Structural Dynamics 1

[teckert]

Why can changing the dt= time step, effect the non-linear time history results for x-displacements?

I hope someone can provide insight.

Thanks,
tre

 

[msquared48]

Sounds like basic calculus to me. The smaller the increment taken, the better the estimate.

Mike McCann
MMC Engineering

 

[BAretired]

I think you will have to define the problem a little more clearly than that. Is this a general question or are you addressing a real situation?

BA

 

[teckert]

This is just a general question. When doing a non-linear time history analysis, changing the time step drastically changed the results. For instance a time step was used of 0.002 was changed to 0.005 which seem to produce more realistic results.

 

[jhardy1]

teckert,

Take a very basic example - suppose we have a structure which is vibrating with simple harmonic (sinusoidal) motion, with period of 1 second, and zero phase shift.

Sample the response function at 1 second intervals, starting at t = 0.0 seconds, and every time step will return a value of precisely "0". Sample it again at half-second intervals, and you will STILL get "0" at every sample. This might lead you to think (erroneously) that there is no response - after all, you've reduced your time interval, and the solution shows no more convergence!

Now sample at 1/4 second intervals - you will get a saw-tooth function, which is a much better fit to the true sinusoidal function, but still not very good. Sample at 1/100th or 1/1000th second intervals, and you will start to get a good approximation of the real behaviour.

Bottom line - your time step must be "small enough" to capture the time variability of the forcing function AND the response of the system. This typically means that your time step must be rather smaller than the period of the highest natural frequency which is "of interest".

Hope this helps!

 

[FeX32]

2*(highest freq. of interest)=dt ... Nyquist frequency is the standard.


Fe

 

[271828]

You mean 1 over that, right?

I have to admit that this is one of the most amusing threads I've ever read around here.

 

[teckert]

Why is this amusing?

 

[BAretired]

Yes, 271828, what exactly do you find so amusing?

BA

 

[FeX32]

YES. 1 over that...

hahahahah... (im laughing at the big ears)


Fe

 

[FeX32]

I guess im not anal enough here. This is more of a leisure interest to get away from my extremely anal self during the day.



Fe

 

[FeX32]

I hope it's amusing now.
(no offense to the OP)


Fe

 

[BAretired]

Not really. Maybe you are trying too hard.

BA

 

[FeX32]

Excuse me. I had a long day.


Fe

 

[JStephen]

I recall from my antique numerical methods book that if you make the time step too small, you get overcome by roundoff errors.

 

[271828]

What's amusing? Greg's "short" reply and subsequent replies. No offense to the OP, of course. MEs sleep with vibrations books under their pillows, LOL.

 

[hokie66]

Who's Greg?

 

[271828]

HAHAHAHA!! I have the wrong thread. There was another thread about vibrations in which the guy modified the EOM to be something like m*x'' + c*(x')^2 + k*x = f(t) and Greg Locock jumped all over him for squaring the velocity and not realizing that doing this prevents decay. I must've read one right after the other.

 

[FeX32]

lmao. now its funny...


Fe

 

[BAretired]

I agree. Now it is funny, not really funny but a little bit funny. You guys ought to work on your routines a bit more and we would all be rolling in the aisles laughing 'til the tears rolled down our cheeks.

BA