vibration problem



I have difficulity  to model the following vibration problem in LMS Amesim. I have tried a couple pf approaches but not able to exactly model the problem. Can anyone help me with that please?

Attached is the problem and the mathematical solution.

Thank you very much



Re: vibration problem

Siemens Phenom Siemens Phenom
Siemens Phenom

Hi @Hosein


the model itself should be fairly simple, mass with gravity, spring and damper and forced displacement.


Below a sinus is used instead of cosine to avoid starting from non zero displacement and both the mass position and the spring force are initialized in equilibrium.

Using the solution as parameters you can indeed see that the amplitude of the airplane is 0.1 m.



But, there are actually many solution to this problem as it is written.


First, you see in the solution that the stiffness is fixed. If you change it, you can find other answers...

Also, with the same stiffness, if you use a zero damping value for example your amplitude of motion is close to 0.1 but it's not a pure harmonic anymore...



To get the model to give you the answer instead is not that obvious!

You could set Optimization studies with 'good' objectives like the amplitude of the response has to be around 0.1 but I'm not sure how to tell it that it has to be a pure harmonic...