SDOF Response to Harmonic Loading
The importance of studying the response of a SDOF system subjected to a harmonic excitation cannot be overestimated.
Undamped Oscillator
- The complementary solution for a harmonic loading can be studied in terms of static displacement and response ratio.
- A particular attention will be given to the study of the response when starting from initial zero conditions.
- When the excitation frequency equals the natural response frequency we have to study the particular case of resonant response.
Damped Oscillator
- To represent the complementary solution we have to introduce the phase difference.
- The algebra required to derive the complementary solution is easier if we represent the loading in terms of exponentials of imaginary argument!
- It is costumary to refer to the complementary solution as the steady-state response, because the influence of the initial conditions eventually vanishes due to energy loss.
Applications
- Using a properly damped systems it is possible to measure either accelerations or displacements.
- Using a suspension system it is possible to get some degree of insulation from forced vibrations.
- Measuring the response of a harmonically excited system it is possible to derive an estimate of the equivalent viscous damping.
Downloads
Material available for this class:
- the slides i used for my lesson,
- a printer-friendly version of the slides,
- a bunch of blackboard examples,
- the Delta-freq IE design chart,
- the script that generates the design chart, the script must be used with the gnuplot program, using a command line like % gnuplot IE.gp
- a static copy of the notebook about the procedure to estimate $m$, $\zeta$ and $k$ from a pair of dynamic tests,
- a static copy of the notebook about the response of a damped system to harmonic excitation (that I didn't show you during the class, becuse it was really too late...).