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Structural Engineering and Mechanics   Volume 11, Number 4, April 2001, pages 357-372
Evaluation of vertical dynamic characteristics of cantilevered tall structures
Q.S. Li(Hong Kong), J.Y. Xu and G.Q. Li(China)

Abstract     [Buy Article]
    In this paper, cantilevered tall structures are treated as cantilever bars with varying cross-section
for the analysis of their free longitudinal (or axial) vibrations. Using appropriate transformations,
exact analytical solutions to determine the longitudinal natural frequencies and mode shapes for a one step
non-uniform bar are derived by selecting suitable expressions, such as exponential functions, for the
distributions of mass and axial stiffness. The frequency equation of a multi-step bar is established using
the approach that combines the transfer matrix procedure or the recurrence formula and the closed-form
solutions of one step bars, leading to a single frequency equation for any number of steps. The Ritz
method is also applied to determine the natural frequencies and mode shapes in the vertical direction for
cantilevered tall structures with variably distributed stiffness and mass. The formulae proposed in this
paper are simple and convenient for engineering applications. Numerical example shows that the
fundamental longitudinal natural frequency and mode shape of a 27-storey building determined by the
proposed methods are in good agreement with the corresponding measured data. It is also shown that the
selected expressions are suitable for describing the distributions of axial stiffness and mass of typical tall
Key Words
    longitudinal vibration; tall buildings; high-rise structures; natural frequencies; mode shapes.
Q.S. Li, Department of Building and Construction, City University of Hong Kong
Tat Chee Avenue, Kowloon, Hong Kong
J.Y. Xu and G.Q. Li, Department of Civil Engineering, Wuhan University of Technology, Wuhan 430070, China

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