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; inwhich, each tube is individually modeled by a cantilever box beam. By applying the compatibilityconditions on deformation of the two tubes, the governing dynamic equations of the tube-in-tubestructure and their associated boundary conditions are derived using the variational principle of virtualwork. Appling differential calculus with 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-intube 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 a symmetrical building is analyzed and comparisons are made with more accurate results obtained by three dimensional computer dynamic analysis and previous published methods

Keywords:

Tall buildings , Tube-in-tube , Free vibration , Variational principle , Natural frequency , Mode Shape