Vibrations of layered structures with fuzzy core stiffness/fuzzy interlayer slip

Abstract

Mainly the matrix in composite structures exhibits fuzzy randomness of the material parameters. When extending the work on two and symmetric, three layer beam-, plate- and shell structures based on the definition of an equivalent effective homogeneous model, to include either fuzzy interface slip or fuzzy core stiffness, we can avoid numerical analyses schemes and work out the effects on the dynamic properties of these fuzzy structures. Fully analyzed within the scope of this paper is a simply supported sandwich beam with fuzzy core material parameters. The analysis of this illustrative example is based on the interval representation (interval of confidence at a given level of presumption, i.e. α-cut) with a triangular fuzzy membership function of the core shear stiffness prescribed. Fuzzy membership functions of the natural frequencies are defined using fuzzy set theory, however, avoiding artificial uncertainties. Under time-harmonic excitation, the dynamic magnification factors and, with light modal structural damping taken into account, the fuzzy phase angles of the modal response are evaluated. Thus, modal superposition of forced vibrations becomes fuzzy in both, the time and the amplitude response. Where possible, envelope functions are defined.