Unexpected frequency response magnitude and resonant frequency

Yuri S.
Yuri S. Altair Community Member
edited April 2021 in Community Q&A

Hi everybody, 

I have set up a simple 1 DOF system to to practice with frequency response loadcases.

My model has a 0,001ton (1kg) mass placed on a spring with stiffness (4\pi^2)*(10^-3)N/mm. Consequently, the natural frequency is 1Hz.
I also set up G (structural damping, found in the PARAM card) as sqrt(3), in order to have a damped resonant frequency of 0,5Hz (w_damped=w_natural * (1-Z^2); where Z stands for damping factor and G corresponds to 2*Z).
Finally, I imposed a sinusoidal load to the mass with magnitude equal to the spring stiffness (in order to have a unitary displacement at zero frequency). 

I have currently two problems with my model:

  1. The displacement magnitude at zero frequency is affected by the structural damping (which shouldn't be) and has a magnitude of 0,5 instead of 1. Putting G (structural damping) to 0 results in a correct amplitude of 1 (see undamped_freq_resp.hm) .
  2. The resonant frequency is not affected by structural damping (whereas it should, according to the following law: w_damped=w_natural * (1-Z^2). In fact, resonant is found at 1Hz for both damped and undamped simulations.

Could anybody help me? Is my mistake theoretical or practical (modelling)?
Three models to be found attached: Damped frequency response, undamped frequency response and static case. To be found also the graph displacement z vs frequency for the damped frequency response and the displacement for the static case.
Thank you all.

Yuri

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Answers

  • Yuri S.
    Yuri S. Altair Community Member
    edited April 2021

    UPDATE:

    For sake of curiosity I run the same model (damped frequency response) reducing the mass of the plate to zero. The analytical expected result was a constant 1 displacement (independently of the damping; see attached limit calculation). Unexpectedly I obtained a constant 0.5 displacement (coherent with the previous frequency response at 0Hz). 

    This result is theoretically independend of the damping (according to the limit calculation), nevertheless it is wrong (at least it doesn't meet my expectations). This fact hints that my mistakes is unrelated to the damping.

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