2018-03-01

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.

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Giacomo Boffi