A Simplified Dynamic Analysis of Symmetric Tube Structures Based on Hamiltonʹʹs Principle

In this paper, a mathematical model is presented for free vibration analysis of symmetric plan framed tube systems in tall buildings. Then, a closed form solution is derived for obtaining natural frequencies of framed tube structures. The analysis is based on continuum approach in which the framed tube structure is idealized as composed of four equivalent orthotropic plate panels. Therefore, framed tube structure is replaced by an idealized cantilever continuum representing the structural characteristics. Using the analytical method based on the Hamiltonʹs principle and theory of differential equation by considering boundary conditions and normalization of parameters, the governing equation for free vibration of the problem is developed, and the corresponding eigenvalue equation is then derived. A theoretical method of solution is proposed to solve the eigenvalue problem, and a general solution is given to determine the natural frequencies of the framed tube structure. By following the proposed calculation procedure, frequencies of the free vibration are quickly determined. The proposed method for predicting the natural frequencies of framed tube structures is shown to give good agreement with those obtained from computer analysis; thus, the proposed method offers a simple and efficient, yet accurate, means for free vibration analysis of framed tube systems in tall buildings.