%
%  Computations of beam bending vibrations 
%  using a general characteristic  equation
%

% specified 5 case: free-free,fixed-free, s-s,  fix-fix, fix-s     
k=10^7;
k_w1     =[ 0  k  k  k  k];   
k_theta1 =[ 0  k  0  k  k];  
k_w2     =[ 0  0  k  k  k];  
k_theta2 =[ 0  0  0  k  0];

% the bounday condition cases
FreeFree   ='(Free-Free beam)';
FixedFree  ='(Fixed-Free beam)';
SSbeam     ='(Simply supported-Simply supported beam)';
FixedFixed ='(Fixed-Fixed beam)';
FixedS     ='(Fixed-Simply supported beam)';


Kinput =[k_w1; k_theta1; k_w2; k_theta2];
 ncase = size(Kinput,2);

for n=1:ncase,
	k_w1 =Kinput(1,n);
	k_theta1 =Kinput(2,n);
	k_w2 =Kinput(3,n);
	k_theta2 =Kinput(4,n);

betaL= zeros(1,0);
min_root  = zeros(1,0);

for x =0:0.01:20,	

[Cbeam] = CmatrixBeamGeneral( k_w1, k_w2, k_theta1, k_theta2, x);	
[lambda] = MinRootSearch(Cbeam);	

betaL =[betaL x];
min_root =[min_root  abs(lambda)];
end;

figure(n);
semilogy(betaL, min_root );
xlabel('(beta*L)');
ylabel('Determinant Magnitude of Caracteristic Equation');
title('Search for Initial Root Locations');

% pick the corresponding boundary condition 
if n==1 
	symbol = FreeFree;
elseif n==2
	symbol= FixedFree;
elseif  n==3
    symbol = SSbeam;
elseif n==4
    symbol= FixedFixed;
 elseif  n==5
	 symbol = FixedS;
end; 
legend([symbol]);

%axis([0 20 10^(-5) 1.0]);
grid on
end;
% end of the entire cases