2
Letters to the Editor l~opa3~o 6oaee IlpaB~ono~o6Ho TO. HTO 9~aHHoe gB~IeHlle Bt,I3BaHO TeM, qTO lla IIOBepXHOCTII l~llllHa BMeCTO MOHOMOJIeHy~IgpHOFO a3Ff,~HOPO II~III HIITpligIHOPO CJIOg 05pa3yeTcg Ilpll 50~Iee tlp0~0~IH~IITeJII~HOM p a a p ~ e aall~Ha~, ~t~irt ~e HllTpH~gag pemeT~a, HOTOpag gJIll yBeamm- t~aeT pa60Ty BHx0~a Hag me ~perlaTCTByeT nnepell0cy aneprHll, llo~Iyqet~HOi3 Ilpg ilpenpame- HIIII aallR~o~t Moae~y~I~i B MeTaaagHec~o~o pemeT~y i~ll~a. OCliOBHO/~ BOIIp0C, HacaeTcH Jill ~e~IO B ~aHIIOM c~Iyqae OMIICCHII 3~IeHTp0HOB IIOCOIe OHSOTepMHtIecHoro IlpOMemyTOHHOrO IlpoI~ecca, HaM IIOHa-qTO He y;xa~ocb, o~HaH0, paupe- IllllTb. Pesy~I~TaT~I Aa~i~llefim~x llccae;~oBai~ll~ 6y~yT 0IIy6aI~KOBaH~I. Y[OCTyIIII~IO 4. I. 1953. Vdelav St~elka, Hucmumym mex~tuuec~o~t 96uaunu, llpaea ~HMAMHqECHHI~I METO~ H3MEPEHHH HOO(I)(I)HI~HEHTA PACIIIHPEHHYI H TEMHEPATVPHOFO HODCI)(DIJI~HEHTA MO~V3I~I YlIPVFOCTH (A Dynamical Method for Measuring the Expansion Coefficient of and the Temperature Coefficient of the Modulus of Elasticity) ~ag npaHTrtKrl rlMeeT 6ozibluoe 8HaqeHge ll3iepeHlle ~oa~)~rlimeHTa pacm~pena~ rr 8a- BIICHMOCTH MO~ySIft E OT TeMIIepawypl,I, B Oc05eHHOCTg llpH BLlcmgx TeMiiepaTypax. Pac- mHpeHlle oTi~piHo FI3MepYiJIOCb CTaTIIqecHHM CIIOCO~OM II HaMepeHHMe 3HaqeHIIH I4CHOJIb30- na~illcb ~Jia ~mlaMrlqec~oro gaiepeHlla TeMIiepaTypHoro i<oa(~<~)lli~uegTa Mo~yJIg ynpyrocTll E. I{aH HoHa3aJI~l HsMepeHI4g 3OBIIC]/IMOCTHqaCTOTI,I OT TeMllepaTypI~I, 06e I+ICHOMt,IeBeJIHqIIHI, I Momno nonyqHTb npg 0~HOM DTOM HsMepegllll. PaCCMOTpHM MaJIl,II~I llHTepBa~I TeMllepaTyp, B HOT0pOM ~Illita II MO~yJIb II3MeHHIOTs IIO allllei~HOMy 8aKoHy. ~aa ;~zmH llieeM l t lo(1 + at), r~e t -- ~SMeHeHne TeMlIepaTypH, ~ -- KO3q~(~m~eHT pacmnpeH~a, l -- ;~au~a; 0TCIO~a Aa~ y~eabHOfi HJIOTHOCTH @ BhlTeHaeT COOTHOIIIOHIIO qt = Co(1 + at) -3 Anaaor~iHO ~a~ M0~yaa yrqoyrocT~ gMeeM: E t : Eo(1 + 7t) r;Ie y -- TeMnepawyprtall I~03d~d~rIlleHT MO~y~I~ yrlpyrocwrt. I/IciiO~IL3yH DTFI C00THOmeHHK ~ I g BLIpa~HeHKH 3aBHCIIMOCTFI qaCTOTBI IIpO~OJII, HLIX H~III nonepeqm, lx ~oaeTaHn~ OT TeMiiepaTypbi, M~I II0~Iy~mM COOTllomenne /t -- 1o( 1 4- oct) + . (i + yt) . EcJIII 3aBHC]/IMOCTt, BI,ipamaeTca B BI, I6paHHOM ll~ITepBa~Ie TeMnepaTyp IlpgM0~I, TO Ha He~t BblTllpaeM TprI TOqI~ll; B IIpOTHBHOM cayqae OTII T0qHII BalSepeM Ha HacaTeabHofi H HpgBOfi pnll n~ITpa~ll0~I TeMnepaType T~: (T~, ]~), (T v ]~), (Ta, ]~). OSoattaq~B paaitOCTri TeMnepaTyp T~- T x : tt, T a --T~ = t~, MLI IIOayqI~M ypaBgeHllg 1~ = 1:(1 + at:) . (1 + yt:) , ]a = Ix(1 + aQ) . (1 + yt2) . OTrl ypanHeHllg MOH~HO 5bIJIO 5~i T0qHO pemnTb, HO Tall ~a~ pesyal~waw B eB00~I oSi~eI~ ~OpMe wpy~n0 0603pllM, a HHcYIeHHbIITI pacqev 8awpyRHrrWe~IeH, TO MLI pa3JI0~'AnnM CH05Krl B pfl~, B HOTOpOM OT6pOCI~M qZleHhI iiopa~i~a Tpew~,ero II Bblme: ]A : 1 + }(c* + y) t i -- }(a--y)~t~ u t~ -- = 1 + + 7) t~-- }(a-- y) ~t~ ~. 1 Czechosl. Journ. Phys. 3 (1953) 2 169

Димамический метод и змерения коэффициен та расширения и темпе ратурного коэффицие нта модуля упругости

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Page 1: Димамический метод и змерения коэффициен та расширения и темпе ратурного коэффицие нта модуля упругости

Letters to the E d i t o r

l~opa3~o 6oaee I lpaB~ono~o6Ho TO. HTO 9~aHHoe gB~IeHlle Bt,I3BaHO TeM, qTO lla IIOBepXHOCTII l~llllHa BMeCTO MOHOMOJIeHy~IgpHOFO a3Ff,~HOPO II~III HIITpligIHOPO CJIOg 05pa3yeTcg Ilpll 50~Iee tlp0~0~IH~IITeJII~HOM p a a p ~ e aall~Ha~, ~t~irt ~ e HllTpH~gag pemeT~a , HOTOpag gJIll y B e a m m - t~aeT pa60Ty BHx0~a Hag me ~perlaTCTByeT nnepell0cy aneprHl l , llo~Iyqet~HOi3 I lpg i l p e n p a m e - HIIII aallR~o~t Moae~y~I~i B MeTaaagHec~o~o p e m e T ~ y i ~ l l ~ a .

OCliOBHO/~ BOIIp0C, HacaeTcH Jill ~e~IO B ~aHIIOM c~Iyqae OMIICCHII 3~IeHTp0HOB IIOCOIe OHSOTepMHtIecHoro IlpOMemyTOHHOrO IlpoI~ecca, HaM IIOHa-qTO He y;xa~ocb, o~HaH0, p a u p e - IllllTb.

Pesy~I~TaT~I Aa~i~llefim~x llccae;~oBai~ll~ 6y~yT 0IIy6aI~KOBaH~I.

Y[OCTyIIII~IO 4. I . 1953. Vdelav St~elka,

H u c m u m y m mex~tuuec~o~t 96uaunu, l l p a e a

~ H M A M H q E C H H I ~ I M E T O ~ H 3 M E P E H H H HOO(I ) ( I )HI~HEHTA P A C I I I H P E H H Y I

H T E M H E P A T V P H O F O HODCI)(DIJI~HEHTA M O ~ V 3 I ~ I Y l I P V F O C T H

(A D y n a m i c a l M e t h o d fo r M e a s u r i n g t h e E x p a n s i o n C o e f f i c i e n t of a n d t h e T e m p e r a t u r e C o e f f i c i e n t of t h e M o d u l u s of E l a s t i c i t y )

~ a g npaHTrtKrl rlMeeT 6ozibluoe 8HaqeHge l l3 iepeHl le ~oa~)~rlimeHTa p a c m ~ p e n a ~ rr 8a- BIICHMOCTH MO~ySIft E OT TeMIIepawypl, I, B Oc05eHHOCTg llpH BLlcmgx TeMiiepaTypax. P a c - mHpeHlle oTi~piHo FI3MepYiJIOCb CTaTIIqecHHM CIIOCO~OM II HaMepeHHMe 3HaqeHIIH I4CHOJIb30- na~illcb ~Jia ~mlaMrlqec~oro g a i e p e H l l a TeMIiepaTypHoro i<oa(~<~)lli~uegTa Mo~yJIg y n p y r o c T l l E .

I{aH HoHa3aJI~l HsMepeHI4g 3OBIIC]/IMOCTH qaCTOTI, I OT TeMllepaTypI~I, 06e I+ICHOMt,Ie BeJIHqIIHI, I Momno nonyqHTb n p g 0~HOM DTOM HsMepeglll l .

PaCCMOTpHM MaJIl, II~I llHTepBa~I TeMllepaTyp, B HOT0pOM ~I l l i t a II MO~yJIb II3MeHHIOTs IIO allllei~HOMy 8aKoHy. ~ a a ;~zmH l l ieeM

l t - - lo(1 + a t ) ,

r~e t - - ~SMeHeHne TeMlIepaTypH, ~ - - KO3q~(~m~eHT p a c m n p e H ~ a , l - - ;~au~a; 0TCIO~a Aa~ y~eabHOfi HJIOTHOCTH @ BhlTeHaeT COOTHOIIIOHIIO

qt = Co(1 + a t ) - 3 �9

A n a a o r ~ i H O ~a~ M 0~yaa yrqoyrocT~ gMeeM:

E t : Eo(1 + 7t) �9

r;Ie y - - TeMnepawyprtall I~03d~d~rIlleHT MO~y~I~ yrlpyrocwrt .

I/IciiO~IL3yH DTFI C00THOmeHHK ~ I g BLIpa~HeHKH 3aBHCIIMOCTFI qaCTOTBI IIpO~OJII, HLIX H~III n o n e p e q m , lx ~oaeTaHn~ OT TeMiiepaTypbi, M~I II0~Iy~mM COOTllomenne

/ t - - 1o( 1 4- oct) + . ( i + yt) �89 .

EcJIII 3aBHC]/IMOCTt, BI, ipamaeTca B BI, I6paHHOM ll~ITepBa~Ie TeMnepaTyp IlpgM0~I, TO Ha He~t BblTllpaeM TprI TOqI~ll; B IIpOTHBHOM c a y q a e OTII T0qHII BalSepeM Ha HacaTeabHofi H HpgBOfi pn l l n~ITpa~ll0~I TeMnepaType T~: (T~, ]~), (T v ]~), (Ta, ]~). OSoattaq~B paaitOCTri TeMnepaTyp T ~ - T x : t t , T a - - T ~ = t~, MLI IIOayqI~M ypaBgeHl lg

1~ = 1:(1 + at:) �89 . (1 + yt:) �89 ,

]a = Ix(1 + aQ) �89 . (1 + yt2) �89 .

OTrl ypanHeHl lg MOH~HO 5bIJIO 5~i T0qHO p e m n T b , HO Tall ~a~ pesyal~waw B eB00~I oSi~eI~ ~OpMe wpy~n0 0603pllM, a HHcYIeHHbIITI pacqev 8awpyRHrrWe~IeH, TO MLI pa3JI0~'AnnM CH05Krl B pf l~ , B HOTOpOM OT6pOCI~M qZleHhI i iopa~i~a Tpew~,ero II Bblme:

]A : 1 + }(c* + y) t i - - } ( a - - y ) ~ t ~ u t~

- - = 1 + �89 + 7) t ~ - - } ( a - - y ) ~t~ ~ . 1

Czechosl . Journ . P h y s . 3 (1953) 2 169

Page 2: Димамический метод и змерения коэффициен та расширения и темпе ратурного коэффицие нта модуля упругости

I I u c b ~ t a e peOa~ t tum

~0603HaHHM ~ = n l ; ~ = n~ I~ IIO~IO'rKHB 0r -4- y = X; ~ - - y ~ y , n o n y g g M

n~ - - 1 = �89 - - �89 ~ ,

n~ - - 1 = �89 - - }y~ t i ~ .

PemeH~H ypa~r~eHriH HMetOT BHJ~

2 | / 2 ( n ~ - - 1) (n2 - - 1) Y •

t i t2

npHHeM 3Hat~ n e p e ~ HopHeM sz~6~pae~ Ta~, ~TO6~ a 6s~no 6 o n b m e HyHm

- �89 + y ) ,

= �89 - y ) .

Tar~ Hall a ~ y CyTb BeO2KHI, IHLI n o p g A ~ a 10 -5, TO I/HWepBaH Tem~epaTyp MoH~eT 6blTB BbI6pail He 5once 100 ~ HT06BI IIOpH~OI~ Benl~HI~H a t H Yt He HpeBB~maa 10-a; HHaHe MBI He CMoH4eM npeHebpeHb HHeHaMn p a a n o ~ e H ~ g , HaHHHaH C TpeTberO nopggI~a .

X a ~ aaTyHH 5L~a~ Bb~CH~rTaI~B~ cHegy~oiaHe aHa '~eH~: n p ~ WeMHepaType T ~ 50 ~ (T~ = 20 ~ T~ = 50 ~ T s = 80 ~

= 3 , 7 . . 1 0 - s , y = - - 2 , 1 . 1 0 - a ;

n p ~ T e ~ n e p a T y p e T = 270 ~ (T~ - - 203 ~ T~ = 266 ~ T s = 310 ~

= 9 , 6 . 1 0 - ~ , y - - - - 5 , 3 . 1 0 - ~ .

Hoa/I)(])mI~eHv p a c m ~ p e H H n n o a y q a e T e ~ B o b o ~ x c n y q a g x 6 o ~ m e , HeM no T a 6 ~ a a m ~[~H a = - - y aTOT y r t p o ~ e H H b ~ MeT09~ He r~pHro~e~ H Hy~HO 6N/fO 6B~ BBeCTH n paceMOT-

peHge qneHH wpewbero n o p g x ~ a .

IIocwyHma0 10. 2. 1953. K a r e l Mi~e]c, F I u c m u m y m mexsuuec~;o~t g~uau~u q C A H , I I p a e a

H O B b I ~ I M E T O ~ ~JIY[ A B C O J I I O T H O F O H 3 M E P E H H f I HOOcD(DI/II~I/IEHTA

T E I 1 J I O I I P O B O ~ H M O C T H H E B O J I E I l I I i X O B P A 3 1 4 O B

(A N e w M e t h o d fo r t h e A b s o l u t e M e a s u r e m e n t of t h~ T h e r m a l C o n d u c t i v i t y of S m a l l S a m p l e s )

M e r npgMeHs~eMble ~as~ a6ooJIk~TgOPO ~aMepeg~H c e n a o r r p o s o g H o c r ~ npH y c r a H o - BIJIBIIIOMCfI COCTO/tKKII, wpe6yeT 3HaHNTOJIBItBIX p a a ~ e p o s o 6 p a a a a , e c n g ~ip~ gaMepeHg~ }~eaaTeHbHO IIoglyHKTb 60Hee TOHHble 3HaHeHKH. OXH0~I II30CHOBHbIX npHHHH HeTOqtIOCTI~ ~{B~IHIOTCK HeMgHyeMMe n o r e p g Tenaa , BO3HH~atOn~He H3-aK HecoBepmegcTBa TelIJIOBO~ HaOHHI~KK. II03TOMy, HTObBI OTHOC!~TeJIbHO IIOHK3KT5 BJIKKHKe OTI~X n o r e p b , BbI6Hpa~oTCg 0 6 p a a a ~ C 60a~m~Mrr r ~JIK He6OgIbIII~IX 05paaaoB OTH MeTOAB~ B OTttOHIeltKI~ TOtIHOCTI/I HeBBIPO~tt]bI..

I Ipe~:~araeML~ H O B ~ MeTo~ H3MepeHH~ wena0npoBo~HOCTrI He60:~bmHx obpaa~oB r to- 3BOJlgeT noJlyHaTb peay:IbTaTbI ~{3MepeHH~i He3aBIICIlMO OT TOFO, HaCHOHBHO coBepmeHHa ~ a o a a a ~ n o b p a a a a OT o ~ p y m a ~ o m e ~ cpegb~. IIpH awo~ ~ewo~e gamepgeML[i3 obpaaeI~ o ~ p y m e H cpe~ot~ c nocwog~Ho~ TeMHepaTypO~ T ' , s cHxy Hero C ero noDepxHOCTg HaCTaHeT yCTaHO- BgsmagC t t nepe~a~ia Tenaa . IIpH DTKX yCHOBIIgX ]/I3MeHeH!/Ie TeM~epaTypb~ T S,~OXb o b p a a q a He Bb~pa~aeTcg y m e $~HHei;iHO~ 3aBHCHMOCTBIO. r~Jfgl JIIO~0I'0 MeeTa obpasi~a TeHHOB0~ nOTOR ~aeTeg co 0THOIIIeHI/IeM

Q __ .~q d T

t -d-~'x "

Ecar r HaBeCTH0 ceqeHHe q o 6 p a a ~ a , a i~a /ffaMeHeKgg we~nepawypBi B~Onb o g p a a a a t ~ a ~ e ~ COOTBeTCTBym~H~ WeMHepaTypHHf~ rpagr~eHT, T0 ~ a n T0rO HT065I o~pe~enrrv~ I~Oa~(~m~r~er~w TeIIHOIIpOBO,~HOCTIzI ~, HalO e a e yCTaHOB[ITb TeHHOBOI~I IIOT0t~. BBrmenpgse~egHoe COOTHO ~ meHHe ,~e]~CTBNTenbHO TaHme ~ ~aH Ha,4ana obpa3Ha. B 3TOM MeCTe, BCTynaIOIIlg~ B o6paaen~ TeIUIOBOITI IIOTOH~ EaMep~tewe~ aHe~<TpggecI~nM HaYIOpHMeTpOM.

1 7 0 ~Iexocm r mypn. 3 (t953) 2