Robust characterization of the vibrational behaviour of light assembled structures with random parameters

Abstract

Predictive simulations of assembled structures raises some computational challenges for usual industrial structures. It is indeed necessary to deal with non-linear phenomena, such as contact or friction, and to consider sources of uncertainties mainly responsible for the deviation between the effective behaviour of the structure and results from deterministic simulations. Each of these two features of assembled structures requires intensive computational resources and the significant number of joints of actual structures increases even more the computational cost. In order to address such problems, this work aims to provide a pragmatic approach to robustly characterize the vibrational behaviour of light assembled structures considering the variability of the parameters of the joints. All the uncertainties of the whole problem are assumed to be associated to the joint interfaces. First, a nominal model of a joint consistent with the studied structure is identified using experimental data. Then a stochastic model of a joint is defined by considering the mechanical design variables of the nominal model as random variables. Based on an approximation of the maximum likelihood principle, the parameters of this stochastic model of joint are identified. A straightforward non-intrusive strategy referred to as the Stochastic Model Reduction (SMR) approach is used in the identification procedure of the stochastic model of the joint. The ease of implementation and the efficiency of the SMR approach justify this choice. The proposed approach is applied to an academic structure which is representative of light assembled structures: a three beam bolted frame. A stochastic model of joint characterized by its stiffness is thus implemented for each elementary joint of this frame. It allows us to characterize the variability of the vibrational behaviour of the frame taking into account the variability of each joint. Finally the comparison of the predicted stochastic response with the experimental behaviour of the structure shows that the proposed approach allows to tackle the variability of the actual structure. The proposed approach has been developed in the purpose of industrial applications. Based on a pragmatic modeling of the joint, a non-intrusive numerical tool and a stochastic modeling, the whole strategy could be indeed easily implemented on more complex industrial assemblies.

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