% ssbeamdispex.m Last modified 7/31/2008 % Steady-state response of a simply-supported Bernoulli-Euler beam with % sinusoidal motion with amplitude Y0 at the left end (x=0). % Input is the ratio of driving frequency to the first natural freq. % This m-file was written at the University of Wyoming in the Electrical % and Computer Engineering Department and is to be distributed without % cost. clear all set(0,'DefaultAxesFontSize',12); set(0,'DefaultTextFontSize',12); fratio=-1; while fratio<=0|fratio==1 string1=' The ratio of excitation freq. to first natural freq. = '; fratio=input(string1); if fratio==1 disp(' ') disp(' This is the resonant case choose another freq. ratio'); disp(' ') end end xoverL=linspace(0,1,201); betaL=sqrt(fratio)*pi; betax=betaL*xoverL; cL=cos(betaL); sL=sin(betaL); chL=cosh(betaL); shL=sinh(betaL); c1=cos(betax); s1=sin(betax); ch1=cosh(betax); sh1=sinh(betax); A=cL/sL; C=chL/shL; amplitude=0.5*(c1+ch1-A*s1-C*sh1); lim=max(abs(amplitude)); figure(1);clf; axis([0 1 -.2*lim 1.2*lim]); hold on plot(xoverL,abs(amplitude)); hold on plot([0 1],[0 0]); text(.8,1.1*lim,['f/f_1 = ',num2str(fratio)]) xlabel('Dimensionless distance from the Driven End, x/L') ylabel('Dimensionless Amplitude, |y(x)/Y_0|') text(.1,1.1*lim,'Press Enter to Continue') box on pause figure(2);clf; axis([-.3 1.3 -2*lim 2*lim]); hold on box on plot([0 1],[0 0],'o'); hold on xlabel('Distance, x/L') ylabel('Displacement, y(x,t)/Y_0') texthandle2=text(-.1,-1.6*lim,['f/f_1 = ',num2str(fratio)]); ys=amplitude*0; plot(xoverL,ys,'k','LineWidth',[1.5]); hold on ydata=[ys]; texthandle2=text(0,1.5*lim,'Press Enter to Animate one Frame at a Time'); %xlabel('Distance , x/L'); pause t=linspace(0,8*pi,257); sine=sin(t); for k=1:2:65 ys=amplitude*sine(1,k); plot([0 1],[ys(1,1) ys(1,201)],'o'); hold on plot(xoverL, ys,'k','LineWidth',[2.5]); hold on set(texthandle2,'String', 'Press Enter to Animate One Frame at a Time'); pause end set(texthandle2,'String','Press Enter to Continue'); pause figure(3);clf; axis([-.3 1.3 -2*lim 2*lim]); hold on box on P=plot([0 1],[0 0],'o'); xlabel('Distance from Driven End, x/L') ylabel('Displacement, y(x,t)/Y_0') x1=[-.3 1.3];y1=[0 0]; plot(x1,y1) hold on texthandle2=text(-.1,-1.6*lim,['f/f_1 = ',num2str(fratio)]); ys=amplitude*0; L=plot(xoverL,ys,'k','EraseMode','xor','LineWidth',[2.5]); ydata=[ys(1,:)]; texthandl=text(0,1.5*lim,'Press Enter to Animate'); xlabel('Distance from Driven End, x/L') ylabel('Displacement, y(x,t)/Y_0') pause set(texthandl,'String',' '); t=linspace(0,8*pi,257); sine=sin(t); for k=2:257 ys=amplitude*sine(1,k);; set(L,'Ydata',ys); set(P,'Ydata',[ys(1,1) 0]); pause(.05) ydata=[ydata ;ys(1, :)]; end set(texthandl,'String','Press Enter to Continue'); pause figure(4);clf; [X,T]=meshgrid(xoverL(1,1:201),t); mesh(X,T,ydata) axis([0 1 0 30 -1.2*lim 1.2*lim]); text(1,5,-lim,'Dimensionless Time, \omegat','Rotation',-10) text(1,30,-lim,'Dimensionless Distance, x/L','Rotation',32) zlabel('Displacement, y(x,t)/Y_0') text(0,5,1.1*lim,'Press Enter to Continue','Rotation', -10) view(120,30)