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Velocity function will not integrate

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Garnet

Velocity function will not integrate

Hi,

I am trying to simulate a base excitation using a velocity versus time waveform as the base excitation. I have imported an excel file and developed a velocity time function using "linterp". When I try to integrate this it flags an error.

Further down the sheet I use an indefinite integral to derive the base input displacement from my velocity waveform. Is this OK. Any assistance would be appreciated. Cheers Ross

1 ACCEPTED SOLUTION

Accepted Solutions
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Re: Velocity function will not integrate

1. In M15 the indefinite integral of sin(x) works ok!

g0.jpg

 

2.  I've fixed some errors in the sheet and pointed out some mistakes in units - see attached.

View solution in original post

6 REPLIES 6
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Re: Velocity function will not integrate

Your GY(t) is defined for only numerical applications. Asking for the indefinite integral (the integral without borders) is a symbolic operation. You can't even numerically evaluate an indefinite integral for symbolically known functions like sin(x):

LucMeekes_0-1603175719966.png

in contrast to:

LucMeekes_1-1603175748962.png

To determine the integral of the dataset that you input, simply summing is the best way.

Your datapoints are discrete values. You cannot achieve more accuracy by interpolation.

So:

LucMeekes_2-1603176536625.png

Success!

Luc

 

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Re: Velocity function will not integrate

Luc,

Many thanks for your interest, knowledge  and feedback on my integration issue.

Cheers

Ross

Highlighted

Re: Velocity function will not integrate

1. In M15 the indefinite integral of sin(x) works ok!

g0.jpg

 

2.  I've fixed some errors in the sheet and pointed out some mistakes in units - see attached.

View solution in original post

Highlighted

Re: Velocity function will not integrate

"In M15 the indefinite integral of sin(x) works ok!"

Yes, symbolically, but try that numerically...

 

Luc

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Re: Velocity function will not integrate

@ Luc

"Yes, symbolically, but try that numerically..."

 

Of course not numerically!  As you demonstrated, the result is a function, not a number (though I missed the fact that you'd shown a numerical = rather than a symbolic -> !).

Highlighted

Re: Velocity function will not integrate

Alan,

Thanks again for coming to the rescue!. My text in the sheet said the input waveform was acceleration when in fact it should have read velocity. This means that your integrated waveform is in fact displacement. I rejigged the equations to reflect this and bingo I have a solution. Brilliant!😁

Cheers Ross

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