Advanced Mathematics and Mechanics Applications Using MATLAB phần 7 ppsx

... 43 .71 55 38.1598 57. 6538 76 .9699 69 .72 30 276 : 25 .70 51 44.9 577 39.6032 59.0409 78 .3305 71 .2205 277 : 26.9 074 21.21 17 41.0308 60.4194 52.6241 72 .70 65 278 : 28.1024 22 .76 01 42.4439 61 .78 93 54.1856 74 .18 27 279 : ... 74 .18 27 279 : 29.2909 24. 270 2 43.8439 63.1524 55 .72 97 75.6493280: 30. 473 3 25 .74 82 45.2315 64.5084 57. 2 577 77 .10 67 281: 31.6501 27. 1990 46.6081 65.8564 58 .77 09 78 .5555282: 32.8218 28.6266 47. 974 3 ... 32.18 97 52.0 077 71 .4639 63.6114 272 : 20.8 070 39.9526 33 .71 66 53.4352 72 .8506 65.1593 273 : 22.0 470 41.2135 35.21 87 54.85 17 74.2302 66.6933 274 : 23. 275 8 42.4 678 36.6990 56.2 576 75 .6032 68.2142 275 :...

... [m,k]=cablemk(masses,lngths,gravty) 272 : % 273 : % [m,k]=cablemk(masses,lngths,gravty) 274 : % ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 275 : % Form the mass and stiffness matrices for 276 : % the cable. 277 : % 278 : % masses ... bet=’,b4,’, gam=’, 73 : g4,’, tol=’,e4]; 74 : legend(c1,c2,c3,c4,4); shg 75 : dum=input(’\nPress [Enter] to continue\n’,’s’); 76 : %print -deps pinvert 77 : 78 :% plot a phase diagram for case 1 79 : clf; plot(z1(:,2)/w,z1(:,1));80: ... Zone for Explicit Integrator of Order 6© 2003 by CRC Press LLC284 ADVANCED MATH AND MECHANICS APPLICATIONS USING MATLAB 8 .7 Motion of a ProjectileThe problem of aiming a projectile to strike...

... ’); 73 : if sum(isnan([q0,s,p,q2]))==1, break; end 74 : fprintf([’\nDATA ERROR. ONE AND ONLY ’, 75 : ’ONE VALUE AMONG\n’,’THE PARAMETERS ’, 76 : ’q0,s,p,q2 CAN EQUAL nan \n\n’]) 77 : end 78 : end 79 :80:nt=101; ... points approximating the square 73 : % b - coefficients in the truncated 74 : % series expansion which has the 75 : % form 76 : % 77 : % w(z)=sum({j=1:m},b(j)*z*(4*j-3)) 78 : % 79 : % User m functions called: ... else 67: 68:% Choose time limits for the solution69: tmax=30; n=351; t=linspace(0,tmax,n); 70 : 71 :disp(’ ’) 72 : disp(’Press return to see two examples’), pause 73 : 74 :w0=2.42; W0=num2str(w0); 75 :...

... 1 1]); 72 : shg, disp( 73 : ’Press [Enter] to show a contour plot’), pause 74 : % print -deps membdefl; 75 : contour(x,y,dfl,15,’k’); hold on 76 : plot(xb,yb,’k-’); axis(’equal’), hold off 77 : xlabel(’x ... the series 67: % solution68: % y - function values for the solution69: % 70 : % 71 : 72 :% Create evenly spaced points to impose 73 : % boundary conditions 74 : th1=linspace(0,alp,nf); 75 : th2=linspace(alp,pi,ng+1); ... number’); 72 : ylabel(’frequency and % error’) 73 : legend(’exact frequency’,’approx. frequency’, 74 : ’percent error’,2) 75 : s=[’MEMBRANE FREQUENCIES FOR AX / BY = ’, 76 : num2str(ax/by,5),’ AND ’,num2str(nx*ny),...

... end 73 : tbpwf=etime(clock,t0)/nloop; 74 : 75 :% Perform the Gauss integration using a 76 : % vector integrand. Save results in array G 77 : 78 :ngquad=0; tim=0; t0=clock; 79 : while tim<secs80: v=ftest(bp,6)*wf;81: ... A VOLUME OF REVOLUTIONResults Using Function VOLREVVolume = 59.1 476 Rg = [0.91028 0.91028 0.1 375 5]Inertia Tensor =1.0e+003 *0. 577 3 0.1168 -0.00900.1168 0. 577 3 -0.0090-0.0090 -0.0090 1.1010Area ... bp=cbp(:);69: 70 :% Compute the integral 71 : if isempty(func) 72 : val=[]; 73 : else 74 : f=feval(func,bp,varargin{:}); val=wf’*f(:); 75 : end5.3 Comparing Results from Gauss Integration and Function...

... 124:125:tft=[ 126: 0.00 1.26 2.64 4.01 5.10 1 27: 5 .79 7. 74; 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: ... v3L=quadlsqrt(ftest,3,a,b,tol,[],u,v); 71 : vL=[v1L,v2L,v3L]; tL=toc; 72 : 73 :disp(’ ’) 74 : disp(’Results from function quadlsqrt’) 75 : fprintf(’% 17. 9e % 17. 9e % 17. 9e\n’,vL) 76 : disp([’Computation time = ’,num2str(tL),’ sec.’]) 77 : 78 :pctdiff=100*(vg-vL)./vL; ... functions called: gcquad 73 : % 74 : 75 :if nargin< ;7 76: % function gcquad generates base points 77 : % and weight factors 78 : n=12; [dummy,x,W]=gcquad(’’,-1,1,n,1); 79 : elseif size(w,1)==1 &...

... 0.0000e+000 7. 9 976 e+000| 2 1.0101e-002 7. 5 273 e+000| 3 2.0202e-002 7. 0848e+000| 4 3.0303e-002 6.6688e+000| 5 4.0404e-002 6. 277 6e+000Material deleted for publication| 296 2.9596e+000 6. 277 6e+000| ... publication| 296 2.9596e+000 6. 277 6e+000| 2 97 2.9697e+000 6.6688e+000| 298 2. 979 8e+000 7. 0848e+000| 299 2.9899e+000 7. 5 273 e+000| 300 3.0000e+000 7. 9 976 e+000Solution time was 0.55 secs.Reactions ... allowing concentrated loads and linearly 271 : % varying ramp loads. 272 : % 273 : % NoSegs - number of beam divisions for 274 : % integration 275 : % BeamLength - beam length 276 : % Force - matrix containing...

... four-dimensional search.© 2003 by CRC Press LLC 73 : % 74 : 75 :if nargin==0 76 : noplot=0; 77 : z=linspace(0,1,10)’* 78 : exp(i*linspace(0,2*pi,81)); 79 : end80: [n,m]=size(z); z=z(:); u=1/2*ones(size(z));81: ... = ’, 72 : cs,’ d = ’,ds]; 73 : text(6,-1.1,str1); text(6,-1.25,str2); 74 : xlabel(’time’); ylabel(’y axis’); 75 : title([’Data Approximating ’, 76 : ’y = 1.5*exp( 1*t)*cos(2.5*t+pi/4)’]); 77 : grid ... pmin=num2str(min([pt1(:);pt2(:)])); 70 : pmax=num2str(max([pt1(:);pt2(:)])); 71 : 72 :disp( 73 : [’Minimum Principal Stress = ’,num2str(pmin)]); 74 : disp( 75 : [’Maximum Principal Stress = ’,num2str(pmax)]); 76 : fprintf(’\nPress...

... R=[X(j);Y(j);Z(j)];535:536:%=================================================5 37: 538:function R=rads539: % R=rads540: % Radii for the problem solutions541:542:R=[ 543: 0 .70 45 3.2903 0.8263544: 3.2932 0 .70 74 0.8295545: 0 .77 83 3.4 977 0. 376 7546: 3.4994 0 .78 00 ... rdat(4,2)=0; 173 : 174 :u=2*pi*sin(w1)^2; v=sin(w2)^2; 175 : z=interp1(zdat(:,1),zdat(:,2),v); 176 : rho=interp1(rdat(:,1),rdat(:,2),v); 177 : x=rho*cos(u); y=rho*sin(u); 178 : r=r0(:)+m*[x;y;z]; 179 :180:%===========================================181:182:function ... U=cornrpts([0,Rad,Rad+Len,U],Nu)/U; 273 : V=linspace(0,1,Nv); 274 : [X,Y,Z]=cylpts(U,V,Rad,Len,R0,Vc); 275 : surfmany(x,y,z,X,Y,Z), title(titl) 276 : colormap([1 1 0]), shg 277 : 278 :%=========================================== 279 :280:function...

... 2Elementary Aspects of MATLAB Graphics2.1 Introduction MATLAB s capabilities for plotting curves and surfaces are versatile and easy tounderstand. In fact, the effort required to learn MATLAB would be ... and UsingSymbolicMath5.6NumericalandSymbolicResultsfortheExample5.7GeometricalPropertiesofaPolyhedron5.8EvaluatingIntegralsHavingSquareRootTypeSingularities5.8.1ProgramListing5.9GaussIntegrationofaMultipleIntegral5.9.1Example:EvaluatingaMultipleIntegral6FourierSeriesandtheFastFourierTransform6.1DeÞnitionsandComputationofFourierCoefÞcients6.1.1TrigonometricInterpolationandtheFastFourierTransform6.2SomeApplications6.2.1UsingtheFFTtoComputeIntegerOrderBesselFunctions6.2.2DynamicResponseofaMassonanOscillatingFoundation6.2.3GeneralProgramtoPlotFourierExpansions7DynamicResponseofLinearSecondOrderSystems 7. 1SolvingtheStructuralDynamicsEquationsforPeriodicForces 7. 1.1ApplicationtoOscillationsofaVerticallySuspendedCable 7. 2DirectIntegrationMethods 7. 2.1ExampleonCableResponsebyDirectIntegration© ... and UsingSymbolicMath5.6NumericalandSymbolicResultsfortheExample5.7GeometricalPropertiesofaPolyhedron5.8EvaluatingIntegralsHavingSquareRootTypeSingularities5.8.1ProgramListing5.9GaussIntegrationofaMultipleIntegral5.9.1Example:EvaluatingaMultipleIntegral6FourierSeriesandtheFastFourierTransform6.1DeÞnitionsandComputationofFourierCoefÞcients6.1.1TrigonometricInterpolationandtheFastFourierTransform6.2SomeApplications6.2.1UsingtheFFTtoComputeIntegerOrderBesselFunctions6.2.2DynamicResponseofaMassonanOscillatingFoundation6.2.3GeneralProgramtoPlotFourierExpansions7DynamicResponseofLinearSecondOrderSystems 7. 1SolvingtheStructuralDynamicsEquationsforPeriodicForces 7. 1.1ApplicationtoOscillationsofaVerticallySuspendedCable 7. 2DirectIntegrationMethods 7. 2.1ExampleonCableResponsebyDirectIntegration©...