I suggest to increase the sampling time and try to see if the FFT changes. A too coarse sampling produces wrong peaks.

@Florian:

• I have a single DOF system, such that the weight of the cantilever beam can be neglected in comparison to the lumped mass at the end. The cantilever is tied to shake table with four bolts, so it can be assumed to be fixed. The environmental excitation, if any, should be small, although I cannot guarantee it either way. 
• The only excitation to the structure is due to base movement, no forces other than gravity are applied on the structure, Therefore, it wont be possible to measure force excitation. (Is this force that you were talking about ?)
• To ensure that we capture steady state response of the system, we start measuring the accelerometer readings after a few seconds, so that the transient motion is skipped. 

Image of setup attached.

@Pier: U mean sampling rate or sampling time ?

Sampling rate is kept quite high, around 12.5 kS/s, that 12.5 thousand samples/sec. So the sampling time would be inverse of this. This is around 500 times, the suggested rate as per the sampling theorem, which states the rate should be twice the maximum frequency, which for our structure should be around 20 Hz, (Our shake table has a maximum frequency of 25 Hz). Are there possibilities of problem due to over-sampling ?

Yes I meant sampling rate. Your rate seems good. At this point I support the idea of Florian, considering external environmental excitation. Try this: attatch to the system a very bulky mass and compute again the FFT.

Are you sure that the input motion has a frequency of 15 Hz?

Could you plot and share the FFT of input motion?

Chintan, by a purely visual examination of the time-plot, it is evident that the dominant frequency is somewhere near 6 Hz. And indeed, you can see a peak on the FFT near 6 Hz, too. So, both plots seem to be consistent. I would:

1) Verify measurement & data processing settings: for example, is the sampling rate correctly set in the software? Notice that if it is three times (pi times?) higher, then the peak would indeed be near 15 Hz.

2) Verify that the actual excitation frequency is indeed near 15 Hz, for example by fixing the accelerometer directly to the shaking table. Perhaps you can use another measurement system and/or accelerometer.

3) Any other dominant external environmental excitations, as suggested by Florian?

Hi

It seems that you have a  small setup mystery to solve.

As stated, if you excite with 15 Hz, you should get your response at 15 Hz if the system is linear, time invariant and so on.

Looking at your spectrum, it seems to contain wide band excitation. The only way I see for a sine excitation to produce wide band excitation is from rattling, i.e. vibration in gaps that open/close and/or other non-linear mechanisms.

The simplest way to find such places is to use your fingers. The fingertip is quite good at picking up relative motion if you squeeze it into the small gaps that always exist between connected parts. (Do not put finger into large gaps such that you damage it).

Another practical way of debugging strange systems is to tap off the acceleration signal and listen to it using in-ear headphones (use in-ear as these go much further down in frequency than does over ear headphones).

As indicated by Prof. Jankowski - debugging methodology - it usually pays off to start simple and complicate step by step. If you cannot find your problem easily, take off your top system and make sure that your shaker truly behaves the way you currently assume it does. Then add the structure bottomplate, add columns and so on.

Also, verify your measurement system. The best thing is an independent shaker but if you are truly desperate - push it to your chest - heartbeat usually is about 1 Hz (60 peats per minute).

Have fun

Claes

Thanks folks for lending your support. I guess I am gonna need some more.  :)

A quick show of the theoretical calculations: 

• Stiffness of the system shown in the above image is : 4 * stiffness of one column = 4 * 12EI/L3 
• Angular Freq, w = sqrt(k/m), m being the mass of my plate, (blue), columns considered massless. 
• Natural Freq = w/2*pi, which comes out to be around 5.2 Hz

Now then, if this is correct, 

@Pier : I have not been able to get results by varying the mass of the system, should be getting it soon. 

@Rafet: Well, I think the in-exactness of the exciting frequency might be the issue here after-all. Our shake table is a PLC driven servo-motor based setup. The attached images show the acc-time plot and its FFT for shake table excitation frequencies of: 5, 10, 15, 20 and 25 Hz.

@Lucasz: About the environmental disturbances - the room is covered by walls on sides, but there might be some wind. 

@Florian: I have a single shake table and accelerometer and both are uni-axial, and I am only interested one axis so far. 

@Claes: I couldnt finger my system (:)) or hear it, but I tried putting the accelerometer to my heart. I am not confident of the results, as there was some wind. Will definitely repeat this in a more controlled setting. 

The mystery seems to be settling around two points now: 

If the excitation is random and not harmonic, then the FFT seems to be peaking at the natural frequency. Can anyone suggest me a reference for the same ?

Hi

Faulty shaker or rather, a shaker with stick/slip could explain your results.

/Claes

The images of shake table test - accelerometer attached to shake table, 

acc-time plot and corresponding FFT ,i.e. acc-freq plot for shake table setting of 5Hz, 10 Hz, 15 Hz, 20 Hz, and 25 Hz. 

Are you sure you are exciting at 15 Hz? I could think that you did you compute your FFT properly, since the range of your FFT doesn't reach 15 Hz... and you might have a scaling problem and the peak you see can actually be at 15 Hz; but that would imply that your acc vs. time graph was also miss scaled (in time), and that would be stange indeed.

Actually, from your acc vs. time graph, I would say you have a beat problem with several frequancies (excitation and natural) involved. But the most obvious frequency is somewhere below 6 Hz indeed, so: I would say there is a very sharp and very lightly damped mode around 6 Hz that dominates the beam behavior; such mode may be excited by a residual component of the excitation force, since the this is never a perfect sine, as you can check computing the FFT of the excitation (but remember to use a range that goes well above 15 Hz).

I hope my 2p can help.

@Ribeiro: I have intentionally scaled the FFT below 15 Hz because the contribution of all further frequencies was very low, almost negligible, nothing peak-like. 

What can be said about this peak near 6Hz, is it the natural frequency ? 

Hi

The time signal should have looked like a sinus wave. Instead it looks like a series of repetitive acceleration spikes. => Take a look at your shaker.

Sincerely

Claes

@Claes: Our shaker is brand new, but it is a low-cost design, and we are testing it (on it) for the first time. And it is a black-box for us right now. The excitation mechanism it currently hidden/embedded under the moving plate. However, if that is absolutely needed, we will yank the plate open, and look inside. 

Given this kind of excitation, is the shaker totally useless, or can some relevant experiments, to understand vibrations and structural dynamics, be performed on this randomly vibrating shaker ?

If the acquisition setup is ok, than 6 Hz is very likely a natural frequency. You can check it by exciting it with a hammer.

About testing the shaker, I would attach a sensor at the shaker head (no structure attached, or only a rigid mass of known value), start it with several types of known signals and see if the result is the expected.

I just saw your plots for the table: if you wanted an harmonic excitation, they are horrible indeed! What should look a sinus wave is a set of alternate impulses! Unless it is an intended setup option, since impulses are a good way to find natural frequencies.

@Ribeiro : I did attach the accelerometer to the shake table and uploaded the image, the  set of 5 images, one is https://www.researchgate.net/file.PostFileLoader.html?id=55a387a75dbbbdb75b8b4570&key=2bd3306c-0dd1-4ccb-bd50-b81fba43d6df 

Besides, I am also unclear on how to test with the hammer. I havent found any references detailing the hammer process. I have an impact hammer with various tips. Now if I impact my structure with the hammer, I have two inputs, the hammer and the accelerometer on the structure. Now, do I perform FFT of both signals, or just the accelerometer ? 

Some reference with details on the matter would be high appreciated. 

Also, you say that "6 Hz is very likely a natural frequency ", Any reference for this claim ?

Hi

I would

/Claes

Just an idea passing by, did you check several excitation amplitudes ?

If the signals are better at lower amplitudes, that may be a clue for non-linear behavior. Did you check the flexibility of the plate between the shaker and the beam ?

@Guillaume: We checked for many amplitudes and many frequencies and the shaker response is similar. 

Also, the plate is quite rigid, around 14mm. 

A picture of the experiment will be favorable to understand where the extra excitation comes. How do you connect the shaking table and the beam?

At a basic level, when running an experiment where you are trying to find the linear natural frequencies, you must control the amplitude of excitation as you perform a frequency sweep.  You must test different excitation levels to ensure that you have a linear response.  Next you should include an accelerometer at the base of the beam.  If you are seeing anything but a sinusoidal response, then there are interactions between the beam and the clamping.  

Hi

Have you made any progress yet?

The time signals you uploaded show that there are mechanical impulses rather than a sine excitation.

I do not know how your table is built but this 'knocking' implies that there are some gaps in the motor-to-shaker-linkage system and/or that the table is loose and 'jumping' on the floor. 

You can find this relative motion by putting two accelerometers across one interface at the time. The acceleration signals should be quite similar when the interface is gap free and be dissimilar where there is a gap. Follow all load paths when examining loose interfaces.

If it is safe, you can actually use your fingers to do so. Press a fingertip into a narrow gap to get the tactile feel, i.e. only press it such that you feel the gap - do not stick your finger into the gap itself.

The tactile feeling is quite good at identifiying relative motion. I use this approach a lot when working in the field.

When in doubt, use accelerometers rather than your finger (but fingers is way faster when it works).

Sincerely

Claes

Hi

I advice you to see these documents. You will find what you need.

Best regards

http://dsp.stackexchange.com/questions/24517/interpreting-the-fft-results-of-a-structural-vibration-problem

http://dsp.stackexchange.com/questions/24756/how-to-interpret-these-fft-results

Hi

I advice you to see these documents.

Best regards

https://www.google.fr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&cad=rja&uact=8&ved=0CDsQFjADahUKEwiY2__GzcTIAhVGhhoKHdu2Ano&url=http%3A%2F%2Fwww.calpoly.edu%2F~cbirdson%2FPublications%2FAN011%2520Basics%2520of%2520Structural%2520Testing%2520%2520Analysis.pdf&usg=AFQjCNFhcxj6fYN_MInH63soyrRi13k-dg&sig2=UpN1sYIY2ijTO15u-3wy4A&bvm=bv.105039540,d.d2s

https://www.google.fr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=8&cad=rja&uact=8&ved=0CFkQFjAHahUKEwiY2__GzcTIAhVGhhoKHdu2Ano&url=http%3A%2F%2Fwww.lifetime-reliability.com%2Ffree-articles%2Fmaintenance-management%2FFundamentals_of_Vibration_Measurement_and_Analysis_Explained.pdf&usg=AFQjCNFxrlKcabLSQca24JSxQZ9ca43WlA&sig2=YgRLxbdc2lCS4cND3rctbg&bvm=bv.105039540,d.d2s