Conversion of Time History to Response Spectrum 1

[thepricedude]

Hi,

I want to convert a time history record of an earthquake into a response spectrum. I am aware of the theory behind this but would like to locate software that can do it for me without setting out to write something myself. Has anybody developed something that they would bewilling to share, or is there any Freeware out there that you can recommend?

With thanks.

 

[btrueblood]

Do you have access to Micrsoft Excel? There is a fourier transform add-in that comes with the install disk...

 

[electricpete]

Shorter list: What math software DOESN'T do FFT's.

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[rybose]

http://www.vibrationdata.com

It will cost you $40 for the subscription, but it has plenty of simple programs in matlab and C++.

 

[FeX32]

Here's one I just wrote for Matlab:

clear all;

%
fs = 1000; % sampling freq.
T = 1/fs;
TM=3;
t = 0:T:TM;
x = cos(50*t)+2*sin(80*t+pi/3)+3.5*cos(155*t+pi/6)+4*cos(180*t+pi/4); % example signal
%
data=x;
N=length(data);
Fmax=fs;
delta_f=(1/(TM*Fmax))*Fmax;
f = 0:delta_f:Fmax;
F=fft(data);
figure
plot(f(1:N/10),abs(F(1:N/10))),grid
title('FFT'); xlabel('Frequency (Hz)');ylabel('Amplitude')





Fe

 

[FeX32]

Should work for any signal 'x' as long as you remember to change the sampling frequency to yours. As well as the signal 'x' should be your earthquake time signal as well.



Fe

 

[SomptingGuy]

The same code will run unmodified in octave, which is free.

- Steve

 

[FeX32]

Good point Steve. I just tried it. Works fine.

Fe

 

[FeX32]

Oh an don't forget to change 'TM' to your time signals length in seconds.



Fe

 

[thepricedude]

All,

Just returned from vacation hence the late response. Thanks to all who responded, you have all been most helpful. I dont have Matlab but "btrueblood" can you tell me more about the Excel fourier transform capability?

With thanks

 

[FeX32]

Why not try octave? Its all done for you.

Fe

 

[electricpete]

You need to install the Analysis Tookpack as follows:
Tools / Add-ins / check the box "Analysis Tookpack"

Then you can choose Tools/Data Analysis / Fourier Analysis

If you want to use VBA, you can also install the "Analysis Tookpack - VBA" tookpack which will give you access to the VBA "fourier" function. Note that complex numbers are represented as stringes.

The limit for excel's FFT is 4096 points.

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[electricpete]

Another little thing you've gotta do to use Fourier in vba is (in the vba editor window) select Tools/References and check "atpvbaen.xls". You don't have to worry about that if you are not using VBA to access Fourier

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[SomptingGuy]

This all sounds very complicated. I'm with FeX32, why not try a (free) environment designed for this kind of work rather than tailor your one and only hammer for this kind of nail?

- Steve

 

[btrueblood]

Oh, SG. And deprive the gentleman from the wonderful learning experience presented?

Actually, the Excel function is fairly straightforward, if you are at all familiar with FT analysis. It's limited in many ways, but I've used it before to get reasonably quick, cheap, usable data output. Excel is less a hammer than a bloated, expensive, cumbersome swiss-army-knife and food processor all rolled into one. That said, it's usually already installed on most machines, and most users are familiar with it.

 

[FeX32]

Octave is a more wonderful experience..... (more like a light saber compared to the tiny swiss army knife)
....and hell we even wrote the external m-code.. all you have to do is cut and paste.

Fe

 

[FeX32]

... its like trying to compare Linux to windows.....



Fe

 

[tomirvine]

A Fourier transform and a shock response spectrum are two different calculations. Yes, there are some roundabout, indirect, relationships between the two functions; but please consider them separate for now.

I have posted a shock response spectrum tutorial at:

http://www.vibrationdata.com/tutorials2/srs_intr.pdf

The tutorial is geared toward aerospace shock, but the principles and formulas are the same for earthquake shock.

The required input is a base acceleration time history.

Tom Irvine

http://www.vibrationdata.com

 

[electricpete]

Good point. Also:

http://en.wikipedia.org/wiki/Shock_response

So it looks like you have to take the base acceleration TWF, input it into SDOF with frequency f1, damping d0, determine peak acceleration of the response r1, plot point (f1,r1)

Then repeat with frequency f2, damping d0, compute response r2, plot point (f2,r2).

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[electricpete]

... where f1 and f2 are the resonant frequencies of those SDOF systems.

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