R. Heuer, F. Ziegler:

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

in: "Proc. IUTAM-Symp. on The Vibration Analysis of Structures with Uncertainties", A. Belyaev et al. (ed.); issued by: Russian Academy of Sciences; Springer, Dordrecht Heidelberg, 2011, ISBN: 978-94-007-0288-2, 29 - 42.

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. a-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.

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