Elimination of internal structural variables through explicit Taylor-Laurent model reduction, with applications to damped sandwich plates

摘要

This paper introduces and discusses explicit condensation methods based on Taylor-Laurent expansion of dynamic responses. The major contribution is the formulation in free-floating conditions of a "degeneracy theorem", stipulating that Laurent coefficients of an embedded subsystem are always invertible, while those of a free autonomous system are always singular matrices. From this, an original sensitive technique - termed "Covering- Censoring reduction" - where the quality of the results can be checked before condensation is performed, is described and then applied to the problem of vibration and acoustic radiation (transmission loss) of sandwich plates (more precisely, plates with attached constrained layer damping). The method presented in the paper is of great interest in several applications necessitating the condensation of internal and/or secondary degrees of freedom.