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By N. Shanmugam, C. Wang

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Proceedings of First World Conference on Earthquake Engineering, Berkley, California, 1956. S. S. (1958), Engineering Vibrations, McGraw-Hill, New York. K. and Raciti, S. (1989), Recent advances in analysis of laminated beams and plates, part II: vibrations and wave propagation. American Institute of Aeronautics and Astronautics Journal, 27, 935–946. L. E. (1983), Static, dynamic and stability analysis of structures composed of tapered beams. Computers and Structures, 16(6), 731–748. Kirchhoff, G.

1 where (i) (⋅),x ≡ ∂ (⋅)/∂x, (ii) the summation applies to subscript k and (iii) the time-dependent function φk(x, t) stands for the variation of the displacement profiles uk (s), vk(s) and wk (s) along the member length L and with time. g. 2 Thin-walled member: (a) geometry, axes/displacements; (b) cross-section discretisation. 42 Analysis and design of plated structures where E and ν are Young’s modulus and Poisson’s ratio. 3 which incorporate Vlasov’s assumptions of null membrane shear and transverse extension strains along the cross-section mid-line (Vlasov 1959) – the commas denote partial differentiation.

As it would be logical to expect, this study revealed that the local deformations affect even the lower-order vibration behaviour of such members. Another relevant contribution was due to Gavrić (1994), who formulated a shell finite element that was subsequently used to determine the vibration amplitude and number of half-waves of tubular and I-section members excited in a given frequency domain − this researcher concluded that the analytical results based on Euler–Bernoulli’s classical beam theory do not correlate well with the numerical values, owing to the influence of the in-plane crosssection deformation, an effect that was found to be particularly relevant in the I-section members.

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