik; TSIMUNSKIT, K.R.,
inzh,,
Fxperimental balaucing of a flexible shaft iu a
model unit.
Vest.mash. 40 no-9:27--31 S 160. (MIRA 13:9)
. (Balancing of machinery)

GROBOT. Valerian Alokoandrovich; ARTOBOT-WSKIY. I.I..
akBdemik, otv. red.;
DIXUSHIN, V.I., akademik; red,; SARDOW, S.V.,
altaderAk, red.;
FINEGIN, S.Y., doktor tekhn, nauk, prof., red.;
LEYITSKIY,A.:[.,
doktor takhn, nauk. prof., doktor tel:hn.
nauk, red.; KOBRINSKIY, A.Ye.. . dolctor taklm. nauk,
red,, t
ILAYNYSKIY, N.P, kand. tekhn.. nauk, red.; BISSONOT,
A.P., kaxid.taklm.
nauk, red.; ORPIX, S.L.. red. izd-va-. LATTI Y.G.,
toklut. red. -
[Asymtotic methods fqx- calculatingbending vibrntions
of tnrbc-
machine rotoril jlsimpt6mTc-6l3ld.'e-i-getody rescheta
izgibrtykh ko-
labanii valov turbomashin. Moskva, Izd-va Akaa. nquk
SSSR,
1961. 165 (MIRA 14~0)
1. Akademiya nault USSR (for Sorensen)
(livellers-yibration)

S/179/0/000/006/013/036
/.9 0 E191/E135
AUTHORS: Banakh, LoYat, and-Dimentberg,-K.Mv, (Moscow)
TITLE: Flexural Vibrations of a Rotating Shaft Carrying a
Component in Which the Values of the Principal Central
Mass Moment of Inertia are Unequal
PERIODICAL: Izvestiya Akademil nauk SSSR,0tdeli9niye
takhnicheakikh
nauk, Mckhanika i mets,hinostroye-niya, 1960, No. 6,
pp. 91-97
TEXT: The component, for example, a solid disc with a broad
recess milled across; the face has three differiant principal
mass
moments of inertia. It is asstned mountedin the centre of the
shaft which is simply supported on two bearings. One principal
axis of inertia of the disc coincides with the shaft axis. The
other two principal axes of the disc coincide with the two
principal axes of the shaft stiffnesses, which are also unequal.
In the presence of both external and internal friction, there are
several separate regions of instability. These are examined
geometrically in the space of the complex stability parameter,
Card 1/3

S/179/6o/ooo/oo6/023/036
Z191/E135
Flexural Vibrations of a Rotating Shaft Carrying a Component in
which, the Values of the Principal Central Mass Moment of Inertia
are Lnequal
namely the ratio of the coefficients of the internal and external
friction. The displaced position of the component is defined
with reference to different axes. The Lagrange functions are
formulated. The internal friction is assumed to be proportional
to the relat--;-.--- angular velocity of rotation about a
transverse
axis of the cross-section of the shaft. The external friction
moment is Proportional to the absolute angular veloc.Lty of
rotation 0f the component about a transverse axis. The
dissipation function is formulated and the equations of flexular
vibrations of the shaft aire stated. Substitution of complex
exponential functions as solutions leads to the characteristic
frequency equation. This equation is quadratic in -the ratio of
damping coefficients. Examination of the stability ;region
proceeds by studying the complex plane of the damping coefficient
ratio. In the general case, there are either four or two
Card 2/3

S/179/60/000/006/ojL3/o36
E191/E135
Flexural Vibrations of a Rotating Shaft Carrying a Component
in
Which the Values of the Principal Central Mass Moment of
Inertia
are Unequal
non-zero solutions of the frequency equation but there are
always four regions of stability, A numerical example is
givent
Two special cases are considered, namely when the mass moment
of
inertia about the shah axis is zero, and when it is equal to
the
sum of the remaining mass moments of inertia. In the latter
case, the motion is stable.
There are 9 figures and 2 references: 1 Soviet and I German.
VC,
SUBMITTED: April 1!i, 1960
Card 3/3

BANAKH, L.Ya. (Moskva); DTJ4FIJ7'BERO, F.M. (Moskva);
ZVINOGRODSKIY, N.V.
(Hoskva)
Origination of & parametric resonance in a horizontal
shaft with
a weight and supported by a bearing with a radial gap.
I'zv.AN
SSSR.0td.tekh.nz,,uk.Mekh.i mashinostr. no.6:159-16;!
N-D 61.
(MIRA 14:11)
(Shafting)

AGAIAIROV, V.L., kand. teldm. nauk; A~TWYANCHIK,
A.V., inzh.;
ARDREMA, L.Ye.,, kand. tekhn. nauk; BIDERIWI, V.L.,
doktor
telchn. nauk; BOYARSHRIOV, S.V., kand. toklin. nauk;
VOLINIH,
A.S.,, prof., doktor toklin nauk; DIMENTBEIIG-F-M..
doktor
teklm. nauk; KOSTYUK, A.G:, kani~;-'fe-kb-n. nauk;
MAKUSHIII, V.M..,
Icand. tekhn. nauk-; MASLOV, G.S... kand. telcbn.
nauk; NALININI,
N.V., prof., doktor tokhn. nauk; PONOMAREV, S.D.,
prof. doktor
tekbn. nauk; PRIGOROVSKIY, N.I., prof., doktor
tekhn. mauk;
~NSIO, S.V., akademilc; STEPANOVA, V.S., inzh.;
STRELYAYEV,
V.S., inzh.; TRMZIN, I.I... prof., d6ktor tekbn.
nauk;
UMANSKIY, A.A., prof.., doktor telchn. naukj
FEODOSIYbIr, Ll.s
prof... doktcir tekhn. nauk; SHATALOV, K.T.,
doktortakhn.nauk;
YUMA:rGV, V.P., kand. te)chn. nauk; BLAGNTMONOVA,
N.Yu., red.
izd-va; YEVIS'THATIYEV, A. 1. p red. izd--va,-
SOKOLOVAI T.F.,O
tekh3. red.
[Manual for a mechanical engineer In six volumes]
Spravochnik
mashJ'oaistroitelia v shesti tomakh. Red. sovet
N.S.Acherlan i
dr. Izd-3-j ispr. i dop. Moskva,, Mashgiz. Vol.3.
1962. 651 11.
(MIRA .15:4)
1. Akadem*& nauk USSR "'for Sorensen).
(Machinery-Design)

KUSHULI, Mikhail YakDvlevich; DDENTBERG F M ,
doktor tekhn. naul:,
otv. red.; LETNEV, GRIGORIYEVA, Ye.K.,,
tekhr.t. red.
[Natural vibrations of rotors; dynamics of
high-speed
spindleslAvtokolebaniia rotorov; dinamika
bystrokhodnykb
vere'ten. Moskva, Izd-ro Akad.nauk SSSR, 1963.
164 P.
(MIRA 16:4)
(Rotora-Vibmtion)

"MME.MT(III, F.M. (Moscow):
"Modern developments in the theor7 of balancing
flexible rotors."
report presented at the 2nd All4nion Congress on
Theoretical and Applicid
Mechanics,, Moscow, 29 Jan - 5 Feb 64.

DII.-I.ENTIBORG.. F.M.; SUTALOV, K.T.; GUSAROV,
A.A.; ZHITOMIRSYly, V.K.,
---cT;'AH6r tekhn. nauk, ret-enzent; DAVILOV, L.N.,
inzh., red.
[Vibre.tions of inachinery) Kolobanila mashin.
Moskva, Mashino-
stroenie, 1964.- 307 p. (MlRA i7:8)

AVFRIYANOVA,' V.G.. (14oskva); DIII-EN"ll"JIG F.M.
Geometrl-ml interprotation, of the vibratlon Of fin
elastically
suspended solid. I'zv. AN SSSR Mekh. :1 nasKinostr.
no.6-10-19
bl,-D 164. (MIFU 18:2.)

M1497~, 064
UiLgi 'IrieW~p status, of flexible

M?

AVERIYANOVAP V.G. (Mr-sk7a,); VDIENTBEERG, P.M. ()[(:Skva)
Determining the d.Isplacement ocreir by the Initlal and
final position
o:r the solid. Mashino,radenie no.2.1,13-1111 165.
1,
(MIRA Igo) -

DIM., M-EW'. , !-', i'% , doktor tekhn. nauk,
prof ., otv. red.
i-Vibrations and strength at variable stresses]
Kol.eba-
niia i prochnost' pri peremennykh
napriazlieniiakh. Mo-
sk.-va, Nauka, 1965. 198 p. (MIRA 18:10)
1. I-Ioscow. Institut mashinovedeniya.

DIMENTWIM, Fedor Menaslye-vich; AITITONOV,
I.L., red.
[(','alculus of scrows and its applications in
mechanics]
Vintovoe ischiSlEmie I ego prilozheniJA V
meklianike.
Moskva, Naukao 1965. 1S19 P. (MIRA 19t1)

LEVITSKIY, N.I.,, doktor tekhn. nauk prof.,
otv. red.; BLAGOMIAVOV,
A.A., akademik, red.; MSSONOV, A.P., doktor
tekhn.
nauk, red.;-Qj=jZPPG, F~.~I..,.,~doktor tekhn.
nauk, prof.,
red.; ZINOVIYEV, V.A., doktor tekhn. nauk,
prof., red.;
KORNSKIY, A.Ye.v doktor tekhn. nauk, red.;
CIIERKLIDINOV, S.A., doktor tekhn. nauk, red.
[Current problems in the theory of machines and
mechf.,-
niams] Sovremennye problemy teorii mashin i
mokhanimov.
Moskva,, Nauka, 1965. 342 p. (MIRA 19:1)
1. Moscow. Gosudarstvemyy
naucimo-issledovatel'skly in-
stitut mashinovedeniya.

ACC NRt AP7002929 SOURCE CODE: Uq/0020/66/171/006/1293/1296
AUTHOR: Dimentberg, N. F.; Frolov, K. V.
ORG: Institute of Prcblems of,Mechanics, All SSSR, State
Scientific Research Insti-_
tute of Machines (Institut problem mekhaniki AN SSSR,
Gosudarstvennyy nauchno-issle
dovatel'skiy institut mashinovedeniya)
TITLE: The Sommerfeld effect in a system with a randomly varying
characteristic fre-
quency
SOURCE: AN SSSR. Doklady, v. 171, no. 6, 1966, 1293-1296
TOPIC TAGS: elastic medium, oscillation, 11near differential
equation, approximation
method
ABSTRACT: A study is inade of the Somme-r;feld effect observed in
the oscillating be-
havior of a motor rotor supported elastically. Resonance
properties of the linear
oscillating system of'differential equations, brought about by
forces of-inertia of
an unbalanced rotor with random variation of the characteristic
frequency, are studi-
ed. The solution indicates that the Sommerfeld effect may be
reduced under certain
conditions when the parameters are randomly varied; that is, the
rotor may pass be-
yond the critical resonance state without the addition of
supplemental energy to the
motor. The method of awraging is used to find the mathematical
expectations for the
UDC: 531.395
"Card 1/2

ACC NR: AP7002929
substituted variables, the solution for which is givan in standard
form. Oscillo-
grams are presented to show the results of experimeryttal
verification. - Presented by
Academician A. Yu. Ishlinskiy on 18 February 1966. Orig. art. has:
8 formulas, 2
figures.
SUB CODE: 13,12/ SUBM DATE: 1IFeb66/ ORIG REF: 009/ OTH MF: 001

DIVIMBFR~ M.F . Moskva)
Forced vibrations of* plates subjected to random
loading depending
on spa(,,e and time. Inzh.zhur. 1 no.2:97-105 '61'.
(I-IdRA 14: 12)
1. Institut mekhaniki AN SSSR.
(Elastic plates and sbells-Vibration)

SY'179/62/000/003/013/015
Elql/E435
AUTHOR: Dimentberg. M.F.. (Moscow)
TITLE: On the lower estimated limit of endurai,,&(,e life under
stationary random stresses
PERIODICAL: Akademiya nauk SSSR. Izvestiya. Otdele:aj-ye
toklinicheskikh nauk. Mekhamilca i mashinostroyeniye,
no-3, 1962, 167-170
TEXT: The lowest estimated value for the endurance life is given
for structures subject to cyclic stresses which constitute a
stationary Gaussian random process. At first, the problem of the
evaluation of the mean endurance life under a given cyclic stress
is considered when this stress is a stationary random function of
time. The mean value o,f this function can be assumed as zero
without limitation of generality. If Sol the spectrum of the
stress amplitudes is continuous and the aummation of fatigue
stresses is replaced by integration over the amplitude levels.
In most cases, the stress cycles are not all simple or
symmetrical. An attempt is made to evaluate the endurance life
by replacing an. arbitrary process with a more damaging process
Card 1/2

S11. 7 9/62/000 /00 3/013/015-
On the lower estimated ... E191/E435
consisting of simple cycles which are nearly symmetrical. This
will be an evaluation of a lower limit. The hypothesis of a
linear sununation of fatigue damage is employed. An expression
is given for the expected service life. In this expression
use is made of the fatigue curve obtained for symmetrical cycles
which is substituted by a power curve. In random oscillations
of a mechanical system witha single sufficiently sharp maximum
of
the amplitude-frequency characteristic, the probability of
complex
cycles is small. The derivations for the integrals required to
determine the expected service life are given. In the event of
a Gaussian process, V.V.Bolotin (Statistical methods in the
theory
of-.- structures. Gosstroyizdat, 1961) obtained an apProximate
formula for the mean service life. In the limiting case of a
narrow-band Gaussian process, the results of the present paper
coincide with those of 8olotin. It follows that the Bolotin
formula for the evoluation Or anduranan life ut a stAttionAry
random stress having a normal distribution practically coincides
with the lower estimated limit for all values of the parameters
likely to be found in practice. There are 2 figures.
SUBMITTED: January 31, 1962
Card 2/2

4:2103
S/179/62/000/005/0!06/012
E191/E135
AUTHUR: (MOSCOW)
TITLE: Nonlinear oscillations of elastic panels under
random loads
PERIODICAL: Akademiya nauk SSSR- Izvestiya. 'Otdeleniy-~
tekhnicheskikh nauk..Mekhanika i mashinostroyeniye,
no-5, 1962, 102-110
TEXT; In earlier work (Inzh. Zhurnal, no.2, iq6i') the
problem of plate& was considered by the present author with the
help of correlation theory. Here, the analysis is applied to
thin elastic panels. In thin panels, the ftormal deflections can
be so large that the geometric nonlinearity may be significant.
As shown by D.A. Sinith and R.F. Lambert'in their paper on the
effects of dynamical nonlinearity on-extremal statistics W.
Acoust. Soc. Amer., 32, no.12, 196o), the density of the
ptobability of stress maxima for large amplitudes may turn out
to
be higher than those determined in accordance with the linear
theory. The subject of this paper is the problem of determining
the density of probability of deflection and stress extrema
under
Card 1/3

Nonlinear oscillations of elastic... S/179/62/000/005/oo6/ol2
E191/EI35
nonlinear oscillations of panals, which is associated with the
problem of evaluating their dynamic strength. An effective method
of analysing random processes in nonlinear systems is based on
applying the theory of Yjarkov processes and the equations of the
Fokker -Plane k-Ko Imogorov type. Mostly, the excitation process
is
assumed as a "white noise". Recently, however, excitation spectra
described by rational fraction functions have been considered.
The excitation processes are found to be related to white noises
by certain linear differential relationships which are taken into
account when the Fokker-Planck-Kolmogorov equations are set up..
This method has already been applied to automatic control
systems.
The method is applied here to determine the density of
probability
of extremal valuess A thin, elastic, shallow, curved panel with a
rectangular planform is considered. The normal deflection is
commensurate with the panel thickness but small compared with the
length of the edges. The equation of oscillatory motion is
formulated, without taking dissipation forces into account. An
approximate solution is sought by expanding in terms of. special
functions satisfying the boundary conditions for t.he deflection.
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Nonlinear oscillations of elastic ... S/l79/62/000/-Oo5/006/olZ
F-191/E135
Making use of the Galerkin merhod, a system of ordinary
differential equations i.4 obtained. If the special fiknctions
are
natural inode:s and the dissipation ternis are introduced, the
equations of the system contain th'e'attenuation coefficients,
the
generalised coordinates, and the generalised forces. The latter
are assumed to have spectral densities described by rational
fraction functions which can be obtained by passing the white
noises through linear, filters with transTe'r functions
described by
similar rational fractions. The Fokker-Planck-Kolmogorov
equiLtions
are set up, A freely supported circular panel is also
considered.
Some simpler cases are examined in greater.detail. Relations
are
given for the mean number of extrema contained in a certain
interval of values during a unit of time. Finally, it is found
that nonlinearity increases the number of maxima for large
amplitudes and decreases the number for small amplitudes. This
rp-sult is in agreement with the experimental data of Smith and
Lambert.
There are 7 figures. SUBMITTED: April 2, 1962
Card 3/3

lip(a), WWI/zq
1VV I -M
~--AP66-1-15!
SOURCE COZE: up/o424/66/000/ou/0035/00 0
AUTHOR: Dimentberg, M. F.: (Moscow)
ORG: .-none
-TITLE: Resonant properties of t,, s u degree of freedom and -randomly
ystem withon
varying natural frequency
SOURCE~. Inzbenernyy zhurntil Yekhani ka tve rdogo te1a, no. li 1966,
35-ho,
TOPIC TAGS: vibration linaJ,ysis,' vibration dampin Pqrced vibration,
random natural
9
frequency
tABSTRACT: Forced vibrations of a systom with olie: degree of freedom
described by the
differentM equation
All' dZ
+ U + wo [I
dF,
~'~where w is the mean natural frequency' of the system, a is the
damping factor
(a
to cis'a small parameter, and 4(t) is a n;tationitry randoni function,
are I-
alyzea. St chax~'
an
atistical ~acteristics of the random function E(t) are sought such
,that theyVill ensure an ek,fective and stable dec:mtme of the
amplitude of resonant
vibrations. It is assumed 'that the average zero value and the
correlation function
rd 1/2

M6 -66
7
ACC NR, AP6011128
~'K(T) of 4 (t) are given. Fun ction K (t'il is,representeRd in the,
forni of a power series
X (t) xa~, (t) +exi (1)+ O.Z2 (2)
By substituting the series; (2) into, e0uati6n (1) :1
i_ an infinite system of linear
inhomogeneous -differential -equations vith constent coefficients in
fumtions
x
(i= i,2... are derived-from vhiell gene~ai exr.,-,ransionz for 0 d W
( 0 an x:L
obtai ned. Statistical- characte Iristics of x(t-)-(set averaged
value -cx(t)>) are
are
determined, using only the, first three.. terms of e )zinsion (2). On
the basis of the
derived expressions for , it is shown that when the spectral
density '~(W) of
the stati on ary random fun:ci;li on ~ (t) - foi , all w >, 6- is
continuous and Oldw < 0,
then. such random variations of the natural freque~acy reduce, on the
average, the
amplitude of resonant vibrations. In the particuLar case when thc
correlation time
T of the random function. C(t) is small as compamd with I/a, the
first approximation
o~-the magnitude ofthe re6tuction,inthe.amplitude of resonant
vibration! is propor-
tional to the difference of- the spe'ctrzil densities, of the
pr~ocess, ~(t) at low fre-
qUencies '(of the order a2/a%:o) and at the frequency.2wo. The
flexural vibrations of
-W
the elastic thin bar under the simultaneous acti&k of a transverses
load hose
variation is proportional to Cos wit arid a longitudinal load
represented; by a sta-
7
tionary random time function are, cited 'as an exejqile, Re author
thanks K. V. Frolov
for useful re 'LK
marks and discussions. Cirig. art.,hastt, 27 formulas, L
-SUB CODE: 20/ SUBM DATE- ';:06Sep65/,. oKG MF 00!51' ATD.PT(ESS:Zjj
5Z
Card. 2 /2

4U42-66 EWT(d)/MO(I) LIP(c)
I-ACC NR:--
SOURCE, CODE: UR/0424/66/000/002/6WB~6i8
AP6024195
ATJTHORt Dimentber M. F. (Moscow)
ORG: none
TITLE: Amplitude-frequency characteristics of asyllem y~i
Lth randomly va:rying
parameters
SOURCE: Inzhenernyy zhurnal. Mekhanike. tverdogo t.el(L, no. 2j
1966, 176-182
TOPIC TAGS: ordinary differential equetion, random vibration,
frequency characteristic
ABSTRACT: The statistical characteristics of the following type
differential equation
are investigated with regard to small, steady, random changes in its
coefficients;
:dnx d"-1x dx
+ . . .+a,[ I +e',~jy) I -j-,-+ao( I +eFo (I)] x ==ac-'
As a first approximation, thei"meki amplitude"--of vibratiofis is
determ'Ined from the
modulus of ashf)', where
Vj i0 n- I n_1
dig
-0 -0 k-0
and b is a real constant. The different results on random
coefficient changes are
analyzed for even and odd orders in n. The following expression is
derived to show
the possibility of lowering-the resonance amplitudes by a possible
control of the
Card. - 1/2

L 44W-66
:'-ACC -NRI--AP602~ff~5~----
i
coefficients
wn-I M, q-A
a YJ -!L- 1j;,", - (- 1)qJ+
Ak
q-0
A dispersion relation is obtained for the amplitude changes
generated by random
oscillations of the coefficients in the system. Orig. art6*
bast 29 equations.