On the nonlinear dynamics of an inverted double pendulum over a vehicle suspension subjected to random excitations

Americo Cunha Jr (1) , Jorge Luis Palacios Felix (2) , José Manoel Balthazar (3)

1 UERJ - Universidade do Estado do Rio de Janeiro [Brasil] = Rio de Janeiro State University [Brazil] = Université d'État de Rio de Janeiro [Brésil]
2 UFFS - Universidade Federal da Fronteira Sul
3 Instituto Tecnológico de Aeronáutica

This paper deals with the nonlinear dynamics of a mechanical system which consists of an agricultural tower pulverizer, coupled with a vehicle suspension that is subject to random excitations due to soil irregularities. A deterministic mathematical model, where tower is considered as an inverted double pendulum over an vehicle suspension, with three degrees of freedom (one translation and two rotations) is constructed. To take into account the random loadings due to soil variabilities, a parametric probabilistic approach is employed, where the external force is assumed to be a harmonic random process. This stochastic process has random amplitude and frequency, which are modeled as random variables, and a sinusoidal shape in time. Once experimental data are not available for adjusting consistent distributions for these random variables, their distributions are constructed based only on theoretical information, using the maximum entropy principle. This procedure result in a system of stochastic ordinary differential equations, which defines a stochastic model for the problem. The propagation of uncertainties through the stochastic model is computed using the Monte Carlo method. Numerical simulations show large discrepancies in the system response obtained with the mean of the stochastic model and with the nominal (deterministic) model, and a high level of uncertainty associated. Also, an analysis of the system response probability distributions shows that they present asymmetries with respect to mean and unimodal behavior.

Mots clés: nonlinear dynamics; inverted double pendulum; agricultural tower pulverizer; uncertainty quantification; 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, Jorge Luis Palacios Felix, José Manoel Balthazar. On the nonlinear dynamics of an inverted double pendulum over a vehicle suspension subjected to random excitations. 23rd ABCM International Congress of Mechanical Engineering (COBEM 2015), Dec 2015, Rio de Janeiro, Brazil. ⟨10.20906/CPS/COB-2015-1694⟩. ⟨hal-01473586⟩