Advanced Mathematics and Mechanics Applications Using MATLAB phần 4 doc

... LLC192 ADVANCED MATH AND MECHANICS APPLICATIONS USING MATLAB 47 : for j=1:nloop 48 : v1g=quadgsqrt(ftest,1,a,b ,40 ,1,u,v); 49 : v2g=quadgsqrt(ftest,2,a,b ,40 ,1,u,v);50: v3g=quadgsqrt(ftest,3,a,b ,40 ,1,u,v);51: ... Press LLC186 ADVANCED MATH AND MECHANICS APPLICATIONS USING MATLAB 42 : % Each face is traversed in a 43 : % counterclockwise sense relative to 44 : % the outward normal. The column 45 : % dimension ... 8.65 9. 74 10.77 128: 13.06 15.07 21.60 25 .49 ; 27.38 129: 31.56 34. 94 36.66 38.03 40 .67 130: 41 .87; 48 .40 51. 04 53.80 0 131: 000]’;132: yft=[ 133: 0 0.92 -0.25 1.00 -0.29 1 34: 0 .46 -0.16;...

... Press LLC 41 : ’\n(try 0,360,120)\n’]; 42 : fprintf(str); [t1,t2,nt]=inputv; 43 : 44 :% Call function squarmap to make the plot 45 : hold off; clf; 46 : [w,b]=squarmap(m,r1,r2,nr,t1,t2,nt+1); 47 : 48 :% ... Hall/CRC 42 : if isempty(w0) | w0==0 43 : disp(’ ’), disp(’All Done’), disp(’ ’), return 44 : end 45 : disp(’ ’) 46 : t=input([’Input a vector of time values ’, 47 : ’(Try 0:.1:30) > ? ’]); 48 : 49 :disp(’ ... LLC3.5.3TheStructuralDynamicsEquation3.6ComputingNaturalFrequenciesforaRectangularMembrane3.7ColumnSpace,NullSpace,OrthonormalBases,andSVD3.8ComputationTimetoRunaMATLABProgram4MethodsforInterpolationandNumericalDifferentiation 4. 1ConceptsofInterpolation 4. 2Interpolation,Differentiation,andIntegrationbyCubicSplines 4. 2.1ComputingtheLengthandAreaBoundedbyaCurve 4. 2.2Example:LengthandEnclosedAreaforaSplineCurve 4. 2.3GeneralizingtheIntrinsicSplineFunctioninMATLAB 4. 2.4Example:ASplineCurvewithSeveralPartsandCorners 4. 3NumericalDifferentiationUsingFiniteDifferences 4. 3.1Example:ProgramtoDeriveDifferenceFormulas5GaussIntegrationwithGeometricPropertyApplications5.1FundamentalConceptsandIntrinsicIntegrationToolsinMATLAB5.2ConceptsofGaussIntegration5.3ComparingResultsfromGaussIntegrationandFunctionQUADL5.4GeometricalPropertiesofAreasandVolumes5 .4. 1AreaPropertyProgram5 .4. 2ProgramAnalyzingVolumesofRevolution5.5...

... x=varargin{k}; y=varargin{k+1}; 143 : z=varargin{k+2}; 144 : surf(x,y,z); axis(r), hold on 145 : end 146 : 147 :% Set axes and display the combined plot 148 : axis equal, axis(r), grid on 149 : xlabel(’x axis’), ... 2003 by CRC Press LLC 42 : c(k,m(1))=1; k=k+1; c(k,m(2))=1; 43 : end 44 : for j=1:ny 45 : m=sub2ind(s,[1,nx],[j,j]); k=k+1; 46 : c(k,m(1))=1; k=k+1; c(k,m(2))=1; 47 : end 48 : 49 :% Form frequency equations ... Press LLC 41 : % print -deps srfex 42 : 43 :%============================================= 44 : 45 :function [X,Y,Z]=frus(rb,rt,h,n,noplot) 46 : % 47 : % [X,Y,Z]=frus(rb,rt,h,n,noplot) 48 : % ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 49 :...

... azz’) 40 : disp(aprop (4: 6)) 41 : 42 :% Run a second case to generate a dense set of 43 : % surface coordinates to check results using 44 : % function srfv. 45 : 46 :N1=61; T1=-pi:pi/N1:0; N2 =41 ; T2=0:pi/N2:pi; 47 : ... reactions and the last two are 140 : % values of y’(x(1)) and y’’(x(1)). 141 : 142 :if nargin<3, endv=1; end 143 : x=x(:); y=y(:); n=length(x); u=x(2:n)-x(1); 144 : a=zeros(n+2,n+2); a(1,1:n)=1; 145 : ... square hole. 140 : % 141 : % x,y - data points characterizing the data 142 : % icrnr - index vector defining corner points 143 : % 144 : % User m functions called: none 145 : % 146 : 147 :xshift=3.0;...

... j=1:j4 74: [t4,x4]=mckde4i(m,c,k,t0,dsp,vel,tfin,h4,i4);75: end76: tcp4=toc/j4; tr4=tcp4/tcpmr;77:78:I4=1; H4=h/I4; tic;79: for j=1:J480: [T4,X4]=mckde4i(m,c,k,t0,dsp,vel,tfin,H4,I4);81: ... num2str(tr4)];339: lg2=[’h= ’, num2str(H4), 340 : ’, relative cputime= ’, num2str(Tr4)]; 341 : legend(lg1,lg2,2); figure(gcf); 342 : % print -deps deislne4 343 : disp(’ ’), disp(’All Done’) 344 : 345 :%============================================= 346 : 347 :% ... 275 41 : options=odeset(’RelTol’,tol); 42 : [t3,z3]= 43 : ode45(@pinvert,[0,tmax],[0;w*th0], 44 : options,alp,bet,gam,th0,w); 45 : n3=ncal; ncal=0; 46 : 47 :% tight spring with stringent tolerance 48 :...

... 68.2 142 275: 24. 4 949 43 .7155 38.1598 57.6538 76.9699 69.7230276: 25.7051 44 .9577 39.6032 59. 040 9 78.3305 71.2205277: 26.90 74 21.2117 41 .0308 60 .41 94 52.6 241 72.7065278: 28.10 24 22.7601 42 .44 39 ... 84. 27 14 286: 14. 7960 34. 1 543 53. 348 3 46 .2980 66. 147 6 85.6825287: 16.22 34 35 .49 99 54. 6719 47 .8178 67.5905 87.0870288: 17.6159 36.8336 55.9885 49 .32 04 69.0 240 88 .48 46289: 18.9801 38.1563 57.29 84 50.8072 ... 42 .44 39 61.7893 54. 1856 74. 1827279: 29.2909 24. 2702 43 . 843 9 63.15 24 55.7297 75. 649 3280: 30 .47 33 25. 748 2 45 .2315 64. 50 84 57.2577 77.1067281: 31.6501 27.1990 46 .6081 65.85 64 58.7709 78.5555282:...

... ’; f=-1; end 240 : u=a/2*modes(:,:,j); 241 : 242 :for kk=1:nf 243 : surf(x,y,ft(kk)*u) 244 : axis equal, axis(range) 245 : xlabel(’x axis’), ylabel(’y axis’) 246 : zlabel(’u(x,y)’) 247 : title([type,’ ... beam’];59: Printout=12; NoSegs= 144 *4+ 1; BeamLength= 144 ;© 2003 by CRC Press LLC−1−0.500.51−0.500.5−1−0.8−0.6−0 .4 −0.200.20 .4 0.60.81x axisODD MODE 98, OMEGA = 43 .85, B/A = 0.5y axisu(x,y)Figure ... 4. 7506e-001Table of Results:© 2003 by CRC Press LLC 240 : subplot(2,2,2); 241 : plot(x,M,’k-’); grid; xlabel(’x axis’); 242 : ylabel(’Moment’); title(’Moment Diagram’) 243 : subplot(2,2,3); 244 :...

... Press LLC 41 : % in a plate uniformly stressed at infinity. 42 : % 43 : % rx,ry - ellipse semidiameters on the x and 44 : % y axes 45 : % p - values of uniaxial tension at 46 : % infinity 47 : % ang ... zq=spline(t,zb,bp); 142 : zqd=splined(t,zb,bp); nq=length(fq); 143 : fq=fq(:).*zqd(:); 144 : 145 :bdrylen=sum(abs(zq(2:nq)-zq(1:nq-1))); 146 : 147 :closnes=1e100; bigz=max(abs(z)); 148 : for j=1:nq 149 : closnes=min([closnes,abs(zq(j)-z)]);150: ... noise to the data 41 : ydat=ydat+.1*( 5+rand(size(ydat))); 42 : 43 :% Function vibfun defines the quantity to be 44 : % minimized by a search using function fmins. 45 : disp(’ ’); 46 : disp(’The function...

... solutions 541 : 542 :R=[ 543 : 0.7 045 3.2903 0.8263 544 : 3.2932 0.70 74 0.8295 545 : 0.7783 3 .49 77 0.3767 546 : 3 .49 94 0.7800 0.3755 547 : 0.0026 3.0000 2.99 34 548 : 0.0028 1.0000 3.0001 549 : 0.70 34 0.7107 -2.0000550: ... 241 : R0,V,d,’CASE 4 ); hold on 242 : plot3(w(t,1),w(t,2),w(t,3),’linewidth’,2’) 243 : hold off, subplot 244 : % print -deps cylclose 245 : 246 :%=========================================== 247 : 248 :function ... respectively. 40 : % 41 : % User m files called: splincof 42 : % 43 : if nargin<5 | isempty(endc), endc=1; end 44 : if nargin<7, [b,c]=splincof(xd,yd,endc); end 45 : n=length(xd); [N,M]=size(c); 46 : 47 :switch...

... LLC3.5.3TheStructuralDynamicsEquation3.6ComputingNaturalFrequenciesforaRectangularMembrane3.7ColumnSpace,NullSpace,OrthonormalBases,andSVD3.8ComputationTimetoRunaMATLABProgram4MethodsforInterpolationandNumericalDifferentiation 4. 1ConceptsofInterpolation 4. 2Interpolation,Differentiation,andIntegrationbyCubicSplines 4. 2.1ComputingtheLengthandAreaBoundedbyaCurve 4. 2.2Example:LengthandEnclosedAreaforaSplineCurve 4. 2.3GeneralizingtheIntrinsicSplineFunctioninMATLAB 4. 2.4Example:ASplineCurvewithSeveralPartsandCorners 4. 3NumericalDifferentiationUsingFiniteDifferences 4. 3.1Example:ProgramtoDeriveDifferenceFormulas5GaussIntegrationwithGeometricPropertyApplications5.1FundamentalConceptsandIntrinsicIntegrationToolsinMATLAB5.2ConceptsofGaussIntegration5.3ComparingResultsfromGaussIntegrationandFunctionQUADL5.4GeometricalPropertiesofAreasandVolumes5 .4. 1AreaPropertyProgram5 .4. 2ProgramAnalyzingVolumesofRevolution5.5 ... LLC3.5.3TheStructuralDynamicsEquation3.6ComputingNaturalFrequenciesforaRectangularMembrane3.7ColumnSpace,NullSpace,OrthonormalBases,andSVD3.8ComputationTimetoRunaMATLABProgram4MethodsforInterpolationandNumericalDifferentiation 4. 1ConceptsofInterpolation 4. 2Interpolation,Differentiation,andIntegrationbyCubicSplines 4. 2.1ComputingtheLengthandAreaBoundedbyaCurve 4. 2.2Example:LengthandEnclosedAreaforaSplineCurve 4. 2.3GeneralizingtheIntrinsicSplineFunctioninMATLAB 4. 2.4Example:ASplineCurvewithSeveralPartsandCorners 4. 3NumericalDifferentiationUsingFiniteDifferences 4. 3.1Example:ProgramtoDeriveDifferenceFormulas5GaussIntegrationwithGeometricPropertyApplications5.1FundamentalConceptsandIntrinsicIntegrationToolsinMATLAB5.2ConceptsofGaussIntegration5.3ComparingResultsfromGaussIntegrationandFunctionQUADL5.4GeometricalPropertiesofAreasandVolumes5 .4. 1AreaPropertyProgram5 .4. 2ProgramAnalyzingVolumesofRevolution5.5 ... SAVINGS IN $K’) 140 : 141 :% Character label showing data parameters 142 : label=char( 143 : sprintf(’R = %8.3f’,R), 144 : sprintf(’I = %8.3f’,I), 145 : sprintf(’A = %8.3f’,A), 146 : sprintf(’q0...