General Mechanical

General Mechanical

problem with wave reflection – transient analysis

    • Augusto13
      Subscriber

      the structure in question is a fixed-free beam. I apply a pulse called Ricker (figure 1) of displacement at the fixed end of a beam. The expected path of the impulse is that a wave reflection occurs, but this does not happen in the  time history (figure 2).


       


      impulse Ricker:



                                                        Figure 1. Impulse


      Time history in the middle of the beam:


       



                                                                           Figure 2. Time history (ANSYS)


       


      I do not understand why the impulse disappears quickly.  I'm using the controlled damping (0,005) of ANSYS, I'm late, I got some help.

    • sk_cheah
      Subscriber

      I'm guessing your beam is extremely stiff with the first natural frequency far exceeding the impulse frequency. 

      Kind regards,
      Jason

    • Augusto13
      Subscriber

      Hello, I think your analysis is correct.


      I changed the excitation frequency to 5 Hz (axial excitation), the natural frequency of the beam is 4.9 Hz (axial direction). So I got this:


       



                                                                                     Figure 1. Time history


       


      but this seems to me unexpected. I would expect behavior similar to Figure 2 (ignore the captions and numbers):


       



                                           Figure 2. expected behavior.

    • sk_cheah
      Subscriber

      Exciting the system very near the natural frequency with low damping will cause the system to ring at that frequency for a long time. Like a bell... 


      You've now tried two cases. Try the last one: very high impulse frequency relative to natural frequencies. 




      Kind regards,
      Jason

    • Augusto13
      Subscriber

      organizing the tests (natural frequency of the beam is 4.9 Hz):


      1st test - excitation frequency of 79.36 Hz


      2nd test - excitation frequency of 5 Hz


      3rd test - excitation frequency of 0.666 Hz


      in test 3 I got this:



       


      when the excitation frequency is far from the natural frequency, the wave quickly dies. But when both frequencies are close, a sinusoidal behavior is observed. Would you have any other alternative? thank you!

    • peteroznewman
      Subscriber

      Augusto,


      I recommend you plot


      relative tip displacement = tip displacement - base displacement


      which might show that test 3 is mostly rigid body motion.


      If I hold a ruler at one end and go up>down>up, the other end will follow and plotting relative tip displacement will show a flat line at zero.


      Regards,
      Peter

    • sk_cheah
      Subscriber

      For 4.9Hz beam, try excitation impulse of 500Hz. Be sure your simulation time step is about 5000Hz. Also, do a hand calculation on when you expect the wave to reflect back to make sure your simulation time is long enough to capture the reflection.


      Kind regards,
      Jason

    • Augusto13
      Subscriber

      with 500 Hz ansys did not provide solution (I think the period was very small). I applied an excitation of 300 Hz (= 3,3e-3 s natural period), the behavior was identical to test 1 (see figure 1).  I always take care that the time step is much smaller (in this case 10x less).


      Figure 1. Time history


                                                                                         Figure 1. Time history (excitation of 300 Hz).


      In my calculations we have:


      1. time for wave to enter beam = 3,3e-3 s;


      2. time to pass in the middle of the beam = 0.028 s;


      3. time to reflect and return to the middle of the beam = 0.079 s;


      item 2 does not occur in the right time, there is something strange. In the time of 3,3e-3s the maximum peak of displacement occurs in every beam, as if the wave was so fast that all the points reach their peak at the same time.


      In item 3 the wave does not appear (stagnation of the graph to zero). 


      the wave velocity is well calibrated. The beam has 16 m and I use a data input that give me a speed of 316 m/s.

    • Augusto13
      Subscriber

      Peter, I think the result of ANSYS is already with relative displacement, when I add the time history in the fixed support, the result is always zero at all times. So I believe that at the tip (or at any point) the displacement is already relative, or I'm wrong ?

    • peteroznewman
      Subscriber

      Augusto, yes, you are correct. I was thinking of another member's model that used a base displacement. Sorry for the mistake.


      Regards,
      Peter

    • sk_cheah
      Subscriber

      Augusto,


      I ran a simple model and plotted midspan displacement showing the reflection is quite close to the initial wave similar to your Fig 2 in your first post:


       


      Animation of the fixed-free beam: https://i.imgur.com/nFEjE4P.mp4


      Attached is v19.0 archived file of the model. 


       


      Kind regards,
      Jason

    • Augusto13
      Subscriber

      thanks for listening  =]


      I use ANSYS 17. I'm going to download from 19 and try to check where I'm going wrong. When I can, I'll post my mistake here.

    • Augusto13
      Subscriber

      I finally got the final model. I only obtained the desired model when modeling without discretizing the thickness of the beam (model 2d). It seems to me that this experiment is only satisfied with this consideration, I still do not know the physical reason for this difference.



      thank Jason and Peter for the answers!

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