Nonlinear passive control of a pendulum submitted to base excitations

Abstract

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 is 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.