VIBRATION ANALYSIS OF TALL BUILDINGS WITH NARROW RECTANGULAR PLANE CONFIGURATION

In this paper, tall buildings of narrow rectangular plane configuration are treated as one-step or multi-step cantilever flexural-shear plates for the analysis of their free vibrations. The governing differential equations for the vibration of flexural-shear plates considering the effects of both flexural and shear deformation are established. The general solutions for one-step flexural-shear plates are derived and used to obtain the eigenvalue equation for multi-step cantilever flexural-shear plates. A new exact approach is presented which combines the transfer matrix method and a closed-form solution for a uniform flexural-shear plate. A numerical example demonstrates that the calculated natural frequencies and mode shapes of a tall building are in good agreement with the experimentally measured data. It is also shown that the effect of shear deformation on the fundamental natural frequency can be ignored, but its effect on the higher natural frequencies should be considered. © 1998 John Wiley & Sons, Ltd.