exd_beam2_tr¶

Purpose:: This example concerns reduced system analysis for the frame structure defined in exd_beam2_m. Transient analysis on modal coordinates is performed for the reduced system.
Description:: In the previous example the transient analysis was based on the original finite element model. Transient analysis can also be employed on some type of reduced system, commonly a subset of the eigenvectors. The commands below pick out the first two eigenvectors for a subsequent time integration, see constant nev. The result in the figure below shall be compared to the result in exd2.
Example Code:

dt=0.002;    T=1;    nev=2;
% --- the load -----------------------------------------------
G=[0 0; 0.15 1; 0.25 0; T 0];       [t,g]=gfunc(G,dt);
f=zeros(15, length(g));             f(4,:)=9000*g;
fr=sparse([[1:1:nev]' Egv(:,1:nev)'*f]);
% --- reduced system matrices --------------------------------
kr=sparse(diag(diag(Egv(:,1:nev)'*K*Egv(:,1:nev))));
mr=sparse(diag(diag(Egv(:,1:nev)'*M*Egv(:,1:nev))));
% --- initial condition --------------------------------------
ar0=zeros(nev,1);                   dar0=zeros(nev,1);
% --- output parameters --------------------------------------
times=[0.1:0.1:1];        dofsr=[1:1:nev];       dofs=[4 11];
% --- time integration parameters ----------------------------
ip=[dt T 0.25 0.5];
% --- time integration ---------------------------------------
[ar,dar,d2ar,arhist,darhist,d2arhist]...
=step2(kr,[],mr,fr,ar0,dar0,[],ip,times,dofsr);
% --- mapping back to original coordinate system -------------
aR=Egv(:,1:nev)*ar;         aRhist=Egv(dofs,1:nev)*arhist;
% --- plot time history for two DOF:s ------------------------
figure(1), plot(t,aRhist(1,:),'-',t,aRhist(2,:),'--')
axis([0    1.0000   -0.0100    0.0200])
grid, xlabel('time (sec)'), ylabel('displacement (m)')
title('Displacement(time) at the 4th and 11th'...
      ' degree-of-freedom')
text(0.3,0.017,'solid line = impact point, x-direction')
text(0.3,0.012,'dashed line = center, horizontal beam,'...
               ' y-direction')
text(0.3,-0.007,'2 EIGENVECTORS ARE USED')