#### Vol. 6, No. 1-4, 2011

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Modal analysis of laminated beams with fuzzy core stiffness/fuzzy interlayer slip

### Rudolf Heuer and Franz Ziegler

Vol. 6 (2011), No. 1-4, 213–230
##### Abstract

It is mainly the matrix in composite structures that exhibits fuzzy randomness of the material parameters. When extending the work on two-layer and symmetric, three-layer viscoelastic beam, plate, and shell structures based on the definition of an equivalent effective homogeneous model, to include either fuzzy pure elastic interface slip or fuzzy core stiffness, by means of modal analysis we succeed in working out the effects on the dynamic properties of these fuzzy structures. Modal coupling by the light damping forces is neglected. Fully analyzed within the scope of this paper is a simply supported sandwich beam with fuzzy elastic core material parameters. The analysis of this illustrative example is based on the interval representation (that is, on the set of $\alpha$-cuts) with a triangular membership function of the core shear stiffness prescribed. Membership functions of the undamped natural frequencies are defined using fuzzy set theory, however, avoiding artificial uncertainties. Under time-harmonic excitation, the dynamic magnification factors and, with light and deterministic modal structural damping taken into account, the fuzzy phase angles of the steady modal response are evaluated. Where appropriate, envelope functions are defined.

 Dedicated to the memory of the late Marie-Louise and in the honor of Professor Charles R. Steele
##### Keywords
layered beams, fuzziness, interlayer slip, modal analysis, isosceles uncertainty