An analytical model for dynamic response analysis of tubular tall buildings

In this paper, on the basis of the D'Alembert's principle, approximate formulas for dynamic response of tubular tall building structures are presented. Using D'Alembert's principle and applying the compatibility conditions on deformation of the tubes, the governing dynamic equation of the tubular structure's motion is derived. Then, natural boundary conditions of the parallel cantilevered flexural–shear beams are derived, and by using Rayleigh–Ritz method, value problem is solved, and trivial and nontrivial solutions are derived, which can be used for calculating natural frequencies and mode shapes of tubular structures. By solving numerically the frequency equation, a design chart and graph are given for the first five nondimensional natural frequencies of tubular tall buildings. The proposed mathematical model gives dynamic characteristics and provides a simple, efficient and reasonably accurate algorithm for free vibration studies that are needed to be quick at the preliminary design stages of tall buildings with tubular systems. Copyright © 2012 John Wiley & Sons, Ltd.