Nonsmooth modal analysis of piecewise-linear impact systems

Anders Thorin (1) , Pierre Delezoide (2) , Mathias Legrand (1)

1 Structural Dynamics and Vibration Laboratory [Montréal]
2 Independent Researcher

Periodic solutions of autonomous and conservative second-order dynamical systems of finite dimension n undergoing a single unilateral contact condition are investigated in continuous time. The unilateral constraint is complemented with a purely elastic impact law conserving total energy. The dynamics is linear away from impacts. It is proven that the phase-space is primarily populated by one-dimensional continua of periodic solutions, generating an invariant manifold which can be understood as a nonsmooth mode of vibration in the context of vibration analysis. Additionally, it is shown that nonsmooth modes of vibration can be calculated by solving only $k-1$ equations where $k$ is the number of impacts per period. Results are illustrated on a mass-spring chain whose last mass undergoes a contact condition with an obstacle.

Mots clés: Nonlinear modal analysis; Impact oscillator; Structural dynamics; Contact dynamics

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des structures [physics.class-ph]; Vibrations [physics.class-ph]; Génie mécanique [physics.class-ph]; Dynamique, vibrations; Structures

Anders Thorin, Pierre Delezoide, Mathias Legrand. Nonsmooth modal analysis of piecewise-linear impact systems. 24th International Congress of Theoretical and Applied Mechanics, Aug 2016, Montreal, Canada. ⟨hal-01402551⟩