Differences between analytic and Radioss solutions in modal transient dynamic analysis

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.

Altair Forum User

Hi,

can you confirm if the force applied is a dynamic load?

Assuming the mass is in Kgs, the modelled CONM2 is 10Kgs (which is 98.1 N ~100N) which is a static load and a dynamic load factor of 500 will make the dynamic load or force to 100*500= 5*E4.

Altair Forum User

Hi,

the red triangle is a DAREA load with a value of -500N. In the collector Tabled there is the cosine profile of this force.
In the Load Collector TLoad we combine the DAREA Force with the cosine profile to a dynamic load, which excites the mass at the end of the spring.

But the problem is, that we don't get equal solutions with Hyperworks and the manual calculation.

Thanks and regards.

Altair Forum User

Hi,

Sorry for a late response,

could you please let me the location at which you are looking at the results?

is it the excited point?

also, the OMEGA used in equation is it 11/s or 1/s? (1 1/s is what furnished in your previous post)

Altair Forum User

Hi,

no problem.

We are looking at the results at the point, where the mass is applied, because its the only point of the two which can be displaced. Yes, Its the excited point.

The OMEGA is 1/s --> 1 s^(-1)

Thanks and regards

Altair Forum User

Hi,

The omega= sqrt(K/m) holds good for angular frequency, it is not what are you interested, I guess. So it should be the dynamic analysis is natural frequency (rad/time)

to the omega should be (2* pi / T = 2 * Pi * f) where f= 1 / 2*pi ( (sqrt (K/M)).

could you please check the above?

Also, could you give us any reference of the calculation (formula) from which you calculated the displacement?

Altair Forum User

Hi,

your formulas are the same as we used.

We attached a picture of our calculation. We think it is only one part of the analytic solution, because it is only the particular solution. Is it right that we need the homogeneous solution too, to compare the results to the Radioss solution?

Thank you

Altair Forum User

Hi,

the equation seems to be for steady state, can you run the same analysis with frequency response, instead of transient response?

Altair Forum User

FYI

Altair Forum User

Hi again,

our model seems to be correct.We think, that the assumption, that the homogeneous solution was missing in the analytic solution was correct. In the picture above you can see the complete solution.

We will make a frequence response analyse in the next step.

Tanks for your support  

Altair Forum User

Yes, the max displacement is recorded as you specified.

Please go ahead and make a FRA and let us know your findings