Description

EX_EULER_BEAM3 1D Euler-Bernoulli beam vibration example.

[ FEA, OUT ] = EX_EULER_BEAM3( VARARGIN ) 1D Euler-Bernoulli beam model example for. calculating vibration modes and eigenfrequencies. Accepts the following property/value pairs.

Input       Value/{Default}        Description
-----------------------------------------------------------------------------------
L           scalar {1}             Beam length
E           scalar {1}             Elastic modulus
I           expression {1}         Cross section moment of intertia
rho         expression {1}         Material density
A           expression {1}         Cross section area
nx          scalar {100}           Number of grid cells
iplot       scalar 0/{1}           Plot solution (=1)
                                                                                  .
Output      Value/(Size)           Description
-----------------------------------------------------------------------------------
fea         struct                 Problem definition struct
out         struct                 Output struct

Code listing

 cOptDef = { 'L',        2;
             'E',        3;
             'I',        4;
             'rho',      1;
             'A',        6;
             'nx'        100;
             'iplot',    1;
             'tol',      1e-3;
             'fid',      1 };
 [got,opt] = parseopt( cOptDef, varargin{:} );
 fid       = opt.fid;


% Grid generation.
 fea.sdim = {'x'};
 fea.grid = linegrid( opt.nx, 0, opt.L );


% Problem and equation definitions.
% Problem and equation definitions.
 fea = addphys( fea, @eulerbeam );
 fea.phys.eb.eqn.coef{1,end}  = { opt.rho };
 fea.phys.eb.eqn.coef{2,end}  = { opt.A };
 fea.phys.eb.eqn.coef{3,end}  = { opt.E };
 fea.phys.eb.eqn.coef{4,end}  = { opt.I };
 fea.phys.eb.bdr.coef{1,5}{1} = 1;


% Coefficients and equation/postprocessing expressions.
 fea.expr = { 'L',    opt.L ;
              'E',    opt.E ;
              'I',    opt.I ;
              'rho',  opt.rho ;
              'A',    opt.A };


% Solve for eigenvalues and eigenvectors.
 fea = parsephys( fea );
 fea = parseprob( fea );

 [fea.sol.u,fea.sol.l] = solveeig( fea, 'fid', opt.fid );
 efq = sqrt(fea.sol.l)/(2*pi);


% Postprocessing.
 if( opt.iplot )
   n_modes = 4;
   figure, hold on, grid on
   cols = {'b' 'r' 'y' 'g' 'c' 'm'};
   for i=1:n_modes
     postplot( fea, 'surfexpr', 'v', 'solnum', i, 'color', cols{mod(i-1,6)+1}, ...
               'axequal', 'off', 'grid', 'on', 'linewidth', 3 )
   end
   title( ['Vibration modes 1 - ',num2str(n_modes)] )
   xlabel( 'x' )
   ylabel( 'Displacement' )
 end

% Error checking.
 efq_ref = (pi*[0.59686,1.49418,2.50025,3.49999].').^2* ...
           sqrt(opt.E*opt.I/(opt.rho*opt.A*opt.L^4))/(2*pi);
 err = abs(sort(efq(1:length(efq_ref)))-efq_ref)./efq_ref;


 out.efq  = sort(efq);
 out.err  = err;
 out.pass = all(out.err<opt.tol);
 if ( nargout==0 )
   clear fea out
 end