This paper deals with the nonusual case in structural dynamics for which a complex structure exhibits both the usual global elastic modes and numerous local elastic modes in the ¡ow-frequencv range. Despite the presence of these local elastic modes, we are interested in constructing a stochastic reduced-order model using only the global modes and in taking into account the local elastic modes with a probabilistic approach. In the ftrst part, a formulation and an algorithm, which allow the "global elastic modes" and the "local elastic modes" to be calculated, are presented. The second part is devoted to the construction of the stochastic reduced-order model with the global elastic modes and in taking into account the uncertainties on the effects of the local elastic modes by the nonparametrlc probabilistic approach. Finally, an application, which validates the proposed theory is presented.

International audienceThe paper is devoted to the identification of stochastic loads applied to a non-linear dynamical system for which experimental dynamical responses are available. The identification of the stochastic load is performed using a simplified computational non-linear dynamical model containing both model uncertainties and data uncertainties. Uncertainties are taken into account in the context of the probability theory. The stochastic load which has to be identified is modelled by a stationary non-Gaussian stochastic process for which the matrix-valued spectral density function is uncertain and is then modelled by a matrix-valued random function. The parameters to be identified are the mean value of the random matrix-valued spectral density function and its dispersion parameter. The identification problem is formulated as two optimization problems using the computational stochastic model and experimental responses. A validation of the theory proposed is presented in the context of tubes bundles in Pressurized Water Reactors

The present paper proposes a novel hysteretic (non-reversible) bit/rock interaction model for the torsional dynamics of a drill string. Non-reversible means that the torque-on-bit depends not only on the bit speed, but also on the bit acceleration, producing a type of hysteretic cycle. The continuous drill string system is discretized by means of the finite element method and a reduced-order model is constructed using the normal modes of the associated conservative system. The parameters of the proposed hysteretic bit/rock interaction model is fitted with field data. The non-linear torsional vibration and the stability map of the drill string system are analyzed employing the proposed bit/rock interaction model and also a commonly used reversible model (without hysteresis). It turns out that the hysteretic model affects the stability region of the system.

Frequency domain homogenization for the viscoelastic properties of spatially correlated quasi-periodic lattices,