FREE VIBRATION ANALYSIS OF COMBINED SYSTEM WITH VARIABLE CROSS SECTION

This paper deals with determining the fundamental frequency of tall buildings that consist of framed tube, shear core, belt truss and outrigger systems in which the framed tube and shear core vary in size along the height of the structure. A continuous approach is employed and by usiing hamiltons variational principle the governing equation for free vibration of tall building is obtained. The general solution of governing equation is obtained by making appropriate selection for mass and stiffness distribution functions. By applying the separation of variables method for time and space, the governing partial differential equation of motion is reduced to an ordinary differential equation with variable coefficients with the assumption that the transverse displacement is harmonic. A power-series solution representing the mode shape function of tall building is used. Applying boundary conditions yields the boundary value problem; the frequency equation is established and solved through a numerical process to determine the fundamental frequency. 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 sturctures dynamic characteristics it is easy to use yet reasonably accurate and suitable for quick evaluations during the preliminary design stages.

Keywords:

Framed Tube , Shear Core , Outrigger System , Belt Truss , Free Vibration , Variable Cross Section