Hi

My answer is based on some speculations and some stories related by other guys that have looked into this kind of issue. 

One guy from a major car parts vendor told me they were looking at trying to detect defects (cracks) in cogwheels using state of the art gear for FRFs, getting damping values and so on. It all boiled down to, well, nothing. 

The defect was clearly audible so they had to put a human in a box, let this person drop, say, 10 cog wheels onto a steel plate and listen. 

I believe, the problem lies in spectral analysis needing a time duration for the FFT and on top of this averaging away non-linearities, i.e. we try our best to fish out what is linear while crack detection very much is all about detecting the opposite.

In this vein, you find an example here. In this case it shows the difference between spectral and order analysis. http://qringtech.com/2010/09/15/rotating-machinery-angle-order-analysis/

Simply put, nonlinearities are good to study in the time domain, though more modern approaches exist such as Higher Order Spectral Analysis (I have not tried them). 

To continue. Many years later, I came across the ITU-R469 weighting filter. You find a general overview of this filter here

https://en.wikipedia.org/wiki/ITU-R_468_noise_weighting

and I strongly encourage you to read this paper from 1968

http://downloads.bbc.co.uk/rd/pubs/reports/1968-08.pdf

The rule of thumb is that you can detect a tone about 16 dB below a general noise level (covering the tone's frequency range). However, as the BBC paper explains, it turns our that human hearing can detect certain types of distortion 55 dB to 60 dB below signal level. For me, this came as a shock. 

The defects that were heard came from joining tapes between radio shows in the old days. It was the case also for the first solid state amplifiers that had zero level crossing distortion and, I am guessing, it is the case also for crack detection (not location). 

So - I believe you are in business if you can detect an audible difference, either from direct listening or from listening to the sensor signal. If so, give the above a read and give the ITU-R468 filter a try - it is a very simple filter. If you are fortunate, you may even to get away with simple level detection, e.g. RMS response per RMS or peak excitation force. 

As food for thought, here is another method that can be used for surface crack detection/location. It relies on so called Lock-In InfraRed detection where impact testing is made (using light, mechannical, etc excitation) and detection uses the heat wave that does not propagate as effectively across a crack as it does in uniform material. One can do interesting things with this technique, e.g. detect corrosion under paint. 

http://www.flir.se/science/display/?id=68013

Hope this helps

Claes

PS - very good that you have a RG project to show and share progress with. 

Dear Mahabir:

I have only worked with elastically deformable materials, however there are some general common features for impact response test that may be applicable to stone blocks. For impact hammer excitation test, the FFT frequency response curve should show peaks that represent the natural damped frequencies, which are very close to the natural frequencies.

For the cracked test object, the crack in general results in a reduction in stiffness and consequently has a softening effect. However, if the crack is appreciable, then there will be a loss of mass as well. The loss of mass tends to counteract the reduction in stiffness, yet in the case of small cracks the reduction of stiffness is dominant.  

You get some higher peaks compared to others, which is common for hammer excitation, due to the relative sensitivity (or observability)  of some modes to hammering location than others. Simply, it is attributed to how the hammering location is closer to the nodes of some modes. Modes with nodes that are located closer to either the driving point or the hammering point will get less exited; and thus will show relatively smaller peaks. You may wish to repeat the test using different sensor and hammer locations to see that the amplitudes of different peaks will change. 

Cracks, in general do not produce additional degrees of freedom and therefore don't produce new peak frequencies. Crack can affect the peak amplitudes. However, one must note that cracks may produce sidebands to some frequencies. Although, I have not worked with stone blocks, you may be getting sidebands as well. 

I hope that my reflections on your your questions would be of any help.

You are tackling an interesting application. 

Yehia

Hi

What Prof. Khulief writes is all true.

A small boat floats on top of the wave while a large boat drives through the wave, i.e. size versus wavelength greatly matters.

However, there are a few things more that goof things up for us. These have been known in the field of acoustics from experiments since the late 1920's and its theory was developed by M Schröder in the 1950's.

There is something called called the acoustic limit, or the Schröder limit.

Here it goes.

The asymptotic solutions to implies the modal count for a room implies that the number of modes, N, grow with frequency, f, as f3 for a volume. At high frequency, i.e. at a frequency where the wavelength is short in comparison with the dimensions of the volume, there will be a high number of modes as counted per Hertz.

The modal density, n, is the average mode-to-mode separation. 

The half power bandwidth, dfj,  of a mode, j, is dfj = eta/fj , where eta is the damping loss factor.

Now, at high frequency, the half power bandwith will grow with frequency while the modal density will shrink.

Schröder showed that when three modes fall inside the half power bandwidth of a single mode, then a FRF will have random phase and one stadard deviation for the FRF amplitude is 5 dB to 6 dB, i.e. with about 90% confidence, the FRF amplitude variation is in the ballpark +/- 10 dB.

Incidentally, this is the criterion also for diffuse field conditions provided eta is moderate.

The kicker is that when passing through resonance, the FRF phase jumps 180 degrees. Add a tiny bit of uncertainty to the resonance frequency and start summing modes and you will readily see what happens. 

The FRF dispersion has been demonstrated through carefully made tests on production sets of nominally identical cars by various people in the 1990's when FRF measurement became easier to do. It had been shown for other product types long before this.

The mode separation, modal bandwidth relation is called Modal Overlap, where MO = n*eta/fj . MO = 3 at the Schröder limits.

Reliable damping estimation uses some sort of modal algorithm for identification. Such algorithms tend to work up to MO