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# Vibration of a thermally stressed palte with various boundary conditions

Hi Friends,

I would like to have any suggestions or any comments related to a particular problem... There is a thin square cantilevered plate with temperature applied as boundary conditions along 10% of its edges. I would like to extract the first 5 natural frequencies and mode shapes for this problem. The issue is that I am not able to pick the right element (shell) from ANSYS to solve this problem.

Also I would like to know how to solve this problem for multiple temperature inputs. Also could someone give me an insight on the effect of temperature on Youngs Modulus.

This problem appears in an AIAA paper written by C.D.Bailey. I am trying to analyze the FEM model of this plate in a hypersonic flow field and trying to think of this structure as a wing.

Thanks!

Deepak

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## Comments

## Free vibration of thermally stressed Plate:

Hi Deepak,

I don't know much about this problem, so I am also eager to know from others about the solution procedure.

I briefly read the help file, and noticed Shell57, Shell131 and Shell132 can be used.

So what I would do is add both shell57 (thermal) and shell63 (structural equivalent), first do a thermal analysis (with temperature BCs applied), then switch the element type to shell63 and read the thermal file, and (In between, you have to enable the prestress effects on) carry on the modal analysis.

Since you have said about multiple temperature inputs (is it layer by layer?, if so), you may have to use shell131 (in place of shell57) and shell63. Hope this helps.

Gopinath

## Modal Analysis of a gas turbine matrix burner

Hi, Deepak and Gopinath,

With respect to yours discussion held in the month of April 2008 regarding application of temperature field to a plate for carrying out modal analysis I would like to have help from you guys. I am doing Modal analysis of a Gas turbine matrix burner. The as the fmale temperature will be near by 1800°C in the burner, I need to apply a temperature field of 1800C in side a burner. The beam problem as that of given on web site of Universite of Uablerata can be considered as my simple case only diffrence would be that I ned to analyse teh diffrent mode shapes and frequencies at1800°C.

From Ur side I would like to know how can I impose this temperature effect. I just know that I need to use a Prestress option,but I tried it and was not sucessful in doing that. Also I read soem where that I should use some PSOLVE option for getting results but I cant find any such option in my software. Guys I would be grateful to you if you can help me in this matter.

Waiting for your reply,

Take care and ahve a nice day,

Regards Abhijit

## reply to your answer

Hi Gopinath,

Thanks for the info about the element selection...I tried using this method initially...but didn't quite get the desired results. Also the plate is being heated along 10% of its edges uniformly at temp steps of 0, 25,45,50,75 and 100 F. ( I tried using 6 different LS files and solved from LS 1 through LS 6) . I guess in the thread above...Shell 131 may be used only when there are layer by layers.

My natural frequencies are not changing for increase in temperature even when I used the above method...it must have to do with the way temperature is being applied as a boundary condition...

How do we need to apply the temp as a BC ? This problem seems more confusing than it actually is...Any valuable suggestions??

Deepak

## Ansys Tutorials:

Deepak,

You may be interested in this. There is an excellent website tutorial on Ansys , from University of Alberta.

(If link not working, http://www.mece.ualberta.ca/tutorials/ansys/)

Gopinath

## Modal Analysis of a gas turbine matrix burner

Hi, Deepak and Gopinath,

With respect to yours discussion held

in the month of April 2008 regarding application of temperature field

to a plate for carrying out modal analysis I would like to have help

from you guys. I am doing Modal analysis of a Gas turbine matrix

burner. As the flame temperature will be near by 1800°C in the

burner, I need to apply a temperature field of 1800C in side a burner.

The beam problem as that of given on web site of Universite of

Uablerata can be considered as my simple case only diffrence would be

that I ned to analyse teh diffrent mode shapes and frequencies

at1800°C.

From Ur side I would like to know how can I impose

this temperature effect. I just know that I need to use a Prestress

option,but I tried it and was not sucessful in doing that. Also I read

soem where that I should use some PSOLVE option for getting results but

I cant find any such option in my software. Guys I would be grateful to

you if you can help me in this matter.

Waiting for your reply,

Take care and ahve a nice day,

Regards Abhijit

## Steady-state or Transient?

Deepak

I could not understand if your temperature load varies by time or along the edge. So if it is along the edge (as I understood from above post), I guess you may have to apply gradient load or something (I remember applying for beams but its force not temperature). If gradient load option not available for temperature load, then you may have to enter it by Table parameter. Both these will apply continuous load (interpolate between) for the profile. Otherwise we can choose only those nodes along edge (one by one) and specify individual loads. However I think if you are varying temperature only along edges (steady state), we don't need 6 LS files - one load step definition will do.

If temperature vs. time is to be considered, you have to read through help files for transient analysis.

Lastly, you don't have to define temperature boundary for the structural analysis. I guess, once you are done with the thermal analysis (applied temperature through gradient or nodes, i.e. temperature load/BC), and switched the element for structural analysis, and specified the thermal analysis file, you are left with a cantilever plate (prestressed from thermal results - you have turn on prestress options for that), and are ready to carry on modal analysis. Read more on Ansys Help about carrying "Coupled Field Analysis". Hope this helps. Good Luck.

Regards,

Gopinath

*************************************************************************************************

I take back some of the comments here. If you look at the University of Alberta, Coupled Structural/Thermal tutorial , you will get all your answers. I forgot the procedure since I did this long back, I apologize.

*************************************************************************************************

## Re: Steady State or Transient

Hi,

The temperature enters the problem as a load (effects of thermal stress on the plate) and it is constant along the entire 10% of the plate area from left and right hand side. I used 4 Node Shell 63 as the element and modeled the plate in 2d with thickness, t. The biggest problem I am still facing is that for the 2nd, 3rd ,5th mode should have decrease in frequency with increase in temperature. Mode 4 surprisingly has an increase in temeprature and crosses the 5th mode at a particular temperature value.

I am applying the temperature under Define Loads - Structural - Temperature - On Nodes. I am still not getting any change in the frequencies.

Where exactly am I going wrong ? Could anyone give some tips and suggestions on the modeling approach ?

Thanks!

Deepak