Hi,

How much is the the increase of frequency and how are the cracks? did you try a time-frequency analysis of the dynamic response time-series ? I would expect two close frequency peaks for the damaged case: the first peak (lower one) when the crack is open and the second peak (higher one) the crack is closed. I'm jut guessing, I'm not sure about

Best,

Alesandro

What is the material you are investigating?

Are you using two different samples? I mean, do yo have  two samples, one with crack another without crack? If so, perhaps the resonant frequency variation owing to sample to sample variation does not allow you to conclude that you have a reduction of material stiffness. As Alessandro pointed out you can expect too a peak splitting of the resonant frequency, showing open/close states of the crack.

cracks of a cantilever beam will decrease its natural frequencies in theory. You found out the natural frequencies increase experimentally when the beam is cracking. they may be due to: (1) when you  made the cracks, the boundaries of the experimental beam are changed; (2) when you tested the cracked beam, the ambient temperature changed a lot. Both these two factors may lead to the above-mentioned phenomenon.

Dear all, 

I would like to clarify some points:

1-Ambient temperature is almost stable.

2-There is one beam consists of steel skeleton covered with fiber glass composite so the sample variation is not existing. 

3-The cracks in the outer shell of the beam (i.e. in the fiber glass cover).

4-The boundary condition is same for the beam before damage and after cracking.

You must check whether the mode of vibration is the same for that without cracks or has been changed by the formation of cracks....

May by the dominant mode after cracking is higher than that of the beam without cracks??? 

Jazak ALLAH Khair Amjad, 

In case of the dominant mode is higher than that of undamaged beam. 

What could be logically the reasons for such phenomenon? 

I suppose the most logical reason is that the formation of cracks may give the beam additional degrees of freedom is certain locations.

How  high is the increasing of frequencies in percent? What about resonance peaks range and height (damping)?

Damping is a way to modify appearing "natural"  frequency. 

As the crack creates an increasing of differential displacements, it should affect internal friction at interface then damping to.

Lower deformation mode could interact with an higher one to form a more viewable deflection amplitude...

Could be investigated...

Don't forget that experimentally you are always testing a 3D structure. As others have written, the mode shape interaction may change with cracks, not only in frequency but also in complexity of the shape, as different 3D deployment of the deformed structure, as well as different behaviour for damping contribution. A feasible approach might be to test your samples in different directions and characterize the mode shape with 3D measurements and complex-valued representation.

Last, if you have a symmetric section for the beam, you have always to consider the coupling of modeshapes at each eigenfrequency, shifted in space by 90*. As you have cracks, you loose this symmetry, and both modes have now two different frequencies, plus non-linear effects and damping.

Hope to have given you some hints,

my best regards,

Alessandro

You will obtain a decrease of the measured frequencies. Theoretically. it is known that the modal parameters of a structure (frequency and mode shapes) are based on physical properties (mass, stiffness and damping). The modal parameters are the solution of the differential equation of motion (that is in order of mass, damping and stiffness of the structure). Therefore, any change on the physical properties will cause changes in the modal properties. The measured change of the vibration characteristics due to variation of the characteristics of the structure is an indicator of damage. When there is damage on the structure, the stiffness is reduced and, in consequence take place a decreasing the natural frequencies of the system observed. The discontinuities generated  between structural elements due to fractures and cracks  or fatigue, promotes changes on the dynamic properties, mainly sitffness.

Hi Ahmed,  I concur with other colleagues.  If you consider a simple model of the cantilever beam, given that w= sqrt (k/m), once k, the stiffness, is decreased the natural frequency should increase.  However, generation of cracks increase the damping in the system due to higher energy dissipation.  Thus, what you might have been measuring has not been the natural frequent but the frequency of a damped system (which is sometimes is referred to as damped frequency).  As you know the relationship between damped frequency and natural frequency is  damped freq= sqrt(1-zeta squared)gnat freq.   As zeta increases (damping) due to cracks, obviously the new damped frequency will increase, that is not the increase in the natural frequency but in the damped frequency.  So, I am afraid you have been measuring the damped frequency instead of natural frequency, which as I said due to cracks (more energy dissipation) that will increase.  Please check your results to make sure what you are measuring. 

cracks of a cantilever beam will surely decrease its natural frequencies  If it has increased  experimentally there is something is wrong in the  crack location and boundary condition. So you are advised to check the position  of crack and and proper boundary condition.

Can cracks of a cantilever beam increases the natural frequencies?. Available from: https://www.researchgate.net/post/Can_cracks_of_a_cantilever_beam_increases_the_natural_frequencies [accessed Jun 4, 2015].

Other source could be the mass loss. If a cracked zone induces material loss, this would act favourable to frequency increase...anyway, as indicated by previous answers, you should inspect carefully the cracked system looking for changes with respect the nominal one

Hi   Ahmad

Presence of  Cracks increase the local flexibility and decrease the stiffness and consequently the natural frequencies should decrease.

Also, you have to make sure that the experimental setup in not changed during the machining of a crack, because the Cantilever  Beams are very sensitive to the clamped end.  This means that, the BOUNDARY CONDITION "Clamped End", should not be altered during the experiments, i.e.

1)  Fix the Intact Beam

2) Measure the Frequencies

3) make the crack without  dismounting the beam

4) measure the frequencies again.

I hope this will  be  useful for you.  

What type of crack you have ???, is it a slot  or fatigue crack ?

my e-mail : [email protected]

I can send you previous works for me about cracks in Beams and Rotors

Best Regards

Mostly not., the natural frequency is relevant to the stiffness and mass of structure. The stiffness of structure obviously will decrease due to the crack. But, the change of mass is hard to say since it may depend on the type of crack. 

There is an appreciable variation between natural frequency of cracked and un-cracked cantilever beams.  Generally, the natural frequencies of a cracked beam decreases  with increase in crack distance and crack depth due to reduction in stiffness. But, the change in natural frequencies is not only a function of crack depth and crack location but also of the mode numbers.

Not only the aspects of crack such as the position of crack, the depth of crack, the orientation of crack and the  number of cracks influence the frequencies, but also the mode shapes and change of mode shapes can influence the natural frequencies as well.

It is also observed that, for small crack  ratio (a/h), the reduction in the stiffness of beam is less as compared to large (a/h) ratio. Due to the high stiffness, the vibrations are damped and natural frequency does not reduce. For the same severity of crack, the frequency reduction is more for location of crack away from the support because of the stiffness of the structure; vibrations get suppressed near the supports.

Dear Ahmed

The result is strange, but some checks should be done:

Are you sure you are comparing the same modes? (sometimes very high severity of the crack may change the order of the modes)

How much is the decrease in frequency? (small differences may often result from small variations of the setup, ambient conditions or material changes)

Is the clamping force the same? (no clamping has infinite stiffness and a lower clamping force may give lower resonant frequencies and vive-versa)

Is the crack just a crack or was it simulated by an indentation? (for the reasons pointed out by the colleagues above)

I hope I could help.

Yes. If your cracks are opened. In the inflection points of the modal shape, for each vibration mode, the frequency will be increased. For example, see attached picture of natural frequencies shift when crack or open damage it moves along the whole length of the beam.

No, only damping factor changes.

Dear Colleagues, 

Thank you very much for your fruitful comments. 

To be clearer , I started a static bending test on the beam in spanwise and edgewise directions.

Some cracks appeared during these tests. 

 Attached is a graph representing the variations of the value of the first natural frequency and the number of fatigue loading cycles.

the natural frequency decreased after 500,000 cycles and then increased after 1000,000 cycles (this what confused me) 

Please tell me your opinions on this graph.

With cracks the response becomes non-linear, depending on the amplitude, the frequency response may thus change if it is the case.

With cracks a simplist illustration of the phenomenon is that your system response now can be decomposed in two linear phases, closed crack (similar to the original beam) and opened crack (lower frequency). As during vibration both states sequentially exist over a cycle the resulting vibration cycle increases and we observe a decrease of the frequency. This is the idealized view.

Then in practice the crack shape will be critical to the defintion of intermediate states between closed or opened. In the presense of multiple cracks the local deformation of  each crack may induce a variation of the global shape thus changing your mode shape and the corresponding frequency.

What can be seen in your last graph is that all this depicted frequency variations occur under the intial beam frequency. I may well be that a new crack modifies the mode shape so that another crack cannot open as much as it could before.

If your cracks induce dissipation (plastic behavior at crack tips, friction dissipation at crack interfaces) the observed frequency should increase and the response amplitude decrease, but I would have expected a smoother frequency transition in this case (surface mating process local heating,...).

Sometimes considering only the linear behavior of the cracks may cause you become confused about the results of the experiments, because there is a phenomena called ''breathing phenomena'' which is due to non-linear behavir of the cracks. Then it seems that linear behavior is insufficient to describe the behavior of cracks.

breathing phenomena corresponds to the fact that the crack alternately

opens and closes during experimental tests and this may laed to both increase or decrease in natural frequencies of the structure depending on the condition of the crack (be closed and located in a compression zone or be open and located in a tensile zone of section ).

In a cantilever beam the Natural frequency is decreases when a transverse crack is considered.   As  crack depth increases natural frequency decreases and as crack position shifted towards fixed end natural frequency decreases.  I also accept the Soheila Habashi "breathing phenomena"  and at the same time the position of crack is away from the fixed end the natural frequency may increase.

Seeing the spectrum from which you extract the fundamental frequency will be helpful.  Overlaying the shifting spectrum over the different cycles may give the insight into the effect of crack: decreasing the frequency through stiffness reduction and altering the frequency through increase in damping.  The presence of sidebands around the fundamental frequency, though small, may give insight into nonlinearities (you need good dynamic range).   Also if you can capture the mode shape (strobe) this can be helpful.  

In the case of breathing cracks, the frequencies always drop. In the case of open cracks, a frequency increase may occur due to the loss of mass in some specific locations on the beam. This phenomenon is best observable in the weak-axis bending mode 2 of a cantilever beam around the distance 0.275L from the fixed end. Here the curvature has an inflection point (so that the stiffness decrease produces no frequency drop) but displacement exists (thus, the mass loss produces a frequency increase). A location with similar behavior is the beam's free end. In the attached file, the magenta line plots the frequency of the healthy beam, orange line the frequency curve for the breathing crack and green line the frequency curve of the open crack. Note that just the frequency of the beam with open crack exceed the frequency of the intact beam. The blue line represents the frequency increase due to loss os mass alone (no stiffness decrease). This about the theory.

In the case of experiments, an apparent frequency increase can be observed if the acquisition time is not properly set, so that the spectral lines are inadequate located. Obviously, different boundary or environmental conditions alter the frequencies as well. 

http://www.lajss.org/index.php/LAJSS/article/view/1795

We have two models of crack (1) open crack and (2) breathing crack. In both cases, we have a natural frequency reduction of the model but in breathing crack model natural frequency reduction is less than the open crack model.

Hi Ahmed, I faced this problem too.did you solve it at that moment?

I am not sure about this, but I think it might depends on the crack pattern.

Hi,

I think there is some error in your reading because it is obvious that the crack causes a decrease in the stiffness of the structure and hence the frequency decreases,

Regards

Crack generally introduces local flexibility and hence it decreases the natural frequency. However, if it is situated exactly at some of the nodes of vibration mode, it may not have any influence on the corresponding mode's frequency. In such situations, a slight deviation with any parameter may lead to somewhat higher frequency for such modes.