On the nonlinear stochastic dynamics of a continuous system with discrete attached elements

Americo Cunha Jr (1) , Rubens Sampaio (1)

1 PUC-Rio

This paper presents a theoretical study on the influence of a discrete element in the nonlinear dynamics of a continuous mechanical system subject to randomness in the model parameters. This system is composed by an elastic bar, attached to springs and a lumped mass, with a random elastic modulus and subjected to a Gaussian white-noise distributed external force. One can note that the dynamic behaviour of the bar is significantly altered when the lumped mass is varied, becoming, on the right extreme and for large values of the concentrated mass, similar to a mass-spring system. It is also observed that the system response is more influenced by the randomness for small values of the lumped mass. The study conducted also show an irregular distribution of energy through the spectrum of frequencies, asymmetries and multimodal behaviour in the probability distributions of the lumped mass velocity.

Mots clés: uncertainty quantification; maximum entropy principle; nonlinear dynamics; stochastic modeling; Monte Carlo method * Corresponding author; parametric probabilistic approach

Domaines: Mécanique des structures [physics.class-ph]; Mécanique des solides [physics.class-ph]; Vibrations [physics.class-ph]; Mécanique [physics.med-ph]; Probabilités [math.PR]; Statistiques [math.ST]

Americo Cunha Jr, Rubens Sampaio. On the nonlinear stochastic dynamics of a continuous system with discrete attached elements. Applied Mathematical Modelling, 2015, 39 (2), pp.809-819. ⟨10.1016/j.apm.2014.07.012⟩. ⟨hal-01438635⟩