## A harmless looking SDOF vibration problem but...

## A harmless looking SDOF vibration problem but...

(OP)

It took me a while to dig up the solution to this one. It's a fairly realistic SDOF dynamic model of a suspension system subjected to a half-sine pulse of duration

*T*. Since I don't know how to get math into this little forum box, the problem is attached as a pdf. All those who believe they are mathematically-inclined, I challenge you to solve and verify the solution__by hand__.H. Bruce Jackson

ElectroMechanical Product Development

UMD 1984

UCF 1993

## RE: A harmless looking SDOF vibration problem but...

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: A harmless looking SDOF vibration problem but...

H. Bruce Jackson

ElectroMechanical Product Development

UMD 1984

UCF 1993

## RE: A harmless looking SDOF vibration problem but...

Quick google search turn up similar problems: https://www.tcsme.org/Papers/Vol34/Vol34No1Paper8....

http://engweb.swan.ac.uk/~adhikaris/fulltext/journ...

https://www.researchgate.net/profile/Nguyen_Nguyen...

## RE: A harmless looking SDOF vibration problem but...

## RE: A harmless looking SDOF vibration problem but...

theory of vibration with application, Chapter 4, pg 102-103

## RE: A harmless looking SDOF vibration problem but...

H. Bruce Jackson

ElectroMechanical Product Development

UMD 1984

UCF 1993

## RE: A harmless looking SDOF vibration problem but...

do a search for vibrationdata dot com + sdof response due to half sine pulse. The full derivation is there Laplace transform , etc - all the steps

## RE: A harmless looking SDOF vibration problem but...

ElectroMechanical Product Development

(aka Electronic Packaging)

UMD 1984

UCF 1993

## RE: A harmless looking SDOF vibration problem but...

http://www.eng-tips.com/viewthread.cfm?qid=157462

http://www.eng-tips.com/viewthread.cfm?qid=363026

One of those had a link to Tom Irvine's solution

http://www.vibrationdata.com/sbase.pdf

Seems like you have been interested in this for awhile. That's ok... I agree it's a challenging one. Without a computer to do the thinking for me, I wouldn't dare try to solve it.

=====================================

(2B)+(2B)' ?

## RE: A harmless looking SDOF vibration problem but...

Indeed I finally did find the derivation and simplified solution with Tom Irvine. Tom is a wealth of knowledge on vibration and shock and I have been a member of his vibrationdata.com site for longer than I care to admit.

Yeah, I was trying to 'stir the pot' with a seemingly impossible math exercise. As you use Laplace transforms to solve it, the derivation just grows and grows. And I thought I was good at math. The algebra just spun out of control!

ElectroMechanical Product Development

(aka Electronic Packaging)

UMD 1984

UCF 1993

## RE: A harmless looking SDOF vibration problem but...

I took a few pics since it seems it may be of interest: https://www.dropbox.com/sh/z4bt03c01tj8b06/AADbi9o...

## RE: A harmless looking SDOF vibration problem but...

Does that mean that programs such as MathCAD, Matlab, etc. will provide a closed form solution? That would be amazing! Whoever writes the code for these programs to do this kind of thing must be utter geniuses!

ElectroMechanical Product Development

(aka Electronic Packaging)

UMD 1984

UCF 1993

## RE: A harmless looking SDOF vibration problem but...

Steve

## RE: A harmless looking SDOF vibration problem but...

Steve will your math program provide the closed-form solution? Inquiring minds want to know!

ElectroMechanical Product Development

(aka Electronic Packaging)

UMD 1984

UCF 1993

## RE: A harmless looking SDOF vibration problem but...

I have witnessed a colleague using one to provide all the terms of a big jacobian matrix with analytical expressions before (a chemical kinetics problem with dozens of species and a non-sparse jacobian). The thought of trying to do all that by hand made the task seem like madness, I would have just used perturbation to approximate them. As it happened, he gave up on the analytical derivatives anyway, since they became unwieldy - hundreds of terms to transcribe from the math program into actual executable code.

The math program just churned through the known rules without making mistakes, going deeper and deeper into chain, product and quotient rule complexities. It wasn't asked to solve anything. Try writing down something seemingly simple, like piston jerk (third time derivative of displacement of a piston in a crank-slider mechanism) without making mistakes.

Steve

## RE: A harmless looking SDOF vibration problem but...

First question:

Am I right to say that maybe the math program provided the right solution to the chemistry problem but the guy was unable to use the data because there was too much to deal with?

Second question:

If it wasn't asked to solve anything, then what was the program doing?

Third question:

What's so special about a piston jerk problem?

ElectroMechanical Product Development

(aka Electronic Packaging)

UMD 1984

UCF 1993

## RE: A harmless looking SDOF vibration problem but...

These algebraic manipulation programs(software) exist. My favorite a few years ago was Maple (https://www.maplesoft.com/products/Maple/academic/). It is still the best IMO.

Here are 2 screen shots of one of my worksheets.

https://www.dropbox.com/sh/rgtulqofblt28kl/AADeupX...

It can solve (closed form) in a few seconds what would take you days to do and many times not even realize.

This could for sure be used as a means to an end of your original problem in this thread.

There is also http://www.wolframalpha.com/ - it is not too bad sometimes but not that great for anything complicated I found.

Personally, I don't really use this kind of software much anymore - the same end can be obtained numerically with some code much faster and most times there is no closed form solution to real-world type problems.

Cheers,