Response due to Periodic and Non-Periodic Excitations — Lesson 4

This lesson covers the concept of Fourier series representation and its application in structural dynamic analysis. It explains how to represent a periodic function using Fourier series and how to derive the solution for a system excited by a forcing function. The lesson also discusses the use of Fourier transform for non-periodic functions. It provides examples of how to solve problems involving periodic and non-periodic functions, including how to plot the force amplitude spectrum and response amplitude spectrum. The lesson also introduces the concept of frequency ratio and explains how to calculate the coefficients of a Fourier series.

Video Highlights

Explanation of the periodic function and its representation - 0:37
Explanation of the derivation of the solution for a periodic function - 2:23
Example of a forcing function represented by a sign function - 4:50
Explanation of the forcing function - 6:30
Discussion on the response of a single degree of freedom system to a periodic force - 9:35
Explanation of the force amplitude spectrum - 22:41
Discussion on the response of a system to a non-periodic function - 31:50
Example of a non-periodic function - 33:31
Task for viewers to find the response of a function using Duhamel integral and Foral transform - 43:19
Conclusion and preview of the next lecture - 44:37

Key Takeaways:

- Fourier series representation can be used to represent a periodic function in structural dynamic analysis.
- The solution for a system excited by a forcing function can be derived using Fourier series.
- Fourier transform can be used for non-periodic functions.
- The force amplitude spectrum and response amplitude spectrum can be plotted to visualize the behavior of the system.
- The frequency ratio is an important concept in structural dynamic analysis.
- The coefficients of a Fourier series can be calculated using specific formulas.