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.

You can download the notebook using the navigation bar atop of the browser window. To interact with the notebook you need to install Ipython.