On measures of nonlinearities for dynamical systems with uncertainties

R. Sampaio (1) , Christian Soize (2)

1 PUC Rio - Department of Mechanical Engineering
2 LaM - Laboratoire de Mécanique

This paper studies the transient dynamics of a linear dynamical system with elastic barriers excited by a deterministic transient force whose Fourier Transform has a bounded frequency narrow band. The system is then non- linear. In order to measure the degree of non-linearity of the system, one looks for the mechanical energy transferred outside the frequency band of excitation. In addition, it is well known that this type of non-linear dynamical system is very sensitive to uncertainties. For this reason one studies the system as being deterministic, and also stochastic in order to take into account random uncertainties. The proposed analysis is then applied to a Timoshenko beam having its motion constrained by a symmetric elastic barrier at its free end. In particular, one shows the confidence region of the random mechanical energy transferred outside the excitation band.

Mots clés: uncertainty quantification; nonlinear dynamics; transient; elastic barriers; degree of non-linearity; nonparametric probabilistic method; modeling errors; model uncertianties; random uncertainties; random matrix

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Probabilités [math.PR]; Vibrations [physics.class-ph]; Vibrations [physics.class-ph]

R. Sampaio, Christian Soize. On measures of nonlinearities for dynamical systems with uncertainties. 18th International Congress of Mechanical Engineering, COBEM 2005, ABCM, Nov 2005, Ouro Preto, MG, Brazil. pp.1-8. ⟨hal-00689682⟩