Modal analysis of structures in periodic states

Abstract eng:
This presentation focuses on the numerical computation of linear vibrational modes, or Floquet Forms, of mechanical systems in periodic states such as rotating machineries with imperfections or any structures that are in compressive or tensile periodic states. To make our point, we present an original spectral method through the fundamental example of the oscillations of a 2D bi-articulated bar submitted to a periodic compressive load at its end. We show that Floquet Forms generalize the concept of classic modal analysis for structures in equilibrium states. Because of the complexity of the frequency spectrum of Floquet Forms as compared to the classic harmonic modes of vibration, the type of instabilities encountered by periodically-varying structural systems is naturally much richer than systems in equilibrium.

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