A hybrid formulation for mid-frequency analysis of assembled structures

A new formulation able to predict the behaviour of structures in the mid-frequency range is presented in this paper. The mid-frequency field is a hybrid domain for which assembled structures exhibit simultaneously low- and high-frequency behaviours, depending on the material and geometrical properties of different subsystems. Thus, dealing with the mid-frequency field requires simulation methods which are able to account the differences in behaviour of different subsystems. The hybrid formulation is based on the coupling of two different formulations, the finite elements for the low-frequency behaving subparts and a probabilistic formulation, the smooth integral formulation, applied to the high-frequency subsystems. The hybrid method enables to correctly predict the deterministic response of the low-frequency parts which is not affected by randomness, and the smooth trend of the contributions of the high-frequency parts. The paper is concluded with several numerical examples computed for coupled one- and two-dimensional structures.