
[Sponsors] 
July 12, 2013, 03:05 
Amplitude of Oscillation

#1 
Member
mahzad_kh
Join Date: Jun 2010
Posts: 38
Rep Power: 8 
Hi everybody
As you know the amplitude of a sinusoidal curve is measured as the distance of the maximum or minimum of the curve from the mean value. I want to know how should we measure the amplitude when the curve is not sinusoidal, and the mean value does not locate at the middle of the curve. In this case there is not a unique amplitude. I have problem with the amplitude in this case. For example, in unsteady flows, we can consider the solution to reach a periodic state when the amplitude of oscillation doesn't change anymore. But when the curve is not sinusoidal, I don't know how to measure the amplitude, and as a result I don't know how should I understand that the solution is reached to a periodic state! I would appreciate if you could help me with this problem! I've attached a picture in order to better explain what I mean! Thanks in advance 

July 12, 2013, 06:13 

#2 
Senior Member
Lefteris
Join Date: Oct 2011
Location: UK
Posts: 199
Rep Power: 7 
In unsteady flows over airfoils Cl and Cd perform a double oscillation (I'm not sure that "double" is the correct word in English but you'll get the point). That is, they perform an oscillation about the equilibrium point and the equilibrium point itself oscilates sinusoidally. Look at the following pictures.
__________________
Lefteris 

July 12, 2013, 06:16 

#3 
Senior Member
Alex
Join Date: Jun 2012
Location: Germany
Posts: 1,309
Rep Power: 22 
A transformation into the frequency range ("FFT") is useful for analyzing this kind of signal.


July 12, 2013, 08:45 

#4 
Member
mahzad_kh
Join Date: Jun 2010
Posts: 38
Rep Power: 8 
So how should we compute the amplitude in such a curve? I mean the a curve with doube oscillation! And how can you understand that your solution has reached to a periodic state?
Also I would appreciate if you could explain more about the equilibrium point! what is the equilibrium point? 

July 12, 2013, 14:25 

#5 
Member
mahzad_kh
Join Date: Jun 2010
Posts: 38
Rep Power: 8 
So how should we compute the amplitude in such a curve? I mean the a curve with doube oscillation! And how can you understand that your solution has reached to a periodic state?
Also I would appreciate if you could explain more about the equilibrium point! what is the equilibrium point? 

July 12, 2013, 14:39 

#6 
Member
mahzad_kh
Join Date: Jun 2010
Posts: 38
Rep Power: 8 
when you want to check if your solution has reached a periodic solution or not, you can't take FFT in every time step, the only way is to compute relative error of two successive amplitude! If the relative error was for example less than 0.1%, then we can conclude that our curve has reached to a periodic state. Am I right?


July 12, 2013, 17:39 

#7 
Senior Member
Alex
Join Date: Jun 2012
Location: Germany
Posts: 1,309
Rep Power: 22 
I mentioned FFT because it is the tool of choice to evaluate the amplitudes of the signal. I thought that was the initial question here.
Additionally, a FFT can be used to check if the "periodic" state is reached by comparing the FFTs from smaller blocks of the signal. If the FFT result remains the same when sampled from different time intervals of the signal, the "periodic" state is reached. 

July 13, 2013, 00:59 

#8  
Member
mahzad_kh
Join Date: Jun 2010
Posts: 38
Rep Power: 8 
Quote:
Thanks for your reply Do you know any book or paper that can help me know how can I use FFT? Or do you have any example that can show using FFT for an oscillating curve? I will really appreciate that! 

Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Oscillation airfoil in infinite water depth  ldb83  FLUENT  14  June 4, 2013 08:03 
UDF for non sinusoidal or varying amplitude motion with respect to time  lalit kumar  FLUENT  1  November 13, 2010 17:58 
Must periodic oscillation give periodic results?  zonexo  Main CFD Forum  6  May 13, 2007 15:36 
urgent! amplitude and frequency  Sheila  FLUENT  3  June 22, 2006 11:23 
jet oscillation at low inlet Re  wood  Main CFD Forum  1  October 21, 1999 13:45 