机械振动项目（英汉）Mechanical vibration report

IntroductionInourdailylife,vibrationcanbesaidtobeeverywhere,andtheimpactofvibrationonourproductionandlifeisalsogoodandbad.Toimprovetheefficiencyoflargemetallurgicalcoalindustryengineering,vibratoryroller,paverhighwayconstruction,butalsoharmfulvibration:largeequipmentoflargecentrifugalcompressor,nuclearmainpump,aviationturbineengineoncetheconsequencesofunstablevibrationwillbring.Howtomakeuseoftheadvantagesofgoodvibrationandavoidtheharmitbrings,itshouldbeanalyzedfromthemodalanalysisoftheactualstructure.Suchasthevibrationsystem,whichiswidelyusedinthefieldofaerospaceengines,suchasthecombustionchamber,compressor,turbine,etc..Forsuchasystem,inthecourseofoperation,itcanincludevibration,aswellasitsstrengthandstiffnesscanbeartheload,itisrequiredtodesignandcalculate,aheadoftheexperiment.UseMATLABsoftwaretosimulatetheactualvibrationofeachordernaturalfrequencyandnormalmode,itisfoundthatthenaturalfrequencyandthemainformationscanbeobtainedveryeasilyandquickly.在我们的生活中，振动可以说是无处不在，而振动给我们生产和生活带来的影响也是有好有坏。提高对大型冶金煤炭工业工程的效率，振动压路机、摊铺机等公路建设，也有有害的振动：大型离心压缩机、核电站主泵、涡轮航空发动机等大型设备一旦出现不稳定的振动将带来的后果。如何利用好好振动的好处，避免它所带来的危害，就应该先从对实际结构的模态进行分析。如课题所示的振动系统，这是一种在航空发动机领域中广泛应用的盘式轴系统，如燃烧室、压气机、涡轮等。对于这样一个系统，在运行过程中，它可以包括振动，以及它的强度和刚度能否承受负载，它是需要设计和计算，通过实验提前。利用MATLAB软件来模拟实际的振动得到的各阶固有频率和正常模式，可以很方便快捷地得到它的固有频率和主阵型。ContentsChap.1MatrixIterationmethodfornaturalfrequenciesandnormalmodesPart1knowledgeoftheory………………….……..5Part2ProgrammingCgramcode.......................................................................62.Theresultofprogramming....................................................73.Modeshapecurve................................................................8Chap.2TransfermatrixmethodfornaturalfrequenciesandnormalmodesPart1.knowledgeoftheory........................................................9Part2ProgrammingCgramcode.......................................................................102.Theresultofprogramming....................................................113.Modeshapecurve................................................................12Chap3:checktheanswer:(eigenvalueandeigenvetermethod)1.programcode.......................................................................132.Theresultofprogramming...................................................133.conclusions...........................................................................14Chap4:thecomparsionandanalysisoftwomethods……….….……14Conclusion………….…….161固有频率和主阵型矩阵迭代法1.1理论知识................................................................................51.2程序设计计算1.2.1程序代码.............................................................................61.2.2结果.....................................................................................71.2.3振型曲线.............................................................................82固有频率和主阵型的传递矩阵法2.1理论知识………........................................................92.2程序代码2.2.1程序代码.........................................................................….102.2.2结果...................................................................................112.2.3振型曲线...........................................................................123检查答案：（特征值和特征向量法）3.1程序代码..............................................................................133.2结果......................................................................................133.3结论......................................................................................144两种方法的比较和分析...........................................................14结论...........................................................................................16Chap.1MatrixIterationmethodfornaturalfrequenciesandnormalmodes固有频率和主阵型的矩阵迭代法Part1knowledgeoftheory理论知识NaturalFrequency固有频率Initialassumption假设阵型:[D]{A}0[D]=[D]{A}1[D]=a2{A}2i……[D]{A}k-1[D]=If{A}k={A}k-1,ω1=1a1.Iterationequation迭代方程([K]-ω2[M])When{A}={Ai}wehave[K]-1[M]{Ai}=2.[D]=[K]-13.{A}0=C1{A1}+C2{A2}+[D]{Ai}=1ω[D]{A}0=[D](C1{A1}+C2{A2}+⋯=C1ω12{A1}+C2ω22{APart2ProgrammingCalculation程序计算1.Programcode程序代码clcclearn=8;p=7800;Pi=3.14159;d1=0.4;h=0.04;m=p*0.25*Pi*(d1^2)*h;J=0.5*m*0.25*d1^2;a=0.12;d2=0.04;G=7.69e10;k=Pi*G*(d2^4)/(32*a);J=[J0000000;0J000000;00J00000;000J0000;0000J000;00000J00;000000J0;0000000J];K=[k-k000000;-k2*k-k00000;0-k2*k-k0000;00-k2*k-k000;000-k2*k-k00;0000-k1.2*k-0.2*k0;00000-0.2*k1.2*k-k;000000-kk];alf=1;K=K+alf*J;D=inv(K)*J;forj=1:nifj>1D=D*(eye(n)-B*B'*J/(B'*J*B));endA=[10000000]';fori=1:100B=D*A;a1=B(n);B=B/a1;ifmax(abs(B-A))<0.0001omg(j)=1/sqrt(a1);omg(j)=sqrt(abs(omg(j)^2-alf));MM(:,j)=B;breakendA=B;endendomgf=omg/(2*Pi)MMFP=[00000000;MM];plot(FP)holdonzero=[00000000];plot(zero)gridon2.Theresultofprogramming计算结果omg=0.0001135.9690267.1824465.0354640.9083664.6574787.7501876.1578f=0.000021.640242.523474.0127102.0038105.7836125.3744139.4450MM=1.0000-0.58282.1438-4.61571.0012-0.343311.8098-26.49651.0000-0.53031.39870.2444-1.00120.3952-23.872772.53321.0000-0.43010.16734.8472-1.00110.283512.5729-99.52711.0000-0.2912-1.12224.34641.0013-0.438011.0342100.38971.0000-0.1261-2.0217-0.73081.0011-0.2173-23.8439-74.89321.00000.0504-2.2185-5.0387-1.00130.470613.315029.73131.00000.91000.6525-0.0528-0.9999-1.1508-2.0151-2.73751.00001.00001.00001.00001.00001.00001.00001.00003.Modeshapecurve振型曲线Thenaturalfrequencyofvibrationmode振动模态Chap.2Transfermatrixmethodfornaturalfrequenciesandnormalmodes固有频率和主阵型的传递矩阵法Part1.knowledgeoftheory理论知识Separatingtheshaftfromtherotatingdisk,wecanwritingthefollowingequationsandexpresstheminthematrixformSuperscriptsLandRrepresenttheleftandrightsidesofthemembers.从旋转盘分离轴，我们可以用如下方程和矩阵形式表达出来，字母L和R是左、右两侧的部分。Forthedisk:对于圆盘Fortheshaft:对于轴Thematrixpertainingtothediskiscalledthepointmatrixandthematrixassociatedwiththeshaft,thefieldshaft.Thetwocanbecombinedtoestablishthetransfermatrixforthenthelement,whichis:有关圆盘矩阵称为点矩阵和相关矩阵的轴，轴的领域。两者可以联合建立的n个单元的传递矩阵，即：Part2ProgrammingCalculation编程计算1.Programcode程序代码clcclearn=8;p=7800;Pi=3.14159;d1=0.4;h=0.04;m=p*0.25*Pi*(d1^2)*h;J=0.5*m*0.25*d1^2;a=0.12;d2=0.04;G=7.69e10;k=Pi*G*(d2^4)/(32*a);%NaturalfrequenciesJ=[JJJJJJJJ];K=[kkkkkk0.2*kk];step=1;mn=1;T21p=0;fori=1:2000omg(i)=(i-1)*step;T=eye(2);forj=1:nT=[11/K(j);-omg(i)^2*J(j)1-omg(i)^2*J(j)/K(j)]*T;endT21(i)=T(2,1);z(i)=0;ifT(2,1)==0omr(mn)=omg(i);mn=mn+1;endifT(2,1)*T21p<0omr(mn)=omg(i)-abs(T(2,1))*step/(abs(T21p)+abs(T(2,1)));mn=mn+1;endifmn>nbreakendT21p=T(2,1);endomr;f=omr/2/pi%Normalmodesfori=1:nSV(:,1)=[10]';forj=1:nSV(:,j+1)=[11/K(j);-omr(i)^2*J(j)1-omr(i)^2*J(j)/K(j)]*SV(:,j);endMM(:,i)=SV(1,:);endforw=1:nMM(:,w)=MM(:,w)/MM(1,w);endMMplot(MM)zero=[000000000];holdonplot(zero)gridon2.Theresultofprogramming编程结果f=021.640442.523474.0132102.0074105.7820125.3738139.4441MM=1.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.91000.6524-0.0529-1.0000-1.1508-2.0212-2.73741.00000.73810.0781-1.0501-1.0000-0.82651.06413.75601.00000.4997-0.5233-0.94161.00001.27540.9345-3.78821.00000.2164-0.94290.15831.00000.6342-2.01852.82571.0000-0.0864-1.03481.0915-1.0000-1.37101.1268-1.12121.0000-1.56160.30420.0115-0.99963.3463-0.16840.09561.0000-1.71610.4662-0.21660.9997-2.90730.0814-0.01843.Thecurveofmodeshape模态曲线Chap.3checktheanswer:(eigenvalueandeigenvetormethod)结果检查：（特征值和特征向量法）1.Programming程序代码:%clc%clearn=8;p=7800;Pi=3.14159;d1=0.4;h=0.04;m=p*0.25*Pi*(d1^2)*h;J=0.5*m*0.25*d1^2;a=0.12;d2=0.04;G=7.69e10;k=Pi*G*(d2^4)/(32*a);J=[J0000000;0J000000;00J00000;000J0000;0000J000;00000J00;000000J0;0000000J];K=[k-k000000;-k2*k-k00000;0-k2*k-k0000;00-k2*k-k000;000-k2*k-k00;0000-k1.2*k-0.2*k0;00000-0.2*k1.2*k-k;000000-kk];D=inv(J)*K;[Alam]=eig(D);fori=1:nomg(i)=sqrt(abs(lam(i,i)));endomgf=omg/(2*Pi)2.Theresult结果omg=0.0000135.9711267.1842465.0390640.9295664.6586787.7505876.1578f=0.000021.640542.523774.0133102.0072105.7838125.3745139.44503.Conclusion结论Fromtheaboveresults,wecanclearlyseethattheresultsareverysimilartothetheoreticalvaluescalculatedusingmatrixiterationandtransfermatrix.Therefore,wecanthinkthattheapproximatecalculationresultshavecertainreferencevalue.从上述结果过程中，我们可以很清晰地看到，使用矩阵迭代和转移矩阵计算的理论值结果是十分相近的。因此，我们可以认为近似计算结果具有一定的参考价值。Chap.4Thecomparsionandanalysisoftwomethods对这两种方法的比较与分析Accordingtopreviousanalysis,wecanconcludethemodeshapeoftwomethodsasfollows:(normalmodes)根据前面的分析，我们可以得出如下结论：（主阵型）MatrixIteration:矩阵迭代法：1.0000-0.58282.1438-4.61571.0012-0.343311.8098-26.49651.0000-0.53031.39870.2444-1.00120.3952-23.872772.53321.0000-0.43010.16734.8472-1.00110.283512.5729-99.52711.0000-0.2912-1.12224.34641.0013-0.438011.0342100.38971.0000-0.1261-2.0217-0.73081.0011-0.2173-23.8439-74.89321.00000.0504-2.2185-5.0387-1.00130.470613.315029.73131.00000.91000.6525-0.0528-0.9999-1.1508-2.0151-2.73751.00001.00001.00001.00001.00001.00001.00001.0000Transfermatrix:传递矩阵法：1.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.91000.6524-0.0529-1.0000-1.1508-2.0212-2.73741.00000.73810.0781-1.0501-1.0000-0.82651.06413.75601.00000.4997-0.5233-0.94161.00001.27540.9345-3.78821.00000.2164-0.94290.15831.00000.6342-2.01852.82571.0000-0.0864-1.03481.0915-1.0000-1.37101.1268-1.12121.0000-1.56160.30420.0115-0.99963.3463-0.16840.09561.0000-1.71610.4662-0.21660.9997-2.90730.0814-0.0184Aswecannotcomparethenormalmodesoftwomethodsdirectly,wechangethematrixasfollows:由于我们不能直接比较法的主阵型，我们改变了矩阵如下：1.usingthecirculationforw=1:nMM(:,w)=MM(:,w)/MM(1,w);endMM2.resultsMatrixIteration:1.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.91000.6524-0.0529-1.0000-1.150