Hi Amir,

What is the relevance of the attached paper to Aerodynamic damping in FEA procedures?

Hi Mahmoud

The basic concept is simple. As I understand it, it goes like this.

You have an object, say a mass-spring system (we always end up there...) with stiffness K N/m and mass M kg, an area of S and a drag factor Cd. The object is exposed to flow of velocity U m/s and it vibrates with amplitude u m/s.

The force imposed by the flow drag is Fd =  Cd*S*0.5*U2.

The power input to the mass-spring system is 0.5*real(Fd*u'), where u' is the complex conjugate of u when looking in the frequency domain.

Now,

• If your mass spring system oscillates below resonance, i.e. w < sqrt(K/M), then the power input to the system is negative, i.e. you have flow damping.
• f your mass spring system oscillates above resonance, i.e. w > sqrt(K/M), then the sdof system response phase shifts 180 degrees and your power input to the system is positive, i.e. you have flow excitation - also known as flutter. Flutter is important in aerospace as it determines the max speed of airplanes (as wings tend to fall off in case of flutter).

The above implies that the power input will vary with flow speed and frequency.

In a similar vein, looking at the imaginary part of the power input, you see that mass/stiffness is added to the sdof system, though I guess you have to modify from power input to mobility (u/Fd), which enables the solving of new modes etc. 

Nastran can do flutter analysis.

Code Aster has some clever analysis functions and very good QA cases, Perhaps you can get something out of the below?

https://www.google.se/url?sa=t&rct=j&q=&esrc=s&source=web&cd=10&ved=0ahUKEwiatJ6pm7jVAhWB6RQKHd8tALAQFghlMAk&url=https%3A%2F%2Fwww.politesi.polimi.it%2Fbitstream%2F10589%2F56884%2F1%2F2012_03_PhD_Romanelli.pdf&usg=AFQjCNEuNChsxNNC_ue_jjXa8MxtWZ13CQ

http://code-aster.org/doc/default/en/man_u/u4/u4.25.01.pdf

http://www.codeaster.org/V2/doc/default/en/man_v/v2/v2.03.104.pdf

http://code-aster.org/V2/doc/v12/en/man_v/v8/v8.01.108.pdf

http://www.code-aster.org/doc/v12/en/man_v/v8/v8.01.109.pdf

http://www.code-aster.org/doc/v12/en/man_v/v8/v8.01.106.pdf

https://docs.plm.automation.siemens.com/data_services/resources/nxnastran/10/help/en_US/tdocExt/pdf/aero.pdf

FYI - I have never worked with flutter analysis. The concepts border on general aeroacoustics that I dabble with from time to time. Hence, the above is just Trivial Pursuit+ level.

Have fun

Claes

Hi Claes,

I almost lost hope that somebody will reply to this question. I am surprised that none of the Aerodynamics researchers on RG commented on this topic which should be quite straightforward for them.

Nevertheless, thank you for the information. Helpful as always!

Regards,

Mahmoud