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ME 218 lab 12 - v0 =.000832 choose slope of beam at x =...

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Greg Gangluff ME 218 Lab 12 4/22/2008 1. Mfile ex1 function xprime=ex1(t,x) xprime=sin(t*x); Mfile ex1b - [t,x] = ode45( 'ex1' ,[0 15], 1); plot(t,x); grid
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2. M Files: function yprime=ex2(t,y) yprime=[ cos(y(2))+sin(t); sin(y(1))-cos(t) ]; tspan=[0, 10]; y0=[5.1, 6.7]; [t, y]=ode45( 'ex2' , tspan, y0); plot(t, y);
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3. First graph K=4 b= 2 m=2 2 nd graph k= 6 m= 2 b= 2 3 rd graph k=6 m=4 b=2
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4 th graph k=4 m=4 b=2 4. y’=f(y,v,x)=v V’=g(y,v,x)= [1 + (v)^2]^(3/2)*[Ty/EI + wx(x - L)/2EI] 5. function dz= beamfunc(x,z)
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L=100; w=100; E=10^7; T=500; I=500; v= z(2); y=z(1); yprime= v; vprime= ((1+v^2)^(3/2))*((T*y)/(E*I)+(w*x*(x-L))/(2*E*I)); dz= [yprime; vprime]; 6. 7.My value was .000832
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8.
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Final vO value - 0.000833250289601 Error - 3.177811638294809e-007 Beamdeflect.m clear all ; clf xspan = [0 100]; % solve over this interval (length of the beam) y0 = 0; % beam displacement = 0 at x=0;
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Unformatted text preview: v0 = .000832; % choose slope of beam at x = 0; [x,z] = ode45( 'beamfunc' , xspan, [y0 v0]); y = z(:,1); % the deflection of the beam v0(1) = 0; % first guess for slope of beam at x = 0; v0(2) = .002; v1(1) = 0; v2(2)=.002 error(1) = y(length(x)); % the error obtained from the first guess. max_it = 10; tol = 0.000001; i = 1; while (i<max_it)&(abs(error(i))>tol) i = i+1; [x,z] = ode45( 'beamfunc' , xspan, [0 0 v0(i) v1(i)]); y = z(:,3); b = z(:,4); error(i) = y(length(x)); v0(i+1) = v0(i)-((v0(i)-v0(i-1))*error(i))/(error(i)-error(i-1)); v1(i+1) = v1(i)-((v1(i)-v1(i-1))*error(i))/(error(i)-error(i-1)); % new guess from Secant method end format long , v0 format long , v1 error(i) plot(x,z) title( 'Greg Gangluff' ) xlabel( 'Position' ) ylabel( 'Deflection' )...
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