Dynamics of Structures

SDOF system response to Periodic and Non-Periodic Loading

In this class we studied

• the response of a SDOF system to periodic and non periodic loads, using either a Fourier Series or a Fourier Transform representation of loading, the frequency response function and superposition of effects,
• the opportunity of using, in place of the Fourier Transform, the Discrete Fourier Transform (DFT) and the connected issue of frequency aliasing,
• an efficient algorithm, the so called Fast Fourier Transform or FFT, for computing the DFT,
• the response of a SDOF system to a generic load in terms of system response to infinitesimal impulses composed using superposition of effects by a convolutin integral, the so called Duhamel Integral,

The discussion of the relationship that exists between the two general method of solution, in the time and frequency domain, was delayed to next week.

Downloads

Some material used in this class is now available,

• the slides i used,
• a ready to print version of the slides,
• the spreadsheet implementing Duhamel Integral ,
• the FFT example notebook.

The link to the notebook leads to a static version, if you want to play with it you must download the notebook itself, a CSS style sheet and some data required to style the plots, these three files need to stay in the same directory.

To interact with the notebook you need to install Ipython.

Post Scriptum

For unknown reasons, I wasn't permitted to upload the CSS style sheet on www.stru.polimi.it, so I changed the extension from .css to .txt and the system happily accepted the file... should you like to interact with the notebook you have to download this file and later rename it to custom.css.