Harmonic excitation of a SDOF
The exact solution of a damped Single Degree Of Freedom (SDOF) system is excited by a harmonic force is calculated [1]. It is compared to the numerical solution provided by the Matlab built-in function ode 45, the central difference method, Newmark method and the 4th order Runge-Kutta method, the implementation of which is based on the book from S. Rao [2].
[1] Daniel J. Inman, Engineering Vibrations, Pearson Education, 2013
[2] Singiresu S. Rao, Mechanical Vibrations,Prentice Hall, 2011
Cite As
E. Cheynet (2021). Harmonic excitation of a SDOF (https://www.mathworks.com/matlabcentral/fileexchange/53854-harmonic-excitation-of-a-sdof), MATLAB Central File Exchange. Retrieved .
Comments and Ratings (8)
MATLAB Release Compatibility
Platform Compatibility
Windows macOS LinuxCategories
Tags
Acknowledgements
Inspired: Damping ratio estimation from ambient vibrations (SDOF)
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!Discover Live Editor
Create scripts with code, output, and formatted text in a single executable document.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
Select web siteYou can also select a web site from the following list:
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)
Hi Mouss,
Yes, it is possible to do that. However, the central difference is not the best approach. I have uploaded several examples for line-like structures on Matlab FileExchange where the 4th order Runge-Kutta or Newmark mehod is used
is it possible to extend the central difference method to a multiple degree of freedom system?
Hi Vishal Antony,
There won't be much difference in the way to proceed with a rectangular pulse. However, you will probably need a (very) high sampling frequency to properly model the discontinuity that exists in a rectangular pulse.
How to express a rectangular Pulse as forcing function in the numerical method e.g. central difference method?
@Maede I agree with you. I have re-arranged the inputs of the function "Newmark" in the new submission
I think it would be nicer if you had the inputs for both functions (CentDiff and Newmark) in the same order. Just to look better, no big deal :)