A theoretical formulation of the dynamical response of a master structure coupled with elastic continuous fuzzy subsystems with discrete attachments

We present the formulation of the dynamic response of a master structure coupled with a locally homogeneous and orthotropic structural fuzzy, with discrete attachment, composed of elastic continuous fuzzy subsystems. As introduced by Soize, the master structure is the part of the coupled system which is accessible by classical modeling, whereas the structural fuzzy represents systems connected to the master structure, whose characteristics are imprecisely known. A deterministic formulation of the boundary impedance of a general continuous structural fuzzy, which models its action on the master structure, is derived: it is shown that the formulation is different from the solution proposed by Soize in the context of the type I fuzzy law, established from the deterministic model of a linear oscillator excited by its support. Finally, the general boundary impedance is applied to the special situation of a structural fuzzy composed of elastic bars whose geometrical parameters are randomly defined, and numerical results are presented.