Hi

Perhaps this is a good place to start?

https://www.researchgate.net/post/How_did_scientists_got_to_define_the_damping_ratios

and

https://wiki.csiamerica.com/display/kb/Damping+coefficients

In short, Rayleigh damping is lacking in physical mechnisms. It is introduced fpr mathematical convenience. 

Hope this helps

Claes

Hi Claes Richard Fredö,

Thanks for your reply. I have actually had a look at the post your recommended a long time ago.

In terms of Rayleigh damping lacking physical mechanisms, I wonder if there are other better models because researchers in the literature have extensively used in the dynamic analysis of structures.

However, my confusion is about defining the alpha and beta values which are different for the material level and global level. There are equations which can be used to define the damping coefficients alpha and beta if the natural frequency and damping ratio are known in the global level.

The other confusion is multiplying the stiffness matrix by a structural damping factor  and the Structural Damping will modify the global stiffness matrix by a factor 's' where the stiffness matrix will be Ks=sK. 's' is the structural damping factor.

Hi Mahmoud

You know, it is damping or the dam-d thing. :)

All damping models are rather crude. As stated by G.P. Box - All models are wrong, but some are useful. This quote is taken out of context but, I think it applies also for damping.

To compund the issue - if you concentrate damping, e.g. by applying a single dashpot damper - then, you get complex modes. Real modes exist only for light and evenly distributed damping.

'Honest' damping models would be viscous (to emulate sound radiation) and structural (to emulate internal material friction). However, in many situations, things like support friction, connection to other subsystems etc dominate and these can be hard to control.

The remedy in such cases is to actually design stronger damping mechanisms into the system, rather than relying on what you happen to get (aka the design by luck principle). At least, one must acknowledge that there is a variation and make sure end results are acceptable.

Maybe you already have seen these? If not, here are some ramblings of mine on the subject of damping.

http://qringtech.com/2014/06/22/designed-damping-types-mechanisms-application-limitation/

Rayleigh damping - by all means, use it, only - don't trust it.

Sincerely

Claes

Hi Claes,

I have to say a very insightful reply. I cannot agree any more about the fact that all models are wrong, but some are useful.

In my case, I already know in advance that the inherent damping of my composite structure is not enough to reduce the vibration due to the dynamic loading applied on it. Hence, I have to resort to vibration absorbers to make the vibrations within acceptable limits. 

In summary, all I need is a satisfactory damping model which could be the Rayleigh damping and is supported in Abaqus to reflect the material and structural damping which I believe it does to a certain degree?? In other words, the Rayleigh damping model can model the combined effect of material and structural damping?? Of course, it has it own non-physical meaning as you described and read in many instances.

The main focus for me would be to have a good enough vibration absorber to reduce the vibrations.

Hi Mahmoud

Since I have rattled you, you might like this as well?

http://qringtech.com/learnmore/why-simulate-measure-correlate-automate/

Get a base damping description that is in the right ballpark with what you measure or know from experience. Make some max/min assumptions to derive how much damping you need to add. Simulate damping additions and iterate until you have what you need.

FYI - Abaqus has modal dmping models that are based on the Modal Strain Energy concept. It works well as long as damping is not overly strong. http://www.iitk.ac.in/nicee/wcee/article/0304.pdf

Also, don't forget that you can mix damping models just as nature does mix them.

Have fun - beause, this is fun

Claes

Hi Claes,

Would mixing the Rayleigh damping model and the modal damping model lead to double counting of some of the damping features? In other words, the damping will be overestimated because both models may lead to a solution which is very similar. Thus causing the damping to be large. Unless, each model specifically models certain damping features which the other does not.

Hi Mahmoud

Damping is additive.

/C

Hi Claes,

For the material damping, I could use the Rayleigh damping.

However, I wonder if there are easy ways in Abaqus to implement structural damping?

Thanks

Hi Mahmoud

Yes, I believe that you can. Here are the options for material damping in Abaqus

http://130.149.89.49:2080/v6.9ef/books/usb/default.htm?startat=pt05ch23s01abm50.html

You have also modal damping to play with.

Also - a bonus, I happened to see this one when looking for the Abaqus manual. Perhpas it is of interest to you?

https://theses.lib.vt.edu/theses/available/etd-12282005-135319/unrestricted/Vasudeva.pdf

Have fun

C

Hi Claes,

I had a read in the manual about modal damping. It is used for simulations in the frequency domain. My case is in the time domain.

Hello,

As I understand from this and other questions of damping, you have passed the stage of considering the modal solution interesting. How the loads are applied must be very crucial, and often they are not glued at a mass. Already a two dof system has unexpected solutions of dynamic damping where one mass don't move.

If they were glued, could it not divide as inertia,  some part? Especially if the real damping is large and nonlinear.

The modal solution must be the most reliable, and valid if loads are applied occasionally at short times.

 Hi Lena,

Thanks for your comment.

In my case I have random dynamic loads which are wind loading. Also, the material and geometric non-linearity are very important to consider and influence the results significantly. 

Therefore, I must solve my problem in the time domain and not the frequency domain. For the modal damping, it is only appropriate for linear dynamics as the case with the frequency domain.

Another issue is structural damping can be expressed in terms of a real and imaginary parts and this is only applicable when the velocity and force are 90 degrees out of phase which is only the case with simple harmonic excitation which does not exist in my case.

Your advice and suggestions are welcome.

Thanks. 

As I understood it is a linear problem with time history load, and then Rayleigh damping could be used. I have an Ansys manual, where I can check this, and the answers are also in the above links.

Hello Mahmoud Alhalaby

  Before your question can be answered properly certain issues need to be resolved.  (1) As you mentioned there are two types of damping:  viscous damping and structural damping. The former is frequency dependent while the latter is frequency independent (2) You are not correct in your explanation of structural damping. Structural damping is introduced in a system by replacing the real stiffness K by a complex stiffness defined by K* = K(1 + is)  where i =sqrt(-1) and s is a loss factor. (3) In order to simplify the modal analysis of damped MDOF systems a so called proportional or Rayleigh damping is assumed whereby coefficient of viscous damping = c = αM + βK, that is damping is dependent on both mass M and stiffness K. (4) The alfa (α) and beta ( β)  coefficients in Raleigh or proportional damping are defined at element level. Global definition does not arise. When a structure consists of many elements it is possible to assign different α and  β to different elements . The damping  matrices of the various elements can then be combined to obtain the global damping matrix Cg.  This Cg will contain combinations of the various αi and  βi in a complex fashion.  The resulting damping matrix will be non-proportional. (5) If it is assumed that  α and  β  for all elements are the same then the global damping matrix will also be of the Rayleigh type and   α and  β will also have the same values at the global level.. In that case the damping ratio of the structure  takes the form D = (α + βω2)/(2ω).  Then  α and  β  can be determined by measuring D at two frequencies and solving 2 equations with two unknowns.(6) The viscous damping coefficient "c" equivalent to the structural damping loss factor "s" is derivable from  c = sMωn2/(2ω)  where ωn is a natural frequency of the structure and ω is the forced vibration frequency. By this artifice damping dependent on mass only can be attained (7) Viscous damping coefficient is defined by c = 2DMωn. For a problem in which the system is represented by discrete masses the mass matrix is diagonal so that the damping matrix is also diagonal and the solution is considerably simplified    (8) Finally, in your problem it is best to obtain an approximate solution using Raleigh (proportional  damping) before an attempt is made with non Raleigh damping. 

Hi Amaechi J. Anyaegbunam,

Thanks for your comments. Really useful.

According to section 6.3.1 in the abaqus user manual 2016:"

Defining global structural damping

You can define the global structural damping factor, s, to get

Ks= sglobal *K

Global structural damping can be specified for the entire model (default), for the mechanical degree of freedom field (displacements and rotations) only, or for the acoustic field only. "

That is the reason for me mentioning that abaqus requires a factor 's' for the treatment of structural damping. However, these would only work if you have harmonic loading and is not applicable to my case. I wonder how the structural damping can be modelled in the case of non-harmonic loads?

From the research, I have been doing so far, I realised that the Rayleigh Damping model was mainly created, for the treatment of the material damping. Nevertheless, I am still confused if structural damping can be incorporated into this model?? I have seen a book which defines equivalent viscous damping ratios for structural damping that can be added to the material damping and then used in the Rayleigh damping model.

Please let me know what you think would work best for the problems I mentioned above.

Best Regards,

Mahmoud

Hi Mahmoud

I must object a bit here. "a book which defines equivalent viscous damping ratios for structural damping that can be added to the material damping and then used in the Rayleigh damping model Material and Structural Damping in Abaqus?. "

You are at risk to mix apples with pears or rather, make a full fruit salad.

Damping is additive, i.e. you can throw in a mix of damping models and add these numerical values to your damping matrix. This works well as long as the numerical solution structure does not put obstacles in the way.

You can also translate loss factors, e.g. 2*C/Ccrit = eta and, by extension thereof, translate the effect of one damping model to another. I am guessing, this would be the equivalent.

You can never transfer one damping model into another. Viscous nor structural damping can be transferred to Rayleigh.

It is like saying you can take the input of a third order equation and turn it into a second or first order equation or the other way around. Yes you can, in principle, but in practice only within very narrow limits and never for the general case.

The damping effect can be made equivalent though.

As with any transform it will be energy correct but incorrect at any given place in time, frequency and space. In other words, it will work well when lightly damped and evenly distributed and not perform as good when highly damped and damping is concentrated.

I may be a stickler for words here but, I have learned the hard way that once you express yourself ambigously - you will immediately reason the wrong way.

All the best

Claes

Hi Claes,

Thanks for your comments.

What I actually meant was that there is a specific damping ratio 'eta' coming from (1) material damping and (2) structural damping. If both of these could be added, then there will be an equivalent viscous damping ratio representing both the material and structural damping. This overall damping factor can then be used in the Rayleigh damping model along with the structure's natural frequency to obtain the alpha and beta values which could be used in the global Rayleigh damping model.

This overall damping factor can then be used in the Rayleigh damping model along with the structure's natural frequency to obtain the alpha and beta values which could be used in the global Rayleigh damping model. 

I wonder if the eta value from structural damping can be be transformed to an equivalent loss factor 's' to be used in the case of dynamic simulations with non-harmonic loads.

Best regards,

Mahmoud

Hi Mahmoud

Table 9.1 shows a bunch of translations of loss factors.

https://books.google.se/books?id=3srSBQAAQBAJ&pg=PA154&lpg=PA154&dq=damping+ratio+critical+reverberation+time&source=bl&ots=_oqc8t-2Mk&sig=mk6cwsAsOFSUdwF_dgC1YkdT48A&hl=sv&sa=X&ved=0ahUKEwj_9o_QzszUAhXjBZoKHd9uAuMQ6AEIODAC#v=onepage&q=damping%20ratio%20critical%20reverberation%20time&f=false

The translation works, at the risk of sounding very boring, when light and evenly distributed.

/Claes

   Hello all   

   I hope we are not getting confused.  I think Structural damping, material damping, and hysterestic damping are different  names describing the same phenomenon. That is structural damping and material damping are the same but different from viscous damping.

   Secondly,  Claes Richard Fredö claims that "You can never transfer one damping model into another."  That is not strictly true. Structural damping and Viscous can be made equivalent in a restricted sense. For a SDOF system if you wish a structurally damped and viscously damped to have the same resonant amplitude then loss factor   (s) for the structural damping can be obtained from the damping ratio (D) for viscous damping through  

                         s = 2ωD/ωn      where  ω = actual vibration frequency and ωn = a natural frequency of the system. . 

Hello Mahmoud

The true damping characteristics of typical structural systems are very complex

and difficult to define. However, it is common practice to express the damping of

such real systems in terms of equivalent viscous­ damping ratios that which show similar decay rates under free ­vibration conditions (Dynamics of Structures, Clough and Penzien 2003, page 29).

    In my own opinion, the nature of damping in a  system does not depend on the nature of the load; that is whether it is harmonic or non-harmonic.  Based on Clough and Penzien you can select any damping model you wish and then select its damping parameters such that its energy dissipation under load resembles that of the real structure.

   This is shown to be the case if a sdof system is considered in the time domain. The analysis is not influenced by the variation of frequency. A loss factor dependent on frequency is easily incorporated in a time domain analysis.   

  I hope this is helpful.

Hi Amaechi J. Anyaegbunam and Claes,

My understanding is that material damping depends on the material type and is more of a material property than anything else. In terms of structural damping, it is due to friction and energy dissipated at connections and joints which consequently depends on the structure type. Therefore, they are NOT the same according to the numerous books I have been reading. 

They way how structural damping is dealt with in Abaqus is actually suitable only for harmonic loads by assigning a factor 's' where the modified stiffness K =(1+is)*Koriginal. This is because using this method the force on the structure and velocity of the structure will be 90 degrees out of phase. The structural damping can be expressed as a

The structural damping can be expressed as a fraction of critical damping, but this would be only applicable to simulations in the frequency domain. Hence, it will make it tricky when modelling in time domain where Rayleigh damping is actually used for material damping. This will put us back to square one where a specific damping ratio 'eta' coming from material damping and another one from the structural damping. If both of these could be added, then there will be an equivalent viscous damping ratio representing both the material and structural damping. This overall damping factor can then be used in the Rayleigh damping model along with the structure's natural frequency to obtain the alpha and beta values which could be used in the global Rayleigh damping model.

Regards,

Mahmoud

Hello Mahmoud Alhalaby

    I agree with you partially. Material damping depends on hysteristic energy loss as a material (structural element) deforms during vibration and structural damping arises from energy loss at joints and connection. In an actual structure consisting of many elements how can you  distinguish between the contributions from material and structural damping as the structure vibrates?  That is why effect of both components are lumped together and classified as structural damping.

    As I mentioned in previous posts the nature of loading (harmonic or non-harmonic) does not influence the damping characteristics of a structure. An ideal structure with interconnected equal sized elements will have proportional damping. However, when unequal sized elements are connected the damping will be non-proportional.

Hi Mahmoud & Amaechi J. Anyaegbunam

Mahmoud - I believe you need to expand your reasoning a bit. Damping can be a number of things only some of which we are able to capture with accuracy. Take a look here

http://qringtech.com/2014/06/22/designed-damping-types-mechanisms-application-limitation/

Amaechi J. Anyaegbunam - There are those who discern between damping types looking at the phase in the transfer function. It is not a wide spread technique though. Here is one example.

https://www.researchgate.net/publication/283503709_FRF-BASED_FINITE_ELEMENT_MODEL_UPDATING_METHOD_FOR_NON-VISCOUS_AND_NON-PROPORTIONAL_DAMPED_SYSTEM

Sincerely

Claes

Conference Paper FRF-BASED FINITE ELEMENT MODEL UPDATING METHOD FOR NON-VISCO...

Hi Claes and Amaechi,

If the material and structural damping are very much interlinked, then a single damping ratio can represent the damping effect coming from both.

Hence, it is then possible to use the Rayleigh damping model or Modal damping(fraction of critical damping).

I still do not understand how both Rayleigh and modal damping models could be combined where one represents different phenomena from the other as once suggested by Claes.

Regards,

Mahmoud

Hello  Claes Richard

   You seem to forget that I had earlier posted that:

 The true damping characteristics of typical structural systems are very complex

   and difficult to define. However, it is common practice to                                 express the damping of such real systems in terms of equivalent viscous­ damping ratios that which show similar decay rates under free ­vibration conditions (Dynamics of Structures, Clough and Penzien 2003, page 29)

Hello

Mahmoud

The general ODE governing the forced damped vibration of a MDOF system is

MUtt + cUt + K(1 +is) = F(t) ................. (1)

where c = coefficient of viscous damping

s =loss factor for structural damping,  i = sqrt(-1)

The problem with this ODE is how to assign appropriate values to c and s.

Depending on the type of problem It is common to assume that s = 0 and to assume that all damping is viscous in nature.

MUtt + cUt + K = F(t) ................. (2)

In general M and K are n by n matrices and U is an n vector.

When F(t) is non-harmonic the solution of the matrix ODE of equation (2) is daunting for a general damping matrix c..

A simple solution is possible only if c is taken to be of the Rayleigh type whereby

c = αM + βK

Subsequently, Eq (2) can be transformed into principal modal coordinates whereby all

modes of vibration are uncoupled and such that the solution of equation of motion is readily obtained in each mode. The procedure for doing this is available in textbooks on structural dynamics

It could be shown that the damping ratio for each mode of vibration is given by

               Di = (α + βωi)/(2ωi)

where ωi = sqrt (Kpi/Mpi) = natural frequency of mode i.

This is the relationship between the modal damping ratio and the parameters α and β of the Raleigh damping model. Di varies from mode to mode and is frequency dependent.

Hello Amaechi J. Anyaegbunam,

Thanks for taking the time to mention the procedure above for Rayleigh damping. However, I believe this would only work if it is assumed that the damping of each element is the same and damping is considered at the global level only?

Regards,

Mahmoud Alhalaby

Hello Mahmoud

You are correct but remember I wrote: 

MUtt + cUt + K = F(t) ................. (2)

In general M and K are n by n matrices and U is an n vector.

When F(t) is non-harmonic the solution of the matrix ODE of equation (2) is daunting for a general damping matrix c. 

       Only by assuming Rayleigh damping can a tractable solution be possible. A vibration test can always be used to determine mean values of α and β for a structure for a limited frequency range. 

Hello Amaechi J. Anyaegbunam ·

Why would it daunting if Rayleigh damping is not used?

Hello Mahmoud

Refer to a book on Structural dynamics for full understanding of the problem

Assuming in the simplest case that the mass matrix is diagonal, you will be solving a system of n ODES each of the type

M1(U1)tt + c11(U1)t +c12(U2) t + .................+.c1n(Un)t + K11U1 + K12U2+............+ K1nUn =   F1(t) 

 When F(t) is non-harmonic the solution of this system  of n ODE's is next to impossible. Why not try an example for n = 2.   

Hi,

I know what you mean. I actually read this once in a dynamics textbook.

Thanks for elaborating on that anyway. 

It seems that Rayleigh damping is the most suitable and efficient model to be used in Abaqus despite its deficiency?

Hi Mahmoud

No one has been arguing the mathematical convenience of Rayleigh damping. To the best of my knowledge, it is the one and only damping model that covers all simulation scenarios, e.g. non-linear, which, I guess, is why it is used in Abaqus.

As it does not have any physical damping mechanism to lean on it will be hampered when adressign real world problems.

At the risk of being seen as the stubborn fool - try simulating two flat plates joined at 90 degrees with a single viscous dashpot located at one of the plates.This will be a case with heavy and concentrated damping once the dashpot adds decent damping.

Next, try an mimic this case with any other damping model. They will all fail.

This case may seem academic but remember that steel's material loss factor is somewhere in the range eta = 5E-4 to 5E-5 depending on the steel type. Yet we usually find loss factors in the ballpark ~1% for most built up structures.

For a pipe system damping usally is added at its supports and arises from friction and transmission to adjacent structure.If the pipe is large and thin, damping may be added from the fluid inside and when buried undergound tranmission to adjacent soil likely matters.

For plate structure sound radiation can be shown to provide damping that varies from ~1E-2 at low frequency to 1E-3 at high frequency. 

We get away with using almost any damping model as long as damping is weak.

As real world damping is governed by phenomena we do not control, it logically follows that our ability to correctly predict real world dynamic response is limited.

Peak response is damping controlled for steady state wide band random vibration. If you guess your loss factor a factor X wrong, your response prediction will immediately be a factor X wrong. Differently stated, for problems where damping truly matters, this statement will likely also hold.

Take a look at Table 1 here: http://qringtech.com/2014/06/22/designed-damping-types-mechanisms-application-limitation/

The values are %of critical and were found from four experimental modal analyses made of four, for all practical purposes, identical pipe systems. The pipes all started and ended at the same locations and has the same number of supports. There were some differences in lengths as they were differently routed but these differences were, if memory correctly serves me were ~10% or less.The difference in fundamental natural frequency between the system was minor.

Without prior knowledge, I would have guessed on quite similar loss factors - at least for the first handful of modes. Yet, we see a nearly factor six (=2.93%/0.53%) difference in damping for the fundamental pipe system modes. 

Now, I very much doubt that any damping model could be favored over the other in a priori predicting the real world response for these pipes. In any case, I had a hard time getting a fit between EMA and FE for these models as the pipe system behavior was entirely controlled by its support stiffness.

In the end, I managed to get a fit using assumptions that could be physically motivated for ten modes of one of the systems and 5-8 modes for the other three systems.

Trying to improve on this situation by designing damping into the structure implies adding more than the background damping which tends to make damping strong, say 10% and above, and one often must concentrate its location. For piping it would typically be Gerb Viscodampers that would be added, i.e. local and heavy damping. Things then tend not to be simple at all (running the FE software is simple but to accurately predict is a different matter).

I do not mean to sound defeatistic but the above becomes something of a circular argument. You know - it is damping or the da-d thing.

The way I have handled the situation when doing consulting has been (best) to measure system damping to get an idea of the backround damping and then to add 10x or more damping to assure success. This crude way of working is OK for single installations but would not suffice for high volume production. In the latter case, I suspect one would have to use a combination of simualtion and test. 

I believe that we must greatly improve our understanding of damping to make any real headway for 'true' prognosis.

This statement, of course, does not help you when picking models form the Abaqus toolchest but as I suspect you aim at simulating real world problems the above caveats may be worth keeping in mind.

What got me, once upon a time was the below statement

"In Rayleigh damping the assumption is made that

the damping matrix is a linear combination of the

mass and stiffness matrices, where alpha and beta are user defined constants. Although the assumption that the damping is proportional to the mass and stiffness matrices has no rigorous physical basis, in practice the damping distribution rarely is known in sufficient detail to warrant any other more complicated model. In general, this model ceases to be reliable for heavily damped systems; that is, above approximately 10% of critical damping.

... skipping a bit ...

In most linear dynamic problems the proper specification of damping is important to obtain accurate results. However, damping is approximate in the sense that it models the energy absorbing characteristics of the structure without attempting to model the physical mechanisms that cause them. Therefore, it is difficult to determine the damping data required for a simulation.

Occasionally, you may have data available from dynamic tests, but often you will have to work with data gleaned from references or experience. In such cases you should be very cautious in interpreting the results, and you should use parametric studies to assess the sensitivity of the simulation to damping values."

See page 222-223 (7-5 & 7-6) here

https://www.sharcnet.ca/Software/Abaqus/6.14.2/v6.14/pdf_books/GET_STARTED.pdf

As a side note - have you seen this?

http://abaqusdoc.ucalgary.ca/books/bmk/default.htm?startat=ch01s04ach39.html

Sincerely

Claes

Hi Claes,

Very insightful reply. 

Thanks for the abaqus link at the end of your reply. The reason I never seen it before because it come from Abaqus manual 6.10 which is an almost extinct version of Abaqus. At the university we use, Abaqus 6.13 or 2016 which are the most the recent version. 

However, damping of a SDOF system is normally very easily dealt with by only defining the damping ratio which would then give you the damping value 'C'. I believe it become more complicated and involved when you have a tower with connections and a number of structural members. 

Regards,

Mahmoud 

Hi Mahmoud

I believe that you exaggerate the matter.

Remember the bit ...in practice the damping distribution rarely is known in sufficient detail to warrant any other more complicated model...

You can run analysis with a mix of dashpots, modal damping etc, albeit not for every type of analysis.

Beauty lies in the eye of the beholder. In my opinion, damping models, at best, are approximate. Rayleigh even more so as it fails the physics test and hence is all the harder to match with reality. This does not make it useless - good work can be done using Rayleigh damping but it should make you more cautious when relying on it.

The recommendation is for you to be able to use all of them as you must adapt to whatever information is available to you. .

Time to crunch some numbers?

/C

PS - Use of complex numbers can be dampening. Take a lok at the 2002 Ignobel price for Economics. https://en.wikipedia.org/wiki/List_of_Ig_Nobel_Prize_winners

Yes, it is possible. However, if you attach dampers on the structure as dashpots then it is like attaching tuned mass dampers on the structure which represent external dampers and NOT the inherent damping of the structure. 

Hi Mahmoud

True & this would be the exact purpose for such a dashpot (or complex spring, etc.) element, i.e. to provide localized damping where such is present.

A small thing, at the risk of kicking in open doors - for the sake of clarity.

A tuned damper is comprised of a mass-spring system + some losses in this system which can be visous or other types. It can be tuned two ways, either to oppose excitation or to add absorption. In the latter case it adds damping to a specific frequency, usually a resonance frequency. The effect of the tuned damper is narrow frequency range.

A dashpot adds damping to all modes to which it senses relative motion, i.e. its effect is wide frequency range.

Also, the tuned damper uses its inertia at one end to impose support for relative motion while the dashpot is connected to ground or another part of the structure.

The physics and application of a tuned damper and a dashpot hence differ.

The inherent damping of the structure, as damping is additive, would be the sum of a bunch of things such as, but not limited to, internal material friction, sound radiation, boundary friction, transmission to connecting structures and localized damping.

For the classical damping models, I guess we can take the statment made by G.P. Box (which is taken out of context here) to heart - "All models are wrong, but some are useful".

/Claes

Hi Claes,

My understanding of a tuned mass damper that it consists of a vibrating mass which is attached to a spring and dashpot damper. While a dahspot damper would only provide a damping ratio along with a spring.

I might decide to ignore the inherent damping if it proves to be negligible and then rely and assume that the external dampers are the only proper sources of damping for the structure.

Regards,

Mahmoud

Hi Mahmoud

I hope I am not pestering you too much. A lengthy technobabble to follow.

You need intertia and a force that restores equilibrium to have vibration, i.e. a storage of energy in the system.The latter is what makes the pendulum vibrate but in most cases elasticity is what does the job.

At the natural frequency, there os a perfect conversion between kinetic/potential energy and a 50/50 split.

Solve (potential energy) 1/2*K*X2 = 1/2*M*V2 (kinetic energy), where you have X = X0e(j*w*t) and insert V = j*w*X, where j is imaginary and w is angular frequency.

When demoing this in the class room I has a mass-spring system with a stiff spring and the mass hanging from the spring. I then challenged the biggest guy in the room to press the mass down into the built in end stop. No problem when using both hands and leaning onto the weight. I then asked him to repeat the procedure using only two fingers. It failed.

I then lectured on the sdof system using my right hand while exciting the sdof system using my left hand and after a while the mass was thumping against the end stop. It usually grabbed some attention and brought the idea in energy storage home. But, we all know this from riding the swing when we were small.

Damping can mitigate vibration by the conversion of kinetic/potential energy into heat which is a nearly irreversible process. Damping is a take out from the storage of energy.

To discuss, I now distinguish between vibration = oscillation with energy storage and oscillation to be without storage.

A dashpot by itself can provide damping. As a thought exeriment, lacking inertia or the equilibrium restoring force  there would be no  oscillation other than the driving force and, as opposed to a system with interia/equilibrium, the dashpot would immediately stop and stop at any position where a vibrating system would continue for a while and return to equilibrium. To sum up, a damper can be run on its own.

A damper element can react to veloctity, as is the case for the dashpot, or react to displacement, as is the case for a structural damper. These are the most common types of structural dampers.

There are numerous other types of dampers out there working along a bunch of other physical principles. However, they all boil down to conversion of energy into heat.

Adding damping, I must admit is fun, but it does also add cost as well as complexity. Sometimes it can to some extent be designed into a system. The practical way in most cases is to rely on experience, meassurements, study of competitive systems, etc, and make a max/min guess on damping. Then run multiple analyses to see if it works anyhow,  You might want to ignore it, but I suspect it will be difficult to duck.

You know, as long as you stay away from resonance - damping does not affect you in the slightest. This is the most common design strategy. (Try it using FE, zero damping in the model and harmonic excitation off resonance = a limited response)

http://qringtech.com/TryMe/wp-content/uploads/2014/01/sdof.pdf

Designing damping into structures is the odd design strategy and unfortunately, something of a black art. You need it for machines with a wode speed range, for wide band random excittation, e.g. as impose by flow turbulence, etc.

Hope this helps

Claes

Hi Claes,

I now better understand the fact that a dashpot on its own could act as an external damper. Previously, I thought a vibrating mass is required with a dashpot to successfully eliminate any resonance problems.

Hi Mahmoud.

Yes. Good to have this sorted. :)

/C

Hi Claes,

Indeed sorted after may be having one of the most lengthy discussions ever on research gate!!

Happy to help

Time to crunch some numbers? ;)

/C

When you input Structural Damping what value do you use? Q(Damping Ratio) eta (loss factor) zeta?

Hi Eric

At resonance,

Eta = 1/Q = 2*C/Ccrit

where C/Ccrit is the critical damping ratio.

So, yes, you can use all of them.

/C

Thanks! ABAQUS asks for:

'where s represents the material structural damping'

So I input Eta? which is 1/Q and 2*Zeta. Is that it?

Thanks again!

Yup, that would be Eta.

/C

Great, thanks that is what I used.

Hello everyone, I need to use Rayleigh Damping in my Abaqus model. I know how to obtain alpha and beta, but I am not sure how to obtain the damping coefficient value for each mode. I am studying a cantilever beam and when I use my accelerometer I am only able to analyze or 1 specific mode or a timeresponse with all modes together. Does anyone know how could I study the damping factor for each mode? Thank you very much in advance.

How do you activate the beam? If you excite it in a steady-state regime at the different resonant frequency you should be able to get your damping, or with the logaritmic decrement I think.

I am using Abaqus to draw a dam made of a lead oxide powder material and I want to enter the values of elpha and beta for the damping of this material and I don't know how much these values must be entered for this material. Can anyone help me?

Thank you for any help.

Hello everyone

Can anyone help me model the viscoelastic properties of composite resin in ABAQUS?

regards

Shabnam Kiasat

if the resin should stick to the concrete surface, You could use tie interactions such as FRP (of course you have to verify your numerical model). also, there is some method in abaqus for defining material in the surface of Independent member.

there is some model of the first method on the below link;

https://numericalarchive.com/shop?olsPage=t%2Fabaqus