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prop_design15-Moonstone
15-Moonstone
April 20, 2021
Question

Two Square Wave Vibration Examples

  • April 20, 2021
  • 2 replies
  • 9268 views

Hi,

 

Given the recent posts on the forum, I was curious to try and drive a mass, spring, damper system using a square wave. Luc posted an interesting solution for creating a square wave. There are decent quick sheets for mass, spring, damper systems in Mathcad 15. So I just combined the two things. I did have to modify the square wave definition some. The state space solver is faster and more robust. However, using odesolve provides a check. Working with each solver is different. The examples help show how to work with each solver.

 

The examples allow you to see what happens when you use a square wave instead of a cosine wave. Also, what happens when the square wave duty cycle changes. You can see that traditional ode solutions don't match reality. I've seen this before as well. The classic text book solutions are limited in a number of ways.

 

Also, thanks to the other forum members who helped me create these examples. I couldn't have did it without their help.

 

Anthony

 

Update; Added additional information and fixed some bugs. Also added pdf files of the examples.

2 replies

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-MFra-21-Topaz II
21-Topaz II
April 21, 2021

I have adapted your data to a sawtooth excitation with an adjustable duty cycle. What do you think?

System sawtooth response.jpg

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    prop_design15-MoonstoneAuthor
    15-Moonstone
    April 21, 2021

    that's really cool. i love the response you got there.

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    prop_design15-MoonstoneAuthor
    15-Moonstone
    April 25, 2021

    i looked into the slow down, when working with the odesolve output. i was able to prove it had to do with taking derivatives of the function output. the forum won't let me edit my original post. so i have attached the new files to this post. i have optimized versions, which run fast and manually calculate velocity, kinetic energy, acceleration, and the reaction forces. the trick is to use matrix output and do the calculations yourself. rather than taking derivatives of the function output. you see the slow down when setting the number of cycles to 300, using the comparison files. i had to switch the number of cycles to 10, so that the pdf files were manageable. the reason for 300 cycles is that it allows you to compare to the classical magnification/amplitude factor.

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    LucMeekes23-Emerald IV
    23-Emerald IV
    April 25, 2021

    You can edit, up to about a day, maybe two, after initial post.

    After that, the best option is to attach a reaction/reply; which is what you did..

     

    Success!
    Luc

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