A CLOSED FORM SOLUTION FOR FREE VIBRATION ANALYSIS OF TUBE-IN-TUBE SYSTEMS IN TALL BUILDINGS

In this paper the dynamic response of tube-in-tube systems for tall building structures is investigated. Inner and outer tubes are modeled using equivalent continuous orthotropic membranes; in which, each tube is individually modeled by a cantilever box beam. By applying the compatibility conditions on deformation of the two tubes, the governing dynamic equations of the tube-in-tube structure and their associated boundary conditions are derived using the variational principle of virtual work. Appling differential calculus and some simplifications, and deriving non-trivial solution of these equations, a closed form solution is presented to obtain natural frequency and mode shape of tube-in-tube structures. A quick estimate of these quantities is of particular importance at the early stages of tube-in-tube systems design, prior to a full dynamic analysis. In order to illustrate the efficiency of the proposed model two symmetrical buildings are analyzed and comparisons are made with more accurate results obtained by 3D computer dynamic analysis and previous published methods.