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July 12, 2013, 03:05 
Amplitude of Oscillation

#1 
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mahzad_kh
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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 
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Lefteris
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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.
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Lefteris 

July 12, 2013, 06:16 

#3 
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Alex
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A transformation into the frequency range ("FFT") is useful for analyzing this kind of signal.


July 12, 2013, 08:45 

#4 
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mahzad_kh
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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 
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mahzad_kh
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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 
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mahzad_kh
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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 
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Alex
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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  
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mahzad_kh
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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! 

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