Nonlinear passive control of a pendulum submitted to base excitations

Gabriel Hurel (1) , Alireza Ture Savadkoohi (1) , Claude-Henri Lamarque (1)

1 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes

We seek to understand the behavior of a pendulum under parametric excitation coupled with a nonlinear absorber. First, the reference system without any coupled absorber, i.e. a simple pendulum, is analyzed with a multiple scale method thanks to supposed assumptions about the excitation. The equilibrium points of the system are calculated and their stability are determined. The phase portraits are introduced in order to better predict the behavior of the system. Then the same analysis is performed on the pendulum coupled with the nonlinear absorber leading to detection of the slow invariant manifold and its dynamic characteristic points. Both systems are compared to estimate the effects of the absorber on the vibratory behaviors of the pendulum.

Mots clés: Pendulum; Nonlinear absorber; Multiple scale method; Base excitation

Domaines: Vibrations [physics.class-ph]; Mécanique des structures [physics.class-ph]; Dynamique Chaotique [nlin.CD]

Gabriel Hurel, Alireza Ture Savadkoohi, Claude-Henri Lamarque. Nonlinear passive control of a pendulum submitted to base excitations. Acta Mechanica, 2021, ⟨10.1007/s00707-020-02916-z⟩. ⟨hal-03149388⟩