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Re: function fe_eig [ Reply ]
By: Balmes on 2016-09-12 06:52
[forum:843]

You simply did not orient your beam properly

 


%   node#  unused      x            y          z
node=[1    0 0 0       0            0          0;
      2    0 0 0       25.4e-03     0          0;
      3    0 0 0       50.8e-03     0          0;
      4    0 0 0       1            1          0];  % ERROR HERE NEED TO DEFINE BENDING PLANE PROPERLY
elt=feutil('addelt','beam1', [...
 %node1   node2    pl     il     refnode
   1       2       1      1          4       0    %longerons
   2       3       1      1          4       0]);
%     matid       matType        E            nu          rho
pl=[   1            1           10.5e+10     3.4e-01     9e+03];
%     secId      SecType        J                     i1              i2                     A
il=[    1               1             3.75e-10     7.27e-15      3.75e-10     4.452e-06 ];   %longerons

model=struct('Node',node,'Elt',elt,'pl',pl,'il',il);
model=fe_case(model,'fixdof','base',1,'fixdof','2D',[.01;.03;.04;.05]);
% Beam orient along z

def=fe_eig(model);def.data

 


function fe_eig [ Reply ]
By: Mallouli on 2016-09-05 14:10
[forum:840]

Hi

I have done a program to find the natural frequencies of a three node cantilever beam with two methods. But, i don't obtain  the same results.

The matrix D is  diagon matrix that display the square of the natural frequencies. Then, i do a comparaison between D and the square of the result of the eingum function.

The program is below :

%for the correct display of pl


format long g;
format compact;

%   node#  unused      x            y          z
node=[1    0 0 0       0            0          0;
            2    0 0 0       25.4e-03     0          0;
           3    0 0 0       50.8e-03     0          0;
           4    0 0 0       1            1          1];
elt=[ 
%declaration of elemnt groupe
    Inf abs('beam1')
 %node1   node2    pl     il     refnode
   1       2       1      1          4       0    %longerons
   2       3       1      1          4       0];
 
%     matid       matType        E            nu          rho
pl=[   1            1           10.5e+10     3.4e-01     9e+03];

%     secId      SecType        J                     i1              i2                     A
il=[    1               1             3.75e-10     7.27e-15      3.75e-10     4.452e-06 ];   %longerons

%opt=[0 1 2];

%Boundary conditions (Active DOF's)----------------------------------------
adof=[2.02 2.06   3.02 3.06];

%call of function
[m,k,mdof]= fe_mk(node,elt,pl,il);
[adof,ind]=fe_c(mdof,adof);
mr=m(ind,ind);
kr=k(ind,ind);
[V,D]=eigs(kr,mr);
[mode,freq]=fe_eig(mr,kr);
freq
beta1_L=1.875;%------beta1*lenghth----------------------------------------
l=50.8e-03;
omega = eignum( l,beta1_L ); %-----call function eignum--------------------
omega1_carre = omega^2

 

 

 

The eingnum function is :

function omega = eignum( l,beta )
b=31.8e-03;
h=0.14e-03;
E=10.5e+10;
I=(b*h^3)/12;
rho=9e+03;
S=b*h;
omega=(beta^2)*sqrt(E*I/(rho*S*l^4));
end