Effects of a random cubic spring on the longitudinal dynamics of a bar excited by a Gaussian white noise

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

1 PUC-Rio

The study of the stochastic dynamics of continuous structures coupled with discrete elements is of interest in some fields of structural engineering. In this way, this papers deals with the analysis of the effects induced by a cubic spring, with gamma distributed random stiffness, on the longitudinal dynamics of an elastic bar which is also coupled with linear spring and a lumped mass. This system is subjected to a viscous dissipation mechanism and is excited by a Gaussian white noise. The model equations are discretized using the Galerkin method, and the propagation of uncertainties through the model are computed by the Monte Carlo method. Numerical simulations, indexed by the mean value of the cubic spring random stiffness, are conducted and show that this random cubic nonlinearity induces an increase in the level of uncertainty of the system response, in comparison with the linear case. Also, the random nonlinearity generates system responses which exhibit asymmetric and multimodal probability distributions.

Mots clés: nonlinear dynamics; continuous-discrete system; uncertainty quantification; Monte Carlo method; parametric probabilistic approach

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

Americo Cunha Jr, Rubens Sampaio. Effects of a random cubic spring on the longitudinal dynamics of a bar excited by a Gaussian white noise. 2nd International Symposium on Uncertainty Quantification and Stochastic Modeling (Uncertainties 2014), Jun 2014, Rouen, France. ⟨hal-01473588⟩