Effets de la résonance en flexion des planchers sur les vibrations verticales des bâtiments

Abstract : Buildings are made up of beams and plates which are much stiffer in tension-compression than in bending. Thus, the vertical modes of a structure, which are governed by the tension-compression of the walls at the macroscopic scale, can appear in the same frequency range as the bending modes of the floors. This phenomenon is investigated by considering idealized buildings constituted by the periodic repetition of frames. Since the condition of scale separation is respected for tension-compression, the homogenization method of periodic discrete media is used to obtain the macroscopic behaviour. In the absence of the bending resonance of the floors, the vertical vibrations of the structure are described by the usual equation for beams in tension-compression. When there is resonance, the form of the equations is unchanged but the real mass of the floors must be replaced by an effective mass which depends on the frequency and can become negative. The structure has then an atypical behaviour in the neighbourhood of the natural frequencies of the floors. This study focuses on the modal properties and the transfer function. The effects of the resonance are first evidenced theoretically and then illustrated with numerical simulations.
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Céline Chesnais, Claude Boutin, Stéphane Hans. Effets de la résonance en flexion des planchers sur les vibrations verticales des bâtiments. AFPS 2015 - 9ème Colloque National, Nov 2015, CHAMPS SUR MARNE, France. 10p. ⟨hal-01382797⟩

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