Aeroelasticity - Science topic

I hope you can find your answer in this book (AIRCRAFT

DYNAMIC STABILITY AND RESPONSE )

A. W. BABISTER

The strip theory has been addressed and not specified by 3 conditions only

Numerical experiments are mostly the common way to detect or qualitatively comment on the type of bifurcation, particularly if a pitchfork type bifurcation is super or sub-critical. In higher dimensions this becomes a periodic orbit or a limit cycle in the absence of any external forces (limit cycles are self sustained).

One method could be to observe any form of hysteresis in the observed large amplitude oscillations. If while changing the parameter (eg. α) in one direction; say increasing, there persists a stable fixed point which becomes unstable at α_c and a larger limit cycle appears. Now while decreasing the parameter from α > α_c (ensure the initial condition is near the larger limit cycle), the larger limit cycle disappears at α=α_c and the initial fixed point reappears; then this is supercritical hopf. However if the larger limit cycle is still stable below α_c and looses stability at a lower value of α_n<α_c jumping to the initial fixed point; this is a signature of sub-critical bifurcation. The larger limit cycle looses stability by means of saddle node type bifurcation for cycles. This also means that a local unstable limit cycle exists between α_n and α_c located between the fixed point and the larger limit cycle which engulfs the larger limit cycle at the saddle node bifurcation point α_n

One method to detect this unstable limit cycle is to use the method of pseudo arc-length continuation or path following algorithm. Packages like COCO exist which use the method of continuation to detect these unstable limit cycles for dynamical systems.

Rossana Fernandes Can you share the two Nastran models (.bdf)?

Hello Mohsen,

One of my colleagues finished his thesis on this topic (https://commons.erau.edu/edt/440/)

I am sure he would be open to discussions via emails.

Good luck!

Dear Taiwo,

aero-eleasticity new branch of applied mechanics is interaction between fluid matters and flexible solid bodies typical application in aircraft engineering and which played a major role in structural loads of rotor of turbine blades. Many issues are related with civil engineering and mechanical engineering (compressor, turbine blade etc.).Here the forces like dynamic aero-elastics, static aero-eleastics and flight mechanics forces are interrelated.

Ashish

https://pynastran-git.readthedocs.io/en/latest/quick_start/index.html

might be a starting point.

Buffetting and flutter are two completely different things.

Flutter is an aerodynamically triggered aeroelastic stability mode oscillation depending on structural stiffness, damping and mass distribution.

Buffetting is an aerodynamic instability of a shock movement due to shock induced separation onset

Thus, flutter is not limited to transonic flow conditions and buffetting is not linked to structrual stiffness of the wing.

Only, in case that the Eigenfrequencies of flutter and buffetting match, you may end up in a buffetting flutter mode

Dear Mohsen,

an old but useful way is to use the Describing Function method. If I am not mistaken Dr. Ronilson Rocha has used this method with chaotic circuits and systems with good success.

Regards.

Luis

Dear Anastasia Klimova

The given article is evaluating the AOA on the box girder of a bridge; it will help you:

You may find dominent modes (usually the first mode) using centre manifold theories (nonlinear theories)

It may lead to reduced stiffness of the blade and increase the deformation.

Hello Victor,

thanks for the files.

I was thinking about that other users reserve all licences and there are not enough left for you. Thats typically when a bunch of people use nastran. But in this case, there is an other error in the .log-file.

In your case I think, the license server is completly unavailable. For license servers I'm unfortunatly not the expert. Nevertheless, maybe you can check if the license server has network connectivity problems, or other cpu or data intensive jobs "blockade" the server hardware.

Regards, Marinus

I finally find myself. I share it, may be somebody needs.

The best tutorial is MSC Nastran Documentation, in its package.

I use it, there are many training examples and useful subjects.

I also find a good website.

Thanks Janet

At Warsaw University of Technology we have a 30h Vibrations and Aeroelasticity course and we recommend those books for aeroelasticity:

-Bisplinghoff R.L., Ashley H., Halfman R. L, Aeroelasticity, Addison-Wesley, Cambridge, Massachusets, 1955

-Bisplinghoff R.L., Ashley H., Pronciples of Aeroelasticity, John Wiley, New York, 1962

-Dowell E.H., Curtiss H.C., Scanlan R.H., Sisto F., A modern course in aeroelasticity, Sijthof & Noordhoff, Alpen aan den Rijn, Netherlands, 2004.

-Balakrishnan A.V., Aeroelasticity, Springer, New York, 2012

-Wright J. R., Cooper J.E., Introduction to Aircraft Aeroelasticity and Loads, John Wiley & Sons, Chichester, England, 2007

-Hodges D.H., Pierce G.A, Introduction to structural dynamics and aeroelasticity, Cambridge, NY, 2012

Thank you Yeasir Mohammad Akib for the help

You can easily get the divergence speed with the SOL 145. I am also working in the field of Dynamic aeroelastic problems (Flutter). In the SOL 145 output file, check KFREQ=0, that indicated divergence.

The followings are good sources for ground vibration test (GVT):

http://www.garteur.org/Technical%20Reports/SM_AG-19_TP-115_OPEN.pdf

https://apps.dtic.mil/dtic/tr/fulltext/u2/a108262.pdf

I hope it is helpful for you.

All the best.

I think Anays Rigid Dynamics will give you all the possible options in comparison to any other tool. Try for it to cross verify the results.

ANSYS

Thank you very much for this resource, Dr. Pany!

See: http://aes4ac.com/app3/apps3.html

and

I would look on line for the Strouhal number of similar structures at similar Reynolds numbers to see what is already been done. When in doubt 0.22 is a good first guess at the Strouhal number. From there I would set up an excel spreadsheet with different heights above the base plane, then do a 1/7th power law for the boundary layer effect and calculate the wind velocity in 10 or so different points up the height. From there you should be able to get the vortex shedding frequency as a function of wind speed and height to compare to your structural resonances. Figuring out the unsteady lift force is more problematic from first principles but I bet there is a lot out there in the published technical literature. Good luck

В данный задачи дифференциальный оператор будет несамосопряженным, методы решения для соответствующих спектральных задач немногочисленны.

@ Rashid Naseer,

Hi, I just clarified my plan for you through private messaging.

Hi, I am not a specialist of this area but I have a colleague working in AIRBUS Toulouse that certainly can give you some elements. You can contact me directly and I will give you the email of this engineer.

You can try the general-purpose multiscale constitutive modeling which can take a block of material and homogenization it to a beam. The code can be freely launched in the cloud at https://cdmhub.org/resources/scstandard

better go for aero elastic analysis in NASTRAN it is the easy way to find out flutter analysis.  

I am trying to do flutter analysis in ANSYS workbench with 2 way system coupling. However, there is a point am concerning. The problem is that, with the Transient structural module of ANSYS I will transfer only bending (flexural) data to the Fluent but flutter needs torsional deflection at the same time. How can I design my project? Thanks from now for your suggestions.

Regards

My guts feeling is that it has something to do with the flight dynamics. Not really want you to model an airfoil with spring, but just want you to determine its stiffness.

Hi Khairil,

What type of error did you get during compiling? I checked your code and compiled it in one sample, it was compiled successfully without any errors on my computer; the screenshot is attached. Maybe you need to update your compiler. 

Regards,

Siamak 

I experienced the same problem while moving particular zone. Problem is remeshing, remeshing happening only in triangular zone that may be fluent limitation.

So solution is

Thank you for your suggestion. It looks like a good paper.

For your maximum value (for example 34 dB or 15 dB, or -5 dB) you must define the value 0dB. From this maximum value (34dB, 15dB, -5dB) then decrease value 3 dB and you will get the value on level -3 dB, it means (31dB or 12dB or -8dB). On these values (31dB or 12dB or -8dB) then you define searched frequency bandwidth.

Hi Khairil, I had the similar problem in simulating 2D 2 way-FSI problem using FLUENT. Have you found out how to come up with the problem? 

Regards,

Siamak 

As Andrea Da Ronch has stated the divergence is a static aeroelastic phenomenon and from a mathematical point of view it is described by an eigenvalues problem (as happens for all instability phenomena).

Moreover, if you are working with a straight wing (in other word the elastic axis of the wing structure is perpendicular to the asympototic flow direction) you must refer only to the omogeneous torsional equilibrium equation, on the other hand, if you are working with a swept wing, bending and torsion equations are coupled (the coupling effect depends on the definition of the angle of attack along the wing span) ... in this case you must solve a bending-torsion eigenvalue problem.

for more details see: Aeroelasticity – R. L. Bisplinghoff, H. Ashley, R. L. Halfman, 1996

If you know normal and tangential forces (to the rotor disc? To the section?) you can directly use them (be careful to express forces in the same reference of the structural equations, there are only geometric relations). But often you don't know normal and tangential forces and instead you can evaluate drag and lift with some kind of model. It is possibile to pass from lift and drag to normal and tangential, but it requires not only geometric relations but also the knowledge of inflow (induced by wind and wake) over the disc. Here you can find some useful informations:

Introduction to Aircraft Aeroelasticity and Loads by JR Wright (AIAA) and 

A Modern Course in Aeroelasticity by Earl Dowell are good books

Regarding low speed airfoils, you should refer to the NACA series for laminar flow airfoils developed in the 1940s or use one of those referred to in NACA TN 2502.

Regarding modeling of the structure, a finite element method would seem best to determine the torsional and bending stiffness.

If you considered a spring, it will be like considering the elasticity of the structure. In that case based on your BCs an ICs, you could observe damping or diverging or self-sustained response (flutter). But as @Fulvio_Sartor said buzz is related only to ailerons vibration. 

Please read this article

Could you send the characteristics equation as pdf- or png-file ?  

Tilting the rotor maybe a solution to ensure that no collisions will happened due to deflection of the blade. 

However, I think this is increasing the costs of design and manufacturing (not sure). 

Another point, you should make CFD to determine the aerodynamics loads on the blade when rotor is tilted and un tilted then calculate the deflection of the blade due to these loads. 

If you find the deflection is so dangerous then you should think of modifying the tip by inserting some webs beside the main spar of your blade. 

Another option, Try to design different types of the spar I mean:

1- use box girder.

2-one shear web.

3-two shear webs

4-two shear webs with additionally web at the trailing edge.

Try and check the deflections. 

Use Fluid Structure Interaction Method in ANSYS workbench.

follow the attached Fig.

Peter, the constitutive matrix (6x6) gives you the relation between stresses and strains. Writing these strains as a function of nodal displacements implies the definition of the interpolation matrix (6x12). After replacing this discrete version of strains (discrete because it is a function of nodal displacements) in the variational equilibrium equations you get the desired 12x12 stiffness matrix. Please check this for reference: https://www.researchgate.net/publication/257583385_A_composite_beam_finite_element_for_multibody_dynamics_Application_to_large_wind_turbine_modeling?ev=prf_pub.

Hi, can you describe the equations? i have doubts you use non-linear equations when using Theodorsen functions. Where is the nonlinearity?

Another question would be what heat flux is required to maintain this temperature gradient (wall constant temperature heat flux), then how much energy do you need to put in the system, and finally does it worth the benefits ?

Also I don't see the point of increasing lift of an airfoil (if we are not speaking about maximum lift at stall). Increasing the angle of attack will increase the lift. What is important is the drag at a given lift.