FREE VIBRATION ANALYSIS OF TALL BULINDING WITH GEOMETRICAL DISCONTINUITES

This paper deals with to determine the first natural frequency of tall buildings consists of framed tube, shear core, belt truss and outrigger system with multiple jumped discontinuities in the cross section of framed tube and shear core. In this paper, the continuous approach was accepted and by using energy method and Hamilton’s variational principle, the governing equation for free vibration of tall building can be obtained. The entire length of tall building is partitioned into uniform segments between any two successive discontinuity points and therefore partial differential equation of motion, by applying the separation of variables method on time and space, is reduced to an ordinary differential equation with constant coefficients for each segment. Tall building characteristics matrix can be derived based on the boundary conditions and the continuity conditions applied at the partitioned points. This matrix is particularly used to find combined system natural frequencies and mode shapes. A numerical example has been solved to demonstrate the reliability of this method. The results of the proposed mathematical model give a good understanding of the structure’s dynamic characteristics; it is easy to use, yet reasonably accurate and suitable for quick evaluations during the preliminary durations.