FEATool Multiphysics
v1.17.1
Finite Element Analysis Toolbox
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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
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