What damping means: energy dissipation capacity, damping coefficient or damping factor?

It seems that you are referring to the continuous system.

For a given material the energy dissipation/cycle changes with frequency (bell shape pattern).

From frequency response curve you will get modal damping factors (different). To calculate damping coefficient you must be able to calculate modal mass.

 Is the modal mass different from mass of the system?

Yes! Go through the literature on modal analysis.

okay thanks!!!

Just imagine a system composed by 2 different masses connected, let's say m1 and m2. Your system mass will be m1+m2, but depending how you connect, arrange and vibrate these masses (m1 on top m2, m1 next to m2, etc..), your modal masses will vary, but the system mass will remain as the same value.

Modal damping is different for different modes. This is evident when conducting experimental modal analysis (EMA). To explain this, one must recall the different damping mechanisms that contribute to the modal damping. These include internal material damping, structural damping at joints and interfaces, and fluid-structure interaction damping. These damping mechanisms are, in fact, associated with the inertia and stiffness of the structure. This is why the most common model for modal damping is the proportional damping model, which is a linear function of both the inertial matrix and the stiffness matrix. The first term represents the energy loss associated with a change in momentum, while the second term is proportional to the rate of change of the local deformation forces. Since the structural configuration would impose different limits on deformations along different directions, then different mode shapes (modal deformations) will experience different damping.   

Any continuous system has infinite no. of natural frequencies. These natural frequencies have different mode shapes. The body can bend in different ways corresponding to the stiffness and modal mass participation factor in that mode. Since the damping is the measure of amount of energy absorption in a particular mode frequency, it can have different values depending on the complex stiffness and other factors like boundary conditions..

how to calculate the natural frequencies in ANYS-APDL???/

For a continuous system/structure, say a flexible beam, there are infinite number of modes/mode shapes corresponding to the infinite natural frequencies. You can refer to any book, say S.S. Rao's book on vibrations, for the details of the Expansion theorem.

There are infinite modes and the damping ratios corresponding to the infinite NFs of the continuous structure. Meirovitch's book can be referred for the Modal analysis for more detils. 

thank youu

Yes, it's true. I just trust it by a shaking table test in ST@CQU10 days ago, but not good matched with the numerical ones.

Also realize that modal analysis output is a transformation (modal) base, sometimes in a complex-valued form, which turns the coupled motion equations into a system of decoupled 1 SDOF differential equations. This means that each SDOF system has it's specific modal properties, such as modal mass, modal damping and modal stiffness, then transformed/scaled also according to normalization constraints.

Pay also attention that you might have coupled modes, or very frequency tight eigenmodes, therefore with an apparent very similar frequency, but different modal properties.

My best regards,

Alessandro

For every  SDOF system has it's specific modal properties, such as modal mass, modal damping and modal stiffness, then transformed/scaled also according to normalization constraints

Also you can benefit from my project concerning this topic.

Regards

Method Matlab SDOF Vibration Method

By the way, returning to the main question, maybe it is also interesting to know real cases in practice with identical damping for different natural frequencies (if existing any). Of course the damping of different modes (different modes can correspond to identical frequencies) can be identical for symmetrical structural systems. But excluding symmetries, under what conditions and when the damping are equal at different natural frequencies. In any way I am not expert in this area only interested, sorry if . . ; with thanks, Aram

Hi

Please take a look at this discussion.

https://www.researchgate.net/post/Damping-Half_power_bandwidth_method?_tpcectx=qa_overview_following&_trid=Rjv1Pnd391Irk095kcaSj0X7_

You can find also similar discussions on experimental modal analysis and damping if you search the RG Questions section.

/Claes

Definitely, the different resonance frequencies cause a different damping. It is more appropriate here to consider damped frequencies instead of natural frequencies. These can be directly obtained by performing complex modal analysis of the system. As an example, you can see below the table of damped frequencies and corresponding damping factors (=decay rates), and the time history for amplitude in one of those frequencies is shown on the graph. For example, the results shown below have been obtained by AVL software EXCITE Designer. 

https://www.avl.com/excite/-/asset_publisher/gYjUpY19vEA8/content/avl-excite-designer?inheritRedirect=false&redirect=https%3A%2F%2Fwww.avl.com%3A443%2Fexcite%3Fp_p_id%3D101_INSTANCE_gYjUpY19vEA8%26p_p_lifecycle%3D0%26p_p_state%3Dnormal%26p_p_mode%3Dview%26p_p_col_id%3Dcolumn-2%26p_p_col_count%3D1

http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleid=1627438

Do not forget also that to each eigenfrequency it is related a mode shape, which is indeed a distribution of relative displacements. Damping, as a quantity that wants to summarise dissipative phenomena, is thus closely related to the peculiar shape and velocity distribution: it follows that if you have markedly different shape, even if close in frequency, you might have very different energy losses in your system, therefore a different damping.

Have a nice day,

Alessandro

Reference. The relative stability of the system is the condition.

When the system is relatively stable, the natural frequency and the damped value have reached a balance. It's the interaction.

Part successively. Restrict each other.

Here is a recent paper, where this is analyzed.

Conference Paper Complex modes analysis for powertrain and driveline applications