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Differences between analytic and Radioss solutions in modal transient dynamic analysis

User: "Altair Forum User"
Altair Employee
Updated by Altair Forum User

Hey,

we have a mass applied to a spring, which is clamped on the other side. At the mass we apply a Cosinus load [ F*COS(OMEGA*t) ]
F = 500 N
OMEGA = 1 1/s
t = 0 - 8 s [DT 0.01]
Now we do a modal transient dynamic analysis and look at the history of displacements with the help of Hyperview.
The screenshot shows the result in HyperView.

Now the problem is, that the analytic results are not the same.
Our sping has a rate (k) of 500 N/m and the apllied mass has a weigth (m) of 10 kg.

So we calculate with the following equations:
omega=sqrt(k/m)

set-up ratio: eta=OMEGA/omega

magnification function: V=sqrt(1/(1-eta^2)^2)

The whole system is undamped.

The equation for the displacement is:

x(t)=(F/k)*V*cos(OMEGA*t)
for the maximum amplitude: cos(OMEGA*t)=1.

Thank you for your effort.
d358b-history_of_displacements.jpg

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