## 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 (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!