Hello,I am solving the amplitude frequency response of a non autonomous two degree of freedom system, but I have encountered some problems and hope to receive assistance.Hope to get the help, I would offer my sincere thanks.
Whether your system can be investigated with limit cycle continuation only, depends on the response. Do a simulation first, including forcing Do you see a single frequency, or do you see a response with multiple frequencies (torus)? With a single frequency, you would be able to use continuation, otherwise I suggest to use simulations as torus-continuation is hard.
Showing the "no convergence" does not help, as you give no details how you got it, it could come from any step.
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Thanks for your answer,I followed the steps of a duffing equation.Here are my some of my steps.I also try many times,but,I just get the answer"NO,convergence at x0,".
I‘m sorry to waste your times because of lacking detailed description.,I'm going to describe some of my steps in more detail。 First, after establishing my two degree of freedom system, click on the "Initial point" option in the "Type" option and then click on the "Point" option to set my initial value. Afterwards, open the "Window/Output" option and open "2Dplot "in "Graphic "to create visualizations of x1, y1, x2, and y2. Next, set the "Interval" in the "Integrator Window"to ensure that it reaches its limit cycle. After obtaining the limit cycle, click on the "View point" , click on the "Last point", and then click on the" Select point". Set the "Interval "in the "Integrator window" to be slightly larger than the forced period, then click "Compute/forward" to obtain the limit cycle, click "LC Select Cycle", and click "Select point "to start the numerical continuation of the limit cycle. Change the parameters of the horizontal and vertical coordinates in "2DPlot", with the horizontal axis being the maximum value of the forced frequency "w" and the vertical axis being x1 and x2, respectively (I opened two 2DPlot windows). Then click "Forward" in the "Compute window", and you will find that there is no stable solution at x0. I tried "Compute/Backward" again, and that's the same answer:no convergence at x0. This is my entire process.
Could you please help me see if there are any problems with some of my steps, or what should I do (I'm just a newbie for matcont,haha). I will express my sincerest gratitude.
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The steps I did were all based on the following tutorial。I don't know if it can do the same with a 2-degree-of-freedom system。It would be nice if you could give me some advice, thank you very much。
Hello, it is still not clear, what you tried to do:
After you obtained the approximate limit cycle, did you tell MatCont, that you are looking for limit cycles? (I think, MatCont automatically selects that choice, after it finds the approximate circle.) Did you select a proper bifucation parameter?
Looking at your parameters: w is quite close to w1 and w2. You could try to start at e.g. w=4 and decrease it. Since you have two quite similar modes, I would expect a lot of resonances near w=w1=w2.
(PS.: When you describe your solution attempts, you need not mention the plotting setup.)
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Hi, my classmate encountered a similar issue last time, and it turned out that there was an error in the numerical values used for the initial points in his calculations.
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Hello,I am solving the amplitude frequency response of a non autonomous two degree of freedom system, but I have encountered some problems and hope to receive assistance.Hope to get the help, I would offer my sincere thanks.
Whether your system can be investigated with limit cycle continuation only, depends on the response. Do a simulation first, including forcing Do you see a single frequency, or do you see a response with multiple frequencies (torus)? With a single frequency, you would be able to use continuation, otherwise I suggest to use simulations as torus-continuation is hard.
Showing the "no convergence" does not help, as you give no details how you got it, it could come from any step.
Thanks for your answer,I followed the steps of a duffing equation.Here are my some of my steps.I also try many times,but,I just get the answer"NO,convergence at x0,".
Well, these are still just a few steps, and not telling me what you do exactly.
I‘m sorry to waste your times because of lacking detailed description.,I'm going to describe some of my steps in more detail。 First, after establishing my two degree of freedom system, click on the "Initial point" option in the "Type" option and then click on the "Point" option to set my initial value. Afterwards, open the "Window/Output" option and open "2Dplot "in "Graphic "to create visualizations of x1, y1, x2, and y2. Next, set the "Interval" in the "Integrator Window"to ensure that it reaches its limit cycle. After obtaining the limit cycle, click on the "View point" , click on the "Last point", and then click on the" Select point". Set the "Interval "in the "Integrator window" to be slightly larger than the forced period, then click "Compute/forward" to obtain the limit cycle, click "LC Select Cycle", and click "Select point "to start the numerical continuation of the limit cycle. Change the parameters of the horizontal and vertical coordinates in "2DPlot", with the horizontal axis being the maximum value of the forced frequency "w" and the vertical axis being x1 and x2, respectively (I opened two 2DPlot windows). Then click "Forward" in the "Compute window", and you will find that there is no stable solution at x0. I tried "Compute/Backward" again, and that's the same answer:no convergence at x0. This is my entire process.
Could you please help me see if there are any problems with some of my steps, or what should I do (I'm just a newbie for matcont,haha). I will express my sincerest gratitude.
The steps I did were all based on the following tutorial。I don't know if it can do the same with a 2-degree-of-freedom system。It would be nice if you could give me some advice, thank you very much。
FrequencyResponse.pdfhttps://wwwhome.ewi.utwente.nl/~meijerhge/FrequencyResponse.pdf。
Hello, it is still not clear, what you tried to do:
After you obtained the approximate limit cycle, did you tell MatCont, that you are looking for limit cycles? (I think, MatCont automatically selects that choice, after it finds the approximate circle.) Did you select a proper bifucation parameter?
Looking at your parameters: w is quite close to w1 and w2. You could try to start at e.g. w=4 and decrease it. Since you have two quite similar modes, I would expect a lot of resonances near w=w1=w2.
(PS.: When you describe your solution attempts, you need not mention the plotting setup.)
Hi, my classmate encountered a similar issue last time, and it turned out that there was an error in the numerical values used for the initial points in his calculations.