Advanced Mathematics and Mechanics Applications Using MATLAB phần 3 pptx

... 20 03 by CRC Press LLC 131 : 132 :case 2 133 : % Slope given at both ends 134 : [b,c]=unmkpp(spline(xd,[endc(2);yd;endc (3) ])); 135 : 136 :case 3 137 : % Slope at left end given. Compute right end 138 : ... ellipse with 30 : % semi-diameters of 2 and 1. 31 : if nargin==0 32 : m=21; th=linspace(0,2*pi,m); 33 : x=2*cos(th); y=sin(th); x(m)=2; y(m)=0; 34 : end 35 : 36 :% Use complex data coordinates 37 : z=x(:)+i*y(:); ... plot(xd,yd,’ko’,x,y,’k-’)29: 30 :xlabel(’x axis’), ylabel(’y axis’) 31 : title(titl),axis(cubrange([x(:),y(:)],1.2));© 20 03 by CRC Press LLC 32 : axis square; shg 33 : 34 :%========================================= 35 : 36 :function...

... F2*SIN(W*T)’)29: disp( 30 : ’ WITH ANIMATION OF THE RESPONSE’) 31 : disp(’ ’) 32 : 33 :% Example data used when nargin > 0 34 : if nargin > 0 35 : m=1; c= .3; k=1; f1=1; f2=0; w=2; x0=0; v0=2; 36 : tmax=25; ... relat-© 20 03 by CRC Press LLC 3. 5.3TheStructuralDynamicsEquation 3. 6ComputingNaturalFrequenciesforaRectangularMembrane 3. 7ColumnSpace,NullSpace,OrthonormalBases,andSVD 3. 8ComputationTimetoRunaMATLABProgram4MethodsforInterpolationandNumericalDifferentiation4.1ConceptsofInterpolation4.2Interpolation,Differentiation,andIntegrationbyCubicSplines4.2.1ComputingtheLengthandAreaBoundedbyaCurve4.2.2Example:LengthandEnclosedAreaforaSplineCurve4.2.3GeneralizingtheIntrinsicSplineFunctioninMATLAB4.2.4Example:ASplineCurvewithSeveralPartsandCorners4.3NumericalDifferentiationUsingFiniteDifferences4 .3. 1Example:ProgramtoDeriveDifferenceFormulas5GaussIntegrationwithGeometricPropertyApplications5.1FundamentalConceptsandIntrinsicIntegrationToolsinMATLAB5.2ConceptsofGaussIntegration5.3ComparingResultsfromGaussIntegrationandFunctionQUADL5.4GeometricalPropertiesofAreasandVolumes5.4.1AreaPropertyProgram5.4.2ProgramAnalyzingVolumesofRevolution5.5 ... integration tolerances 30 : ops=odeset(’reltol’,1e-5,’abstol’,1e-5); 31 : 32 :% Interactively input angular velocity repeatedly 33 : if nargin==0 34 : 35 :while 1, close, disp(’ ’) 36 : disp(’Select the...

... and location 30 : IntSupX= [1; 2]; IntSupDelta=[0; 0]; 31 : % End (left and right) conditions 32 : EndCondVal= [0; 0; 0; 0]; % magnitude 33 : % 1=shear,2=moment ,3= slope,4=delta 34 : EndCondFunc= [3; ... interior supports 31 2: ns=size(IntSup,1); 31 3: if ns > 0 31 4: ysprt=IntSup(:,1); r=IntSup(:,2); 31 5: snf=sngf(x,r,1); 31 6: else 31 7: ysprt=[]; r=[]; snf=zeros(NoSegs,0); 31 8: end 31 9: 32 0:% Form ... governing y’’(x) 32 1: smat=kk(:,ones(1,ns +3) ).* 32 2: [x,ones(NoSegs,1),snf,me]; 32 3: 32 4:% Integrate twice to get slope and deflection 32 5: % matrices 32 6: smat=trapsum(0,BeamLength,smat); 32 7: ymat=trapsum(0,BeamLength,smat); 32 8: 32 9:%...

... df and nf 30 : rb=df(1); rt=df(2); h=df (3) ; 31 : [xf,yf,zf]=frus(rb,rt,h,nf); zf=zf 35 *h; 32 : 33 :% Plot four figures combined together 34 : hold off; clf; close; 35 : surfmany(x1,y1,z1,x2,y2,z2,x3,y3,z3,xf,yf,zf) 36 : ... equationxa2+yb2+zc2=1© 20 03 by CRC Press LLC 131 : x=varargin{k}; y=varargin{k+1}; 132 : z=varargin{k+2}; 133 : x=x(:); y=y(:); z=z(:); 134 : r(1)=s(r(1),x); r(2)=b(r(2),x); 135 : r (3) =s(r (3) ,y); r(4)=b(r(4),y); 136 : r(5)=s(r(5),z); ... to the equation© 20 03 by CRC Press LLC2.8 .3 Program Output and CodeFunction srfex1: function [x1,y1,x2,y2,x3,y3,xf,yf,zf]= 2: srfex(da,na,df,nf) 3: % [x1,y1,x2,y2,x3,y3,xf,yf,zf]= 4: % srfex(da,na,df,nf)5:...

... 131 : 000]’; 132 : yft=[ 133 : 0 0.92 -0.25 1.00 -0.29 134 : 0.46 -0.16; -0.97 -0.49 -0. 83 135 : 0.95 0.86 -0.76 0.85; -0.55 136 : 0 .36 -0.52 -0 .38 0.02 -0.19 137 : 0.08; -0.26 0.24 0.00 0 138 : ... -b2 38 : % c = [-2,2] 39 : %40: % Then the exact value is 128*pi/5.© 20 03 by CRC Press LLC184 ADVANCED MATH AND MECHANICS APPLICATIONS USING MATLAB −2−1012012 3 400.511.522.5 3 3.54x ... may 30 : % be involved in the call list. For example, 31 : % when the integrand and limits are: 32 : % 33 : % f = x.^2+y^2+z^2 34 : % a2 = sqrt(4-y^2-z^2) 35 : % a1 = -a2 36 : % b2 = sqrt(4-z^2) 37 :...

... Implicit ’, 33 4: ’4th Order Integrator’]); 33 5: xlabel(’time’); 33 6: ylabel(’solution error measure’); 33 7: lg1=[’h= ’, num2str(h4), 33 8: ’, relative cputime= ’, num2str(tr4)]; 33 9: lg2=[’h= ... cputime= ’, num2str(Tr2)]; 32 8: legend(lg1,lg2,2); figure(gcf); 32 9: disp(’Press [Enter] to continue’); pause 33 0: % print -deps deislne2 33 1: 33 2:plot(t4,er4,’-’,T4,Er4,’ ’); 33 3: title([’Solution ... CABLE\n’) 31 : fprintf( 32 : ’\nNote: The calculations take awhile\n’) 33 : 34 :% Set up data for a cable of n_ links, 35 : % initially arranged in a triangular 36 : % deflection configuration. 37 : 38 :%...

... 79.99602 83: 33 .9887 30 . 033 7 49 .33 08 68. 533 9 61.7567 81.4291284: 11.7916 31 .4228 50.6782 43. 1998 63. 231 3 82.8 535 285: 13. 3 237 32 .7958 52.0172 44.75 93 64.6947 84.2714286: 14.7960 34 .15 43 53. 34 83 46.2980 ... 38 .68 43 32.1897 52.0077 71.4 639 63. 6114272: 20.8070 39 .9526 33 .7166 53. 435 2 72.8506 65.15 93 2 73: 22.0470 41.2 135 35 .2187 54.8517 74. 230 2 66.6 933 274: 23. 2758 42.4678 36 .6990 56.2576 75.6 032 68.2142275: ... 65. 839 9 85.2 738 268: 15.7002 34 . 830 0 53. 9559 47.64 93 67.2577 86.66 03 269: 17.0 037 36 .1 237 55.2466 49.1157 68.6681 88.0408270: 18.2876 37 .4081 30 . 634 6 50.5681 70.0699 62.0485271: 19.5546 38 .6843...

... numerical 130 : % integration 131 : % 132 : % F - The value of the Cauchy integral 133 : % corresponding to matrix argument z 134 : % 135 : % User m functions called: gcquad splined 136 : % 137 : 138 :n=length(fb); ... abs(C(2:ntrms+1)).^2); 31 : ster=100*abs(stfaprx-stfexct)/stfexct; 32 : 33 :% Plot circumferential and normal stresses at 34 : % the boundary 35 : th=180/pi*theta; 36 : clf; plot(imag(z),tr/2,’k:’,imag(z),ta/2,’k-’) 37 : ... DATA’); 30 : fprintf(’\nPress [Enter] to list function\n’); 31 : fprintf(’vibfun which is to be minimized\n’); 32 : pause; 33 : 34 :% Generate a set of data to be fitted by a 35 : % chosen equation. 36 :...

... mat=[null(v’),v]; 33 2: if det(mat)<0, mat(:,1)=-mat(:,1); end 33 3: 33 4:%=========================================== 33 5: 33 6:function [xmin,fmin,m,ntype]=nelmed( 33 7: F,x0,dx,epsx,epsf,M,ifpr,varargin) 33 8: ... R=[X(j);Y(j);Z(j)]; 535 : 536 :%================================================= 537 : 538 :function R=rads 539 : % R=rads540: % Radii for the problem solutions541:542:R=[ 5 43: 0.7045 3. 29 03 0.82 63 544: 3. 2 932 0.7074 0.8295545: 0.77 83 3.4977 0 .37 67546: 3. 4994 0.7800 0 .37 55547: ... 0.0026 3. 0000 2.9 934 548: 0.0028 1.0000 3. 0001549: 0.7 034 0.7107 -2.0000550: 1.5 139 1. 532 0 -0. 738 2];551:552:%=================================================© 20 03 by CRC Press LLC612 ADVANCED...

... and UsingSymbolicMath5.6NumericalandSymbolicResultsfortheExample5.7GeometricalPropertiesofaPolyhedron5.8EvaluatingIntegralsHavingSquareRootTypeSingularities5.8.1ProgramListing5.9GaussIntegrationofaMultipleIntegral5.9.1Example:EvaluatingaMultipleIntegral6FourierSeriesandtheFastFourierTransform6.1DeÞnitionsandComputationofFourierCoefÞcients6.1.1TrigonometricInterpolationandtheFastFourierTransform6.2SomeApplications6.2.1UsingtheFFTtoComputeIntegerOrderBesselFunctions6.2.2DynamicResponseofaMassonanOscillatingFoundation6.2.3GeneralProgramtoPlotFourierExpansions7DynamicResponseofLinearSecondOrderSystems7.1SolvingtheStructuralDynamicsEquationsforPeriodicForces7.1.1ApplicationtoOscillationsofaVerticallySuspendedCable7.2DirectIntegrationMethods7.2.1ExampleonCableResponsebyDirectIntegration© 20 03 by Chapman & Hall/CRC 131 : kap=nr12./nr1. ^3; 132 : 133 :% Compute the torsion only when R’’’(t) is given 134 : if nargin= =3, tau=dot(B,R3)./nr12; 135 : else, tau=[]; end 136 : 137 :%============================================== 138 : 139 :function ... integration tolerances 30 : ops=odeset(’reltol’,1e-5,’abstol’,1e-5); 31 : 32 :% Interactively input angular velocity repeatedly 33 : if nargin==0 34 : 35 :while 1, close, disp(’ ’) 36 : disp(’Select the ... [R,T,N,B,kap,tau,arclen]= 30 : aspiral(r0,k,h,t) 31 : % 32 : % [R,T,N,B,kap,tau,arclen]=aspiral(r0,k,h,t) 33 : % ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 34 : % 35 : % This function computes geometrical properties 36 :...