Proper Generalized Decomposition for the dynamic analysis of uncertain structures
Résumé
The paper deals with the random frequency response of uncertain structure in the low frequency band and with a parametric vision of uncertainties. The dynamic analysis of uncertain structures requires fine spatial and stochastic approximations to well describe the non smooth random response with respect to the input parameters for the studied excitation frequency can be a resonance or anti-resonance depending depending on the values taken by the input parameters. In order to ease the solution of the stochastic partial differential equations in the context of spectral stochastic methods, we use the Proper Generalized Decomposition method which relies on the a priori construction of a separated representation of the solution and which only requires the solution of relatively small deterministic or stochastic problems. Two strategies are considered for multidimensional dynamic problems. The first one introduces a full separated representation associated with the tensor product space of the solution. The second one consists in first applying a two dimensional separated representation (deterministic/stochastic) and to consider a second level of separation by exploiting the tensor product structure of stochastic approximation spaces.
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