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171Vo1.17.No.120073JournalofHunanInstituteofEngineeringMar.2007:2006-07-06:(1975-),,,:.MATLAB,(,411201):MATLAB,MATALB,MATLAB,.:MATLAB;;:TU311.3:A:1671-119X(2007)01-0091-040,.,,FORTRAN,.,,,.MATLAB.MATLABMatrixLaboratoty,,,MAT2LAB,[1].,MATLAB,MATLAB,,FORTRAN,MAT2LAB,.,MATLAB,,[2],,.MATLAB,.1[3],,.,,.(1),[K]{x}+[M]{x}=0(1),,{x}={}cost(2)(2)(1),cost[K]-2[M]{}=0[K]{}=2[M]{}(3)(1)(3)2{},.=2,{}.(3)([K]-[M]){}=0(4),{},,|[K]|-[M]|=0(5)K11-M11K12-M12K1n-M1nK21-M21K22-M22K2n-M2nKn1-Mn1Kn2-Mn2Knn-Mnn=0[K][M]n,n,n,ni,i=1,2,,n,ni=i,(i=1,2,n).i,(4){i},n.,n,i(i=1,2,,n),,,,MATLAB.2MATLABMATLAB:11,m1=180t,m2=270t,m3=360t;k1=98MN/m,k2=196MN/m,k3=294MN/m,.1matlab,:%()clear;%,123k0(1)=98000000;k0(2)=196000000;k0(3)=294000000;m0(1)=180000;m0(2)=270000;m0(3)=360000;n=3;%fori=1:n;ka(i,1)=k0(i);%;m(i,i)=m0(i);%;end%k(n,n)=ka(n);fori=1:n-1;k(i,i)=ka(i+1)+ka(i);endfori=1:n-1;k(i,i+1)=-ka(i+1);k(i+1,i)=-ka(i+1);endmn=inv(m)3k;w2=eig(mn);%w=sqrt(w2)%f=w/(233.1415926)%T=1./f%%fori=1:n;L=k-w2(i)3m;L00=L(2:n,2:n);L01=L(2:n,1);X=-inv(L00)3L01;xa(:,i)=X;endx1=ones(1,n);x=[x1,xa:x=1.00001.00001.00000.6485-0.6066-2.54190.3018-0.67902.4396.3,(6).(6)292007,,t,,.[K],[M],[C];-[K],[M],[C]..:(1)t1,t2,,tn,[M]{x}+[C]{x}+[K]{x}=[F](6),,,{X}{x}{x}.(2)t,.t,.,Wilson-.Wilson-:(1)1),.2){x(0)},{x(0)},{x(0)}13)t(=1.4),,a0=6(t)2,a1=3t,a2=21,a3=t2,a4=a0a5=-a2,a6=1-3,a7=t2,a8=t264)[K]=[K]+a0[M]+1[C](2),1)t+tF](t+t)={F(t)}+({F(t+t)}-{F(t)})+[M](a0{X(t)}+a2{x(t)}+2{x(t)})+[C](a1{X(t)}+2{x(t)}+a3{x(t)})2)t+t{X(t+t)}[K]{X(t+t)}=F(t+t)}3)t+t{x(t+t)}=a4({X(t+t)}-{X(t)})+a5{x(t)}+a6{x(t)}{x(t+t)}={x(t)}+a7({(t+t)}+{x(t)}){X(t+t)}={X(t)}+t{x(t)}+a8({x(t+t)}+2{x(t)})4MATLAB2,,03.5s.,.(2)2MATLAB(3):3%(wilson-)theta=1.4;%theta=deltat=0.28;%delta=t/n0.1T(T:391:MATLAB,T=2.8s)%y(0),:v(0)=0,x(0)=0:my+cv+kx=p(t)y:,v:,x:,p(t)=F;x0=[0;0];v0=[0;0];y0=[0;10];a0=6/(theta3deltat)^2;a1=3/(theta3deltat);a2=23a1;a3=theta3deltat/2;a4=a0/theta;a5=-a2/theta;a6=1-3/theta;a7=deltat/2;a8=deltat^2/6;K=k+a03m;%fori=1:14F(1:2,i)=[0;10];Y(1:2,i)=[0;0];V(1:2,i)=[0;0];X(1:2,i)=[0;0];t=(i-1)3deltat;f1=F(1:2,i)+theta3[0;0]+m3(a03x0+a23v0+23y0)+c3(a13x0+23v0+a33y0);%f1=f(t+theta3deltat)x1=inv(K)3f1;%x1=x(t+theta3deltat)y2=a43(x1-x0)+a53v0+a63y0;%y2=y(t+deltat)v2=v0+a73(y2+y0);%v2=v(t+deltat)x2=x0+deltat3v0+a83(y2+23y0);%x2=x(t+deltat)Y(1,i)=y2(1,1);Y(2,i)=y2(2,1);V(1,i)=v2(1,1);V(2,i)=v2(2,1);X(1,i)=x2(1,1);X(2,i)=x2(2,1);F(1,i)=0;F(2,i)=10;y0=y2;x0=x2;v0=v2;endt=0:deltat:3.64;X1=X(1,:)X2=X(2,:)plot(t,X1,’g’,t,X2,’r’);axis([05-1515]);title();xlabel();ylabel();:X1=Columns1through80.00600.05250.19600.48960.95161.54252.16232.6702Columns9through142.92262.81822.33401.5415X2=Columns1through80.36631.33932.63943.92354.87935.30935.17814.6064Columns9through143.81823.06052.52332.28625,MATLAB,,,.MATLAB,,.,.[1].MATLAB[M].:,2004.[2].MATLAB[M].:,2001.[3](),.[M].,.:,1983.[4].VisualC++[M].:,2004.ApplicationofMATLABinStructureDynamicsZHOUHou-zhi,LENGHui-ping(SchoolofCivilEngineering,HunanScienceandTechnologyUniversity,Xiangtan411201,China)Abstract:ThispaperintroducesMATLABapplicationinthestructuredynamicsthroughtwoexamples,Withtherealizationofthenaturalvibrationfrequency,vibrationmodeanddynamicresponsebyMATLAB,MATLABpower2fulfunctionanditsconvenienceinthestructuredynamicscalculationareillustrated.Itcanrelyhelppeoplebefreefromthecomplicatedcalculation.Keywords:MATLAB;free2vibrationcharacteristic;dynamicresponse492007