A simple approximate method for free vibration analysis of framed tube structures

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Abstract
SUMMARY: A simple approximate method is developed for determining natural frequency of tall buildings. Timoshenko's beam model, which considers the influence of shear and flexural deformation, was used in modelling framed tube structures. In this paper, natural frequency and mode shape of framed tube structures were calculated based on the flexural and shear rigidities along with the effects of rotational inertia. Dynamic model of Timoshenko's beam can be obtained by writing equilibrium equations of forces acting on an infinite element. The solution of the dynamic model was obtained by first applying the separation of variables to time and space, followed by the assumption of harmonic motion in time, the steady state eigen system was obtained. Natural frequencies of framed tube structures were calculated by solving the eigenproblem. A numerical example has been presented to demonstrate the ease of application and accuracy of the proposed method. The structure's fundamental frequency was computed using ETABS V9.0.0 (Computer and Structures, Berkeley, California, USA) and compared with the result obtained from proposed method, which shows that the percentage of error was low and acceptable. The proposed method can be adopted as an alternative procedure to evaluate the natural frequency of framed tube in the preliminary stages of structural design. Copyright © 2010 John Wiley & Sons, Ltd.

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