An upper bound for normal form asymptotic expansions

Claude-Henri Lamarque (1) , Cyril Touzé (2) , Olivier Thomas (3)

1 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes
2 UME - Unité de Mécanique
3 LMSSC - Laboratoire de Mécanique des Structures et des Systèmes Couplés

In the nineties, analytical methods based on normal form theory have been used to obtain approximate expressions of free or forced responses of non-linear (smooth) mechanical systems. A large amount of interesting results can be obtained by these approaches, however no practical limits of validity are available. In this paper, a method to obtain simple upper bounds for amplitudes of changes of coordinates is proposed. Simple conservative mechanical examples are provided to illustrate the bounds estimation and their validity.

Domaines: Systèmes dynamiques [math.DS]; Science non linéaire [physics]; Vibrations [physics.class-ph]

Claude-Henri Lamarque, Cyril Touzé, Olivier Thomas. An upper bound for normal form asymptotic expansions. DSTA 2011, Dynamical Systems Theory and Applications, 2011, Lodz, Poland. ⟨hal-01154715⟩