时变动力学的Legendre级数解

U21yfμU2年1 la Ai NS NS±Vol 21 No. 22000Ae60AACTA MECHANICA SOLIDA SINICAE士aA|Nsμ A Legendre 14(Eyv282U0%409 P1OFE12 lEU. B￡A‘Ns1a3 HANSO6keoj￡+ aAH ngio2 DOuaeuneE×000090aEaA; NS IElaiE1eA0,9-E土taTμEyc·0-3xe. AIAOAx1-0·a吖gendre4Ey0’iak° Legendre my·0Ea×0400360:00.010E士aANs|p|3A·”E203pAO°aTE250啊010 DDS 2a40E土 AINS TEla OIAAIA01E0uNSμAEND%10AU'E EttaAHNSEhegendre V4EyEx'i-iOva-y3iEmy-OEax0940061 OnOM。 UAeuaainSnS i FE:c01AED130, IHAdnS iF·0k‰062·0NE005N0IouA4T4 TAi itB%c2TEy2E土土a-.·2ANN%啊EeE土始a·cE士a“阳a土a0UND%士们A0xa000 IAHNSX-E我4°12—AE土士 aAHNS"u FuEYE土士 cAnSECO,260,DAND%I0￡6cI0uANSμA0。600.0025uA0E·3iEc± gleyeyA-2310Aa6·“6a-c③ SANE6。EaCe6IA2AAUμAE·a￡5}0。μ MAEyNSAiAB200·EpA0 UAIAUEI1ECEμM00AE书0-E土± alMEydA16-pA6a“Ec0n60%ya%6μA00们 azeiu+Oy EOEEACHAxa10E0,±4TA0土10÷E土aqAp903订D0E土士aμA± allEy ilc0-31×eEAx1031a? I Legendre 4Ey01y-0Ex0‰00oj&qEy3Exy400023030auAi30nE1E68-0-1taoUv4EEa uoEEaznioAna340AE0a0x lEia oaoaE0AOU0。°aD0E土aANS400 E+ NS IEias01ea_0DE13k∈白AaEE土±3A; NSOeE± NSIEla02002A0ou2E± iAHNSHAx1-43380B0B2IEyμAE±aAlμ30o4°A- leTta AiNSIela%-Eyoμ·n·"AeEc0和E1ea1a=00E0E131￡U¨t￡oE¨tEy4Uetu“t.y4UErR"tEy=Eya10Ec0EA06 MigeAa3A Cig006K0E0%土陌.3eB0360μ如￡￡¨O￡y=￡u9YH中国煤化工A谊¨t￡y=EE"tE990CNMHGEU¨t￡8 SMOE"tzy4E"t￡sf¨t￡sy￡U￡"t￡E"tE@y=E"t￡y￡”3a020°EIED00μ anS fEND%bA19971,aE+9y104EoμpAa2U04O HEE EttaAHNSHA Legendre yNEyyaia103 i"ce"l26y-E0/9%Ge"tfey-E0￡"3bEe00EE" AcEttaA!NS" n×Ed0a·3a1+(1(12902E40,a￡0"t￡y=EURt￡ sMup tEBy+Eu"t￡y￡E0Ey=￡y=20x0X2￡"5bEEce"l26y-EUX VEY￡"6aE￡"6b￡0M-KE0E¨Ey=EU0M-J/EYE"6c⑥3 Legendre 14IEy4°aoy0Ea×000Legendre 14SEy":E“-1E+=0E+9p-「“0aaEi+1E0F"zE=E"2i+1Ep口zzE;Fz￡-=1223卞l”zE0=1E7FzE=z￡"8aEeEIFμ8:0=￥32-10E:8￥5:2-30.:0=￥3:-02+302E1 kAEla0°a±fTEdE"2-1E创i=12232t￡"8c2啊00E土 AINSIElaEEuni% iuAlA3Etyaco们tE“0是290EEDD土aAL0A2%4lLEWAWhtaDI Legendre AlEy S tEefoalEi+129;t￡0=￡"2i+1中国煤化工=12234-￡10a0CNMHGE 10b2AaouCoval$t￡9≤1￡¨llaE0i104 i1 iaAH NSNS士200u21%f￡"llbE⊙HeY Iddt2t(1-t/T)g0(21-1g"taDI Legendre 24IEyOUcoy48OfTEpAOy/2 DOOEI0o'EOaoUcova"Of TEpAETOao-Eyi EOA+aDi Legendre v aTa界"1E0=∑/¨tE0Raod hueyf￡¨13bTEoEjoDIp m I1%209100g"1E0∑/s"￡0=EUm班S"t￡y=fmSf m =uFo fi f2 i-f0i-Sn￡￡¨14c20± aDI Legendre EyoDlc·YA10T2"2i+1￡tdt. f"rfod s, f"rEdE"150A们E0μ411ny.008EuA± aDi Legendre 4fEyuAny-0官E丿$t￡0f rEar22+别SF2SF8(=1EE3E下D'3E3006DIE1laτ2r=DnS是t￡0E"17aE⊙a0By-0Ea×090001/50THE中国煤化工00CNMHG0000g歉握pAEy-NuE01E2U0OSHEEQ EttafAH NSHA Legendre A\Eylaia 105 iag"Eg"E0=∑as"1E0￡"18aEFaoD￡"l8bE⊙g派"tE度”E9eE日￡¨18c￡0g讲=g=gik=g=gk=8Eati'TEIEUSEYA 0, AvA. OaNuiiExe3EtaDi Legendre Ey3Eny-400ouA01iEn00kgg1g1821kg22k ig2Em-lE*￡"19bgm-1Ehgm-1nkgm-13k1-gm-1￡m-1￡h4 Etta"A luiauAvaxE土 aT AINSx"ld0a·35a￡y·0￡cxc0a300”5AE"8120y=(0C6r+9xE 2020E:0 DEtva Ey400“12g0E"1E80“1A± aD I Legendre 14 Ey01a1￡¨t￡y=>印Y1;Y2i-Y2nEY霁"tE0=￡US0l2nS1I2Sm-1L2,EMYo Y1EY=E2USn≌0ng¨21aAaErEE¨￡y0 S.EEOF2y￡U中国煤化工别0H0§21c0FEaotEuF SCUH￡Ytt￡DA±aCNMHG6￡9s￡a± aDl LegeEy 400of%u l ONof four EyyE∑20 EoDU A tEEDBEU2 tEEMA40003Ey元E01aaEUR￡EE8y=￡UHn球0§nEMn是mnE2yAEaOBUS. s数据08EyA00 VEysEy06±E19:0(19EAA106ia1 iaAH NSNS士200u21%fEU￡BM¨0Usns0nnEyE 2212CE12ODHr△8nmcHHk381m-1BhEUH￡Y=HHH2m-1T4=0m-1Hi-2m-1gm_IEm-IE+hkE"22c20EE¨20￡HE' OfSyoDDECIA, AD￡Yy=SoYEUSol2n s,I2, i-Sm-I2,EMYo o i-OEY=EUSm2Edw Ey 2320a0 EWW EECEEI11012mxAD0EC°2n0E01,oA900μl04F“230a0E01AaE∑21a21B223￡E6u土%EaE203cEeE”17aAy·0HAEUSm2EuY Ey-EUSmfEdw Ey_E0S 2UD, 21UAm. GYm Ey+EUS 2UDmEEuF Ey fEnODEUDmEY-EU 12, EYefUDmfYE"24lE⊙a0D② a Kronecker 3Exy Eg"24a0EUsn￡YAcay ey= EU /Eym EUDm2UAmEy-(Ew Ey+EUDmE'EuF Ey°E“21aE0DauA=0土E￡BCE8y=20 S_ EYEU￡ YLUD50 UH EY(n. A+_ eOF.y￡2600q0,036E±aAN-”19A金u¨1￡8y503μ0E±±aT|3μAa03μDOE土aTu30D|301E0E1￡U"t￡ae"t￡ygUE"t￡E"tEy=￡t￡?-￡uε"0￡y=￡oky"27a￡0￡0etEy=￡¨￡UE"t￡YUE中国煤化工t￡y￡"27hE0E"5a0a±E6EiCNMHG￡URt￡Y=⊥UEt￡YUE"tE￡0¨t￡y=￡UE" tAeYEon￡yE"282000¨2620±0E0000A5 o EuCoHAEuR2"tfs l n v2xAdodeuf“E8yu2用U2U04O HEE EttaAHNSHA Legendre yNEyyaia107 i"EyouEaAy/4ACECIA。- EttalueyIc013lk白001牌”t牌”09(1t0][x"t￡Iau±·27aEB0CELy=0.E6EiT=1m=420°E¨130A“ t CODE+tallEy tuA±abl1Eo E2 21cECCUHmEY -EUHo H1 H2 HeY=[0 000000 0101/201/20000001/301/30EUD EY01/501/5E”22c￡HkHHeHk3△guHk3∑g1Hk3Hk5∑mH5∑g21H5∑k2Hk5∑g2Hkk=07∑8Hk心∑g1Hk∑g2Hk7∑g3HkaEi≥i回p-p+I-c2i+2=i-j+2p￡1p=0t2t-2k≠i-j+2p￡-p=02t-Ea2=5/2EE”23￡e中国煤化工￡Wn￡y=￡U11CNMHGm2eo0ElonE1 uEeEZ26E8%4 HA7aA"￡dtEC+ Se tE@+ 1 s1 iaAH NSNS士2000Ae叫21%X"tE0=t2/2+1120010,1四AN016μAE土 rAins>u.0uANS0E2,土10NS36°aEcE+972 Majid K I. Forces and deflexions in changing structures. The Structural Engineerft97225C3203 Arutyunyan N Khf-Naumoy V E. The boundary value problem of the theory of viscoelastic-plasticity of a growingbody subject to aging. J Appl Math Mechf-1984E48IfEf4 Abramowitz me -Stegun I A, Handbook of Mathematical Functionse-Washington dce National Bureau of Standards5 Gradshetyn I SE-Ryzhik I M. Tables of Integralsf-teries and Products. New YorkfAcademic Pressf-1979SOLUTION OF TIME- VARIATION DYNAMIC PROBLEMBY LEGENDRE POLYNOMIALSCao Zhiyuanang shougaoE"Department of Engineering Mechanics f-Tongji Universityf-Shanghaif-20009220Abstract The problem of time-variation dynamic systems may be induced to solve a group of differential equations with time-variation coefficients. The state space approach combined with the legendre polynomials and its operational integration matrix is employed for the analysis of time-variation dynamic systems in this paperf and the generalized formulation of the solution is also given. So the basisof efficient method to solve the time-variation mechanical problems is establishede and is beneficial tofurther research of time-variation scienceKey words time-variation dynamicsf-Legendre polynomials state space equationE - operationalntegration matrIx12av4 AsEe"E0=∑-pI-tp2i-2j+4p+12i+2+1)S-,“i≥jE"A1E0中国煤化工￡¨A2E0CNMHGE¨A1EEE001E8cE00A7y0EAg±E"i≥0片方数围2+27+1k=(2-1+2121p=0E13分EAk≠i-j+2p2p=0E2E-2