% 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);
string1='The ratio of excitation freq. to first natl freq. = ';
fratio=input(string1);
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')
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)