Modelling the lateral pedestrian force on rigid and moving floors by a self-sustained oscillator
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Trovato, Andrea
Olivito, Renato S.
Bruno, Domenico
Argoul, Pierre
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Dottorato di Ricerca in Ingegneria dei Materiali e delle Strutture, Ciclo XXI, 2009; For the serviceability analysis of civil engineering structures under
human induced vibrations, a correct modelling of the pedestrian-structure
interaction is needed. The proposed approach consists in thinking the human
body as a Single Degree of Freedom oscillator: the force transmitted to the
floor is the restoring force of this oscillator [1, 2]. In rigid floor conditions, such
an oscillator must be able to reproduce two experimentally observed
phenomena: (i) the time-history of lateral force can be approximated by a
periodic signal with a “natural” frequency related with the single pedestrian
characteristics; (ii) the motion of a pedestrian is self-sustained, in the sense that
the pedestrian produces by itself the energy needed to walk.
Accounting for these aspects, a modified Van der Pol (MVdP) oscillator is
proposed here to represent the lateral pedestrian force. The suitable form of its
nonlinear restoring force is inferred from experimental data concerning a
sample of twelve pedestrians. The experimental and model lateral forces show
an excellent agreement.
For a laterally moving floor, the MVdP oscillator representing a
pedestrian becomes non-autonomous. It is well-known that self-sustained
oscillators in the non-autonomous regime are characterized by the so-called
entrainment phenomenon. It means that under certain conditions, the vibration frequency switches from the ”natural” value to that of the external force: the
response frequency is entrained by the excitation frequency. According to the
physical interpretation considered here, the entrainment corresponds to the
situation where the pedestrian changes its natural walking frequency and
synchronizes with the floor oscillation frequency. The steady response of the
MVdP oscillator subjected to a harmonic excitation is discussed in terms of
non-dimensional amplitude response curves, obtained using the harmonic
balance method truncated at the first harmonic. The model predictions are
compared with some experimental results concerning pedestrians available in
the literature and a good agreement is obtained. These topics are detailed in
this thesis and also in the companion papers [3, 4] and in the report [5].; Università della CalabriaSoggetto
Ingegneria; Strutture; Materiali stradali; Meccanica Laminati; Oscillatori