Exploring Monte Carlo method to access the dynamical behavior of a continuous random system

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

1 PUC-Rio

The dynamics of a mechanical system depends on some parameters such as physical and geometrical properties, external and internal loading, initial and boundary conditions, etc. If all of these parameters are constant, then the system is deterministic and its behavior is described by a single set of differential equations. On the other hand, if one or more of the these parameters are random, the mechanical system is stochastic and there is a family of differential equations sets (one for each realization of the random system) associated to the same. Therefore, it is necessary to compute statistics of the random system realizations to characterize the dynamics of the stochastic mechanical system. This work illustrates the analysis of a one-dimensional elastic bar, with random elastic modulus and subjected nonlinear external force. The analysis is done through Monte Carlo method, where a large amount of realizations of the random system is obtained via numerical simulations. Then statistics of these realizations are computed, and these statistics reveal information about the average behavior of the random system.

Mots clés: Galerkin method; uncertainty quantification; stochastic modeling; nonlinear dynamics; Monte Carlo method

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. Exploring Monte Carlo method to access the dynamical behavior of a continuous random system. Congresso de Matemática Aplicada e Computacional - Nordeste (CMAC-NE 2012), Nov 2012, Natal, Brazil. ⟨hal-01487367⟩