Dynamics of Machines - Part II - IFS.pdf

%_____________________________________________________
%Graphical Results
figure(2)
title(’Simulation of 2 D.O.F System in Time Domain’)
subplot(2,1,1), plot(t_integ(1:n_integ),
real(y1_approx(1:n_integ)),’r’)
title(’Numerical Solution (delta T = 0.005 s)’)
xlabel(’time [s]’)
ylabel(’y1_{approx}(t) [m]’)
grid
subplot(2,1,2), plot(t_integ(1:n_integ),
real(y2_approx(1:n_integ)),’r’)
xlabel(’time [s]’)
ylabel(’y2_{approx}(t) [m]’)
grid
%_____________________________________________________
%Graphical Results (Comparison Exact vs. Numerical)
figure(3)
subplot(2,1,1), plot(t,real(y1_exact),’b’,
t_integ(1:n_integ),real(y1_approx(1:n_integ)),’r’)
title(’Simulation of 2 D.O.F System in Time Domain -
Exact Solution vs. Numerical Solution
(delta T = 0.005 s)’)
xlabel(’time [s]’)
ylabel(’y1_{approx}(t) [m]’)
grid
subplot(2,1,2), plot(t,real(y2_exact),’b’,
t_integ(1:n_integ),real(y2_approx(1:n_integ)),’r’)
xlabel(’time [s]’)
ylabel(’y2_{approx}(t) [m]’)
grid
1.7.6 Analytical and Numerical Results of the System of Equations of Motion
y1 exact (t) [m]
y2 exact (t) [m]
y1 approx (t) [m]
y2 approx (t) [m]
2
0
−2
−4
x Exact 10−5
4
Solution
−6
0 5 10 15
time [s]
20 25 30
4
2
0
−2
−4
−6
x 10−5
6
−8
0 5 10 15
time [s]
20 25 30
x Numerical 10−5
5
0
Solution (delta T = 0.005 s)
−5
0 5 10 15
time [s]
20 25 30
4
2
0
−2
−4
−6
x 10−5
6
−8
0 5 10 15
time [s]
20 25 30
Figure 25: Analytical and Numerical Solutions – (a) Analytical solution with initial velocity
condition at ˙y1(0) = 1 mm/s, ˙y2(0) = 0 mm/s, y1(0) = 0 mm and y2(0) = 0 mm; (b) Numerical
solution (time step of 0.005 [s]) with the same initial conditions – Transient Analysis.
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