Forced Vibrations of Circular Plates: From Periodic to Chaotic Motions

e ∗ Unit´ e de M´ ecanique (UME) ENSTA-ParisTech Chemin de la Huni` ere ABSTRACT A numerical study of the transition from periodic to chaotic motions in forced vibrations of circular plates, is propose d. A pointwise harmonic forcing of constant excitation frequen cy Ω and increasing values of the amplitude is considered. Perfe ct and imperfect circular plates with a free edge are studied wi thin the von K´ arm´ an assumptions for large displacements (geometric non-linearity). The transition scenario is observed for di fferent excitation frequencies in the range of the first eigenfreque ncies of the plate. For perfect plate with no specific internal resona nce re- lationships, a direct transition to chaos is at hand. For imp erfect plate tuned so as to fulfill specific internal resonance relations, a coupling between internally resonant modes is first observ ed. The chaotic regime shows an attractor of large dimension, an d thus is studied within the framework of wave turbulence.