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Structural Engineering and Mechanics
  Volume 8, Number 3, September 1999 , pages 243-256

Flexural free vibration of cantilevered structures of variable stiffness and mass

    Using appropriate transformations, the differential equation for flexural free vibration of a cantilever bar with variably distributed mass and stiffness is reduced to a Bessel\'s equation or an ordinary differential equation with constant coefficients by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass. The general solutions for flexural free vibration of one-step bar with variable cross-section are derived and used to obtain the frequency equation of multi-step cantilever bars. The new exact approach is presented which combines the transfer matrix method and closed form solutions of one step bars. Two numerical examples demonstrate that the calculated natural frequencies and mode shapes of a 27-storey building and a television transmission tower are in good agreement with the corresponding experimental data. It is also shown through the numerical examples that the selected expressions are suitable for describing the distributions of stiffness and mass of typical tall buildings and high-rise structures.
Key Words
    vibration, natural frequency, mode shape, tall building
Li QS, City Univ Hong Kong, Dept Bldg & Construct, Tat Chee Ave, Hong Kong, Hong Kong
City Univ Hong Kong, Dept Bldg & Construct, Hong Kong, Hong Kong

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