Nonlinear dynamics of structures

This theme concerns the development of models and methods for analyzing and simulating the response of structures in non-linear dynamic regimes. The non-linearities in question can have several origins: material, geometric or boundary conditions. As far as numerical methods are concerned, whether they involve deterministic or random models, the aim is to develop alternative analysis tools to time integration, which is not very effective for obtaining steady-state conditions. Another difficult but important challenge is the construction of reduced models based either on "Proper Generalised Decomposition" techniques, or on the extension of concepts usually used in linear analysis. The calculation and exploitation of non-linear modes of structures is an activity for which the LMA has gained a certain international recognition. Finally, we are also interested in the construction of models dedicated to particular structures (enriched models for structural deployment). Applications range from musical instruments to the study of the vibratory behavior of nuclear fuel rods.