Help---- Engineering Maths

[normm]

I have just started reading a bit about Fourier Series. I have been told this series has applications in Structural Engineering problems like Beam on Elastic Foundation, Dynamics, Buckling etc. All I have learnt so far is that by Fourier series you can break up a complicated periodic function into addition of several simple periodic functions.

Although I see many maths book that deal with Fourier Series, I have not found any book or publication that deal with application of Fourier Series in Civil Engineering problems.

If any of you know of any such publication where the series has been applied to Civil Engineering Problems (ideally with examples), can you let me know the reference please.

 

[dik]

I'll let someone else respond to this... I don't see much of a use for Fourier series... maybe mechanically or electrically... but, not for the structural work I do...

Dik

 

[rb1957]

maybe in structural dynamics ?

another day in paradise, or is paradise one day closer ?

 

[dik]

not even sure there...

Dik

 

[271828]

"Advanced Engineering Mathematics" by Kreyszig

 

[271828]

Fourier series and transforms are used a lot in vibrations, plates and shells, and stability.

 

[IRstuff]

A Fourier series is akin to the outcome of a Fourier transform on an arbitrary time domain input. The resultant frequency domain data can be used to identify resonances or the transfer function of a structure.

That said, almost no one actually uses the math that way. In the age of digital computers, software is written around the Fast Fourier Transform (FFT) and analysis with FFTs. THAT said, almost no one uses FFTs directly, since they're embodied in much of the analysis software people use. Nevertheless, understanding Fourier series, transforms, and FFTs provides you with an understanding of how time/frequency domain analysis is performed. Frequency domain analysis is more often used by mechanical engineers for modal analysis of structures.

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[dik]

271828 and IRS... thanks

Dik

 

[Guest262653]

Footfall analysis of floors uses Fourier series to break up the impulsive forces and the response into manageable equations. Try the following publications for detailed description of this application:
- SCI P354: Design of floors for vibration: A new approach (Link)
- A Design Guide for Footfall Induced Vibration of Structures (Link)