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take home: step size, beta, gamma

Unread postPosted: Mon Dec 20, 2010 9:44 am
by Dan Negrut
Hi Dan,

While running the code for the take home exam II, I found that my simEngine2D is very sensitive to the time step, gamma and beta values in Newmark-beta. If possible can you tell me which method and time step was used in the text book. Also, what is the best way to find healthy time step?


Abdul Aziz Khaja.

Work with \beta=0.3025, and \gamma=0.6.  Don't change these.
About step size: there is no universal rule for choosing one.  Think of a slider crank that starts moving faster and faster and faster.  In the beginning, a large step size will suffice.  But as the motion gets quicker, in order to capture what's going on you'll have to gradually decrease the step size. 
So for your problem, keep decreasing the step size until for two successive step sizes the results look the same.

Finally, the results in the book were not generated with Newmark.  They were generated with a method called "Coordinate Partitioning", which we didn't discussed in class since it's a little bit beyond the scope of ME451.

I hope this helps.

Re: take home: step size, beta, gamma

Unread postPosted: Tue Dec 21, 2010 9:25 am
by Dan Negrut
i wanted to add one thing.

a couple of students saw a decrease in the amplitude of the motion in their plots.
the cause for that is what's called "numerical damping" in the integration formula.  you can get rid of it by reducing the integration step size to a small enough value.  I believe that for your problem if you reduce the step size by a factor of 10 you will get rid of that damping almost entirely.

i hope this helps.