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Harmonic excitation of a SDOF

version 2.2 (276 KB) by E. Cheynet
Implementation of some numerical methods to study forced vibrations of a SDOF in the time domain.


Updated 03 Mar 2019

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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 (2020). Harmonic excitation of a SDOF (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (8)

E. Cheynet

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?

E. Cheynet

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?

E. Cheynet

@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 :)



Added project website

The inputs of the Newmark-Beta funciton are ordered to be consistent with the function CentDiff

Added Newmark and Runge-Kutta methods

- picture added

MATLAB Release Compatibility
Created with R2017b
Compatible with any release
Platform Compatibility
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