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Exciting lower modes of an embedded concrete beam

Exciting lower modes of an embedded concrete beam

Exciting lower modes of an embedded concrete beam

(OP)
Dear all,

I have tested a concrete beam that is embedded into layer of gravel (100 mm thick). I have looked only at vertical direction. The accelerometers are positioned on top of the beam and the impact was applied as close as possible to the positioned accelerometers. In total I have used 10 accelerometers along the beam length and I have applied an impact close to every accelerometer. In total I have applied 5 impacts per impact location and later I have averaged the results from all five.

In Figure 1 you can see the the distribution of the accelerometers (blue circles) on top of the beam. The accelerometers are glued with cyano acrylate adhesive directly to the beam surface.
Figure 1: Accelerometers distribution


Also these are the details of the used equipment setup.
Impact hammer: sledge hammer with plastic tip from Piezotronics Model type PCB 086D50, 5,5 kg.
Sampling frequency: 10 kHz
Accelerometers type: IEPE Accelerometers Dytran 3225M24 and Dytran 3333A
Data logger: Campbel Scientific CR9000X

I will show you only part of the data I've got for accelerometer P1 and for impact applied as close as possible to P1. Usually, I have records from all the accelerometers P1 to P10 when the impact is applied at P1.

My interest is to get the first four translational modes up to 500 Hz.

I have attached you the force auto spectrum, with coherence and one drive point FRF plot for impact at point P1 and recording at P1. Also, I've attached the Bode plot and plot of Imaginary and Real parts of FRF.

Figure 2: Force auto spectrum

Figure 3: FRF magnitude, Coherence and Force auto spectrum

Figure 4: Bode plot for drive point FRF at P1

Figure 5: Magnitude, real and imaginary plot for drive point FRF at P1

Figure 6: Imaginary plots of FRFs for point P1 (H11) to P10 (H110) when the impact is applied at P1.


From Figure 6, 3 modes in total are visible. 1st and 2nd bending at around 130 and 350 Hz; and 1st translational rigid body mode at 30Hz respectively. According to the literature for the beam I have tested I should obtain also the second rigid body mode that corresponds to rotation, but in my test I couldn't get it. Do you think is it possible to obtain the second rigid mode as well?

As you can see the FRF curve under 100 Hz is not that clear in Figure 3. I have one peak around 30 Hz and something between 40 and 60 Hz. The second peak that should correspond to the second rigid body mode should be also very close to the first one, but it is not visible from the FRF plot. Do you have any suggestions how could I improve the testing in order to get this second mode? Do you think I can get the second mode at all?

Also, my concern is related to the phase shift at location of resonant frequencies. According to the books it should be from 0 to 180, but I don't have this as you can see on Figure 4. It's also not even close to the perfect phase plots I have seen in the literature. Also, I don't know what the dip between 180 and 210 Hz means in the phase plot. And what about the phase plot up to 100 Hz for the rigid body modes?

The next step in my work is to extract the modal data from the FRFs plots. But until then I would like to be sure that the FRFs I am using are the best ones and most representative for my setup.

Any suggestions on my testing would be of great benefit.
Also if I could get some comments on my plots would be of great help.

Many thanks,

Emina

Emina B.

RE: Exciting lower modes of an embedded concrete beam

Quote:

Do you have any suggestions how could I improve the testing in order to get this second mode? Do you think I can get the second mode at all?

Do you have enough info/geotechnical info to do a FEA model and see if it is? (Or approximately what it should be.)

RE: Exciting lower modes of an embedded concrete beam

That's fun. Nice plot. You're gonna need a bigger hammer, or a softer tip, and a much better frequency resolution. You should be able to hand calc an approximate frequency for the pitching RBM as you now know the foundation stiffness.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

RE: Exciting lower modes of an embedded concrete beam

Hi Emina,

The second rigid body mode might be around 50Hz. Try performing multiple driving points to check reciprocity. You could then use a MDOF curve fitting to extract the modes. Hopefully the 2nd rigid body mode appears clearer there.

The dip in the phase plot between 180 & 210 Hz is curious as it appears to be smooth in the real and imaginary plots in Fig 5. It may be worth troubleshooting by exporting the real and imaginary parts to manually compute the phase.

I'm speculating your test has large complex modal damping values that makes it look different compared to book examples.


Best of luck,
Jason

RE: Exciting lower modes of an embedded concrete beam

Leave your accel at P1. If you bang P1 you should excite the pitch mode. If you bang P10 you should alsos excite the pitch mode. If you bang p5.5 you should not excite the pitch mode.

I'm not wild about MDOF fitting in this case, I suspect that gravel is not an ideal elastic foundation.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

RE: Exciting lower modes of an embedded concrete beam

Hi Greg,

I'm curious, why do you think MDOF is not appropriate in this case? SDOF fitting works good for well spaced modes with low damping. In this case, I suspect at the translation rigid body mode frequency, the residual of the pitch mode would contribute to errors if SDOF fitting was used.


Best regards,
Jason

RE: Exciting lower modes of an embedded concrete beam

Quote:

Also, my concern is related to the phase shift at location of resonant frequencies. According to the books it should be from 0 to 180, but I don't have this as you can see on Figure 4. It's also not even close to the perfect phase plots I have seen in the literature.

I believe that 180 degree phase shift only occurs with zero damping.

RE: Exciting lower modes of an embedded concrete beam

It'd be interesting to see the Argand plot (Im vs Re). I don't like the look of that phase plot, the bit around 180 Hz is very odd and does not agree with the Re and Im plots, as Im~0 and Re is large but negative so the phase should be 180.

In heavily damped structures you don't get nice clean phase plots, but that particular bit looks like a signal processing error, not a real response.

You've also got something ugly at 270 Hz.

What windowing are you using?

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

RE: Exciting lower modes of an embedded concrete beam

Having multiple driving points and reciprocity would give an idea of how nonlinear the gravel suspension is. The coherence from 5 averages hints the system is somewhat linear.


Best regards,
Jason

RE: Exciting lower modes of an embedded concrete beam

But if there is nonlinearities, the coherence will be close to unity only if the 5 different inputs are very consistent. Otherwise if the input varies for a nonlinear nonlinear system, the output vs input will also vary thus causing the coherence to drop from unity. Personally, my hammer swings are not consistent so it's a "hint" to indicate nonlinearities. Reciprocity check would be the best way to verify.


Best regards,
Jason

RE: Exciting lower modes of an embedded concrete beam

No, a nonlinear system can give perfect coherence so long as it is phase-stable. This does mean controlling for excitation level. Although in this case the non linearities are dispersed throughout the system, real systems with concentrated non linearities, such as cars with shock absorbers or engines, do not work with poorly chosen MIMO methods as reciprocity and partial coherence fails. So you linearise the system by using SIMO and (ultimately) swept sine excitation.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

RE: Exciting lower modes of an embedded concrete beam

I agree it is possible to have a good coherence for nonlinear systems, e.g. repeatable inputs of a shaker but for Emina's particular test case I'm guessing controlling excitation level with a sledgehammer is quite difficult.


Best regards,
Jason

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