Low-frequency/medium-frequency analysis of a master structure coupled with fuzzy substructures

Abstract

Interest has been expressed in predicting the linear vibrations of a complex structure constituted of a weakly damped master structure coupled with weakly damped substructures presenting structural complexity. In the analysis frequency band, the master structure has a modal response (low-frequency behavior) and the substructures have nonmodal responses (medium-frequency behavior). The master structure is modeled by an inhomogeneous anisotropic linear viscoelastic bounded three-dimensional solid continuum. The substructures, which are not accessible to conventional modeling (because details are unknown or are imprecisely known), are modeled within the context of fuzzy structures theory, previously developed by the author. The response of this fuzzy structure is calculated using the Ritz–Galerkin method based on the modes of the master structure. The model of fuzzy substructures depends on parameters which are the dimensionless mean coefficients of participating fuzzy masses. Two methods are presented for estimating these parameters. One is adapted to the identification by experiments, the other one is based on a theoretical approach which uses a mean power flow equation of the fuzzy structures. An example is presented.