Nonsmooth modal analysis of a N-degree-of-freedom system undergoing a purely elastic impact law

Mathias Legrand (1) , Stéphane Junca (2) , Sokly Heng (2)

1 Structural Dynamics and Vibration Laboratory [Montréal]
2 COFFEE - COmplex Flows For Energy and Environment

The dynamics of a N-degree-of-freedom autonomous oscillator undergoing an energy-preserving impact law on one of its mass is investigated in the light of nonlinear modal analysis. The impacted rigid foundation provides a natural Poincaré section of the investigated system from which is formulated a well-defined smooth First Return Map away from the grazing trajectory. Continuous one-parameter families of T-periodic orbits featuring one impact per period and lying on two-dimensional invariant manifolds in the state-space are shown to exist. The geometry of these piecewise-smooth manifolds is such that a linear "flat" portion (on which contact is not activated) is continuously attached to a purely nonlinear portion (on which contact is activated once per period) exhibiting a velocity discontinuity through a grazing orbit. These features explain the newly introduced terminology "Nonsmooth modal analysis". The stability of the periodic orbits lying on the invariant manifolds is also explored by calculating the eigenvalues of the linearized First Return Map. Internal resonances and multiple impacts per period are not addressed in this work.

Mots clés: spectral stability analysis; vibro-impact systems; frequency-energy plots; nonlinear normal modes; nonlinear modal analysis; First-return map

Domaines: Sciences de l'ingénieur [physics]; Vibrations [physics.class-ph]; Systèmes dynamiques [math.DS]; Mécanique des structures [physics.class-ph]

Mathias Legrand, Stéphane Junca, Sokly Heng. Nonsmooth modal analysis of a N-degree-of-freedom system undergoing a purely elastic impact law. 2015. ⟨hal-01185980v1⟩