Phase shift in forced oscillations and waves

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We consider the phase shift between the load and the energy flux-related response of the structure. It occurs in regular and resonant oscillations and waves excited by the harmonically oscillating and moving-oscillating loads. The phase shift does exist in forced steady oscillations of a rigid body, because the period-averaged energy flux is zero. However, it is not so in the case of a resonance, where the shift is found to be zero. In the case of propagating waves, the energy flux is not zero by necessity, and the phase shift can take any value in 0≤φ<π/2 depending on specific conditions. We determine the phase-shift-related conditions and the shift dependence on the load frequency and speed. We show that it is an ordinary case where the phase shift is not zero and the load does not work at total capacity.

Original languageEnglish
Article number104762
JournalEuropean Journal of Mechanics, A/Solids
StatePublished - 1 Nov 2022


  • Phase shift
  • Waves


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