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Free longitudinal vibrations of tall buildings and high-rise structures

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Abstract:

In this paper, tall buildings and high-rise structures are considered as cantilever bars with variable cross-section for the analysis of their free vibrations. The differential equations of free longitudinal vibrations of bars with variable cross-section are reduced to Bessel’s equations by selecting suitable expressions, such as power functions and exponential functions, for the distribution of stiffness and mass. An approach is proposed for determining the natural frequencies and mode shapes in the vertical direction for tall buildings and high-rise structures with variably distributed stiffness and variably distributed mass. The derived solutions are expressed in terms of Bessel functions. A numerical example shows that the value of the natural frequency computed by the proposed method is close to full scale measured data. It is shown that the selected expressions are suitable for describing the distributions of stiffness and mass of tall buildings and high-rise structures. It is demonstrated that the proposed method has practical significance for free longitudinal vibration analysis. © 1998 John Wiley & Sons, Ltd.

Document Type: Research Article

Affiliations: Structural Dynamics Research Centre, Department of Building and Construction, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

Publication date: 1998-06-01

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