Advanced Mathematics and Mechanics Applications Using MATLAB phần 10 pdf

... 0.7034 0. 7107 -2.0000550: 1.5139 1.5320 -0.7382];551:552:%=================================================© 2003 by CRC Press LLC612 ADVANCED MATH AND MECHANICS APPLICATIONS USING MATLAB Routine ... LLC608 ADVANCED MATH AND MECHANICS APPLICATIONS USING MATLAB Routine Chapter Descriptionsplinerr 2 Program showing differential geome-try properties of a space curve.curvprpsp 2 Function using ... right end 105 : % slope. 106 : [b,c]=unmkpp(spline(xd,yd)); 107 : c=[3*c(:,1),2*c(:,2),c(:,3)]; 108 : sright=ppval(mkpp(b,c),xd(end)); 109 : [b,c]=unmkpp(spline(xd,[endc(2);yd;sright])); 110: 111:case...

... Edition Advanced Mathematics and Mechanics Applications Using Howard B. WilsonUniversity of AlabamaLouis H. TurcotteRose-Hulman Institute of TechnologyDavid HalpernUniversity of Alabama MATLAB ®© ... plotted in the 104 : % animation are retained on the screen, 0 105 : % if each image is erased after it is 106 : % drawn 107 : 108 :if nargin<5, trac=0; end; if nargin<4, tim=.05; end; 109 : if nargin<3, ... LLC 10. 6 Accuracy Comparison for Euler Beam Natural Frequencies by FiniteElementandFiniteDifferenceMethods 10. 6.1MathematicalFormulation 10. 6.2DiscussionoftheCode 10. 6.3NumericalResults 10. 7VibrationModesofanEllipticMembrane 10. 7.1AnalyticalFormulation 10. 7.2ComputerFormulation11BendingAnalysisofBeamsofGeneralCrossSection11.1Introduction11.1.1AnalyticalFormulation11.1.2ProgramtoAnalyzeBeamsofGeneralCrossSection11.1.3ProgramOutputandCode12ApplicationsofAnalyticFunctions12.1PropertiesofAnalyticFunctions12.2DeÞnitionofAnalyticity12.3SeriesExpansions12.4IntegralProperties12.4.1CauchyIntegralFormula12.4.2ResidueTheorem12.5PhysicalProblemsLeadingtoAnalyticFunctions12.5.1Steady-StateHeatConduction12.5.2IncompressibleInviscidFluidFlow12.5.3TorsionandFlexureofElasticBeams12.5.4PlaneElastostatics12.5.5ElectricFieldIntensity12.6BranchPointsandMultivaluedBehavior12.7ConformalMappingandHarmonicFunctions12.8MappingontotheExteriorortheInteriorofanEllipse12.8.1ProgramOutputandCode12.9LinearFractionalTransformations12.9.1ProgramOutputandCode12.10Schwarz-ChristoffelMappingontoaSquare12 .10. 1ProgramOutputandCode12.11DeterminingHarmonicFunctionsinaCircularDisk12.11.1NumericalResults12.11.2ProgramOutputandCode12.12InviscidFluidFlowaroundanEllipticCylinder12.12.1ProgramOutputandCode12.13TorsionalStressesinaBeamMappedontoaUnitDisk12.13.1ProgramOutputandCode12.14StressAnalysisbytheKolosov-MuskhelishviliMethod12.14.1ProgramOutputandCode©...

... CRC Press LLC 100 : b=b/sum(b); w=z.*polyval(b(m:-1:1),z.^4); 101 : 102 :%============================================== 103 : 104 :function [a,b]=ratcof(xdata,ydata,ntop,nbot) 105 : % 106 : % [a,b]=ratcof(xdata,ydata,ntop,nbot) 107 : ... arranged 103 : % in order of increasing absolute value 104 : 105 :if nargin==0 % Generate default data using 2 masses 106 : m=eye(2,2); k=[2,-1;-1,1]; c=.3*k; 107 : f1=[0;1]; f2=[0;0]; w=0.6; tlim=[0 ,100 ]; ... % 106 : % [a,b]=ratcof(xdata,ydata,ntop,nbot) 107 : % ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 108 : % 109 : % Determine a and b to approximate ydata as 110: % a rational function of the variable xdata.111:...

... val=ppval(mkpp(b,C),x);99: 100 :end 101 : 102 :%============================================== 103 : 104 :function [b,c]=splincof(xd,yd,endc) 105 : % 106 : % [b,c]=splincof(xd,yd,endc) 107 : % ~~~~~~~~~~~~~~~~~~~~~~~~~~ 108 : ... quadl)/’, 102 : ’(Total time using gcquad)’]) 103 : disp([’equals ’, 104 : num2str(sum(L(:,end))/sum(G(:,end)))]) 105 : disp(’ ’) 106 : 107 :%============================================= 108 :© 2003 ... match at both ends 101 : 102 :if nargin<5 | isempty(endv), endv=1; end 103 : n=length(xd); sx=size(x); x=x(:); X=x-xd(1); 104 : 105 :if nargin<6, c=spcof(xd,yd,endv); end 106 : 107 :C=c(1:n); s1=c(n+1);...

... w=2*pi/per*(0:nsum-1); 100 : y=2*real(exp(i*t(:)*w)*c); 101 : 102 :%============================================= 103 : 104 :function ybase=imptp(t,period) 105 : % 106 : % ybase=imptp(t,period) 107 : % ~~~~~~~~~~~~~~~~~~~~~© ... tmin,tmax,ntimes)151: %152: % [t,ys,ys0,vs0,as]= © 2003 by CRC Press LLC186 ADVANCED MATH AND MECHANICS APPLICATIONS USING MATLAB 42: % Each face is traversed in a43: % counterclockwise sense relative ... ybar=a*(y(n)+y(n1))/a6; 100 : ayy=a*(y(n).^2+y(n).*y(n1)+y(n1).^2)/12; 101 : axy=a*(x(n).*(2*y(n)+y(n1))+x(n1).* 102 : (2*y(n1)+y(n)))/24; 103 : axx=a*(x(n).^2+x(n).*x(n1)+x(n1).^2)/12; 104 : 105 :%============================================= 106 : 107 :function...

... MidpointFigure 8.12: Horizontal Position of the Cable Midpoint0 5 10 15 20 25 10 −16 10 −14 10 −12 10 10 10−8 10 −6 10 −4 10 −2 10 0timeasymmetry errorGrowing Loss of Symmetry in Vertical DeflectionFigure ... 294 ADVANCED MATH AND MECHANICS APPLICATIONS USING MATLAB 0 5 10 15 20 250.20.250.30.350.40.450.5x coordinatetimeHorizontal ... center radius and 99: % its velocity. 100 : % 101 : % t - the time variable 102 : % z - the vector [x; y; z; vx; vy; vz] 103 : % uz - the vector [0;0;1] 104 : % c1 - wt*len^2/jtrans 105 : % c2 - omegax*jaxial/jtrans 106 :...

... idux iduy 104 : 105 :% Nodal point data are defined by: 106 : % x - a vector of x coordinates 107 : % y - a vector of y coordinates 108 : x =10* [.5 2.5 1 2 0 1 2 3 0 1 2 3 1 2]; 109 : y =10* [ 0 0 1 ... functioneilt:ei=eilt(1,2 ,10, 101,1);[p,y,x]=colbuc (10, ei ,100 ,4);The examples presented illustrate the effectiveness of using Þnite difference meth-ods in conjunction with the intrinsic eigenvalue solver in MATLAB ... LLC0 10 20 30 40 50 60 70 80 90 100 −40−35−30−25−20−15 10 −505 10 COMPARING TWO METHODS FOR EIGENVALUES OF Y"(X)+W2*Y(X)=0, Y(0)=Y(1)=0Eigenvalue IndexPercent Error Using 100 ...

... by CRC Press LLC 100 : 101 :function [frqs,Modes,x,y,alpha,cptim]=frqsimpl( 102 : a,b,type,nlsq,nfuns) 103 : % [frqs,Modes,x,y,alpha,cptim]=frqsimpl( 104 : % a,b,type,nlsq,nfuns) 105 : % ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 106 : 107 :% ... ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 106 : 107 :% a,b - ellipse major and minor semi-diameters 108 : % type - numerical values of one or two for modes 109 : % symmetric or anti-symmetric about the x axis 110: % nlsq - ... axisy axisFigure 10. 13: Elliptic Coordinate Grid and g(ξ) − [α −λ cosh(2ξ)]g(ξ)=0, 0 ≤ ξ ≤ Rwhere the eigenvalue parameters α and λ are determined to make f(η) have period2π and make g(ξ)...

... CRC Press LLC 101 : % User m functions called: none 102 : % 103 : 104 :global timdat ydat 105 : a=x(1); b=-abs(x(2)); c=abs(x(3)); d=x(4); 106 : z=a*exp(b*timdat).*cos(c*timdat+d); 107 : z=norm(z-ydat)^2;13.4 ... the hole, normal and tangential 100 : % stress distributions N and T defined as 101 : % piecewise linear functions are applied. 102 : % 103 : % N - a two column matrix with each row 104 : % containing ... normal stress 105 : % and polar angle in degrees used to 106 : % specify N as a piecewise linear 107 : % function of the polar angle. Step 108 : % discontinuities can be included by 109 : % using successive...

... [(r0+k*t)*cos(t);(r0+k*t)*sin(t);h*t]40: %© 2003 by CRC Press LLC0 20 40 60 80 100 120 10 −6 10 −5 10 −4 10 −3 10 −2 10 −1point indexerror measureError PlotBinormal error Curvature errorFigure ... LLC 10. 6 Accuracy Comparison for Euler Beam Natural Frequencies by FiniteElementandFiniteDifferenceMethods 10. 6.1MathematicalFormulation 10. 6.2DiscussionoftheCode 10. 6.3NumericalResults 10. 7VibrationModesofanEllipticMembrane 10. 7.1AnalyticalFormulation 10. 7.2ComputerFormulation11BendingAnalysisofBeamsofGeneralCrossSection11.1Introduction11.1.1AnalyticalFormulation11.1.2ProgramtoAnalyzeBeamsofGeneralCrossSection11.1.3ProgramOutputandCode12ApplicationsofAnalyticFunctions12.1PropertiesofAnalyticFunctions12.2DeÞnitionofAnalyticity12.3SeriesExpansions12.4IntegralProperties12.4.1CauchyIntegralFormula12.4.2ResidueTheorem12.5PhysicalProblemsLeadingtoAnalyticFunctions12.5.1Steady-StateHeatConduction12.5.2IncompressibleInviscidFluidFlow12.5.3TorsionandFlexureofElasticBeams12.5.4PlaneElastostatics12.5.5ElectricFieldIntensity12.6BranchPointsandMultivaluedBehavior12.7ConformalMappingandHarmonicFunctions12.8MappingontotheExteriorortheInteriorofanEllipse12.8.1ProgramOutputandCode12.9LinearFractionalTransformations12.9.1ProgramOutputandCode12.10Schwarz-ChristoffelMappingontoaSquare12 .10. 1ProgramOutputandCode12.11DeterminingHarmonicFunctionsinaCircularDisk12.11.1NumericalResults12.11.2ProgramOutputandCode12.12InviscidFluidFlowaroundanEllipticCylinder12.12.1ProgramOutputandCode12.13TorsionalStressesinaBeamMappedontoaUnitDisk12.13.1ProgramOutputandCode12.14StressAnalysisbytheKolosov-MuskhelishviliMethod12.14.1ProgramOutputandCode© ... 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...