A new free vibration analysis method for space mega frames of super tall buildings

Abstract

A free vibration analysis method for space mega frames of super tall buildings is developed. The physical model of a mega frame is idealized as a three-dimensional assemblage of stiffened close-thin-walled tubes with continuously distributed mass and stiffness. One-variable functions defined on the nodal lines selected by the analyst are unknown functions (eigenfunctions) employed to describe the dynamic behavior of the model. By a Hamiltonian principle, the governing equations of the free vibration analysis can be obtained, which are a set of Ordinary Differential Equations (ODE) of the eigenfunctions with their corresponding boundary conditions. The desired vibration frequencies and corresponding vibration modes (eigenfunctions) can be obtained by numerically solving the system of ODEs with boundary conditions. The free vibration analysis also includes the coupling vibration modes of the collection composed by several nodal lines. The results from the illustration example show that the method is rational and powerful for the free vibration analysis of space-mega-frame systems.