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By N. Shanmugam, C. Wang

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1(b)) and distortional vibration (fold-line membrane displacements – see Fig. 1(c)). 1 (a) Global (flexural-torsional), (b) local-plate and (c) distortional vibration phenomena. 36 GBT-based local and global vibration analysis 37 The pioneer work addressing the local vibration of isotropic thin-walled members was carried out in the 1950s and disseminated through NACA (National Advisory Committee for Aeronautics) reports co-authored by Budiansky and Fralich (1954), Fitcher and Kordes (1959) and Thomson and Kruszewski (1961).

1 Formulation In a GBT formulation, the displacement field at a given member crosssection is expressed as a linear combination of orthogonal deformation modes, which makes it possible to write the equilibrium equations and boundary conditions in a unique and very convenient fashion − indeed, one is then able GBT-based local and global vibration analysis 41 to perform a very easy and ‘natural’ modal analysis of the cross-section deformed configuration that contributes to a deeper understanding about the thin-walled member structural behaviour.

E. M. Wang (eds), Woodhead Publishing Limited, Cambridge. A. and Abdoli-Yazdi, N. (1999), A modified Newmark method for the second order elastic analysis of beam-columns. Computers and Structures, 71, 689–700. L. and Tabarrok, B. (1992), Finite element formulation of a tapered Timoshenko beam for free lateral vibration analysis, Journal of Sound and Vibration, 152(3), 461– 470. W. and Penzien, J. (1975), Dynamics of Structures, McGraw-Hill, New York. D. F. (1965), Vibration frequencies of truncated-cone and wedge beams.

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Analysis and Design of Plated Structs. [V. 2 - Dynamics] by N. Shanmugam, C. Wang

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