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 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.