Free Vibration Analysis for Step Tubular Structures of Tall Buildings Supported on Elastic Foundation Soil

Abstract

A method based on Ordinary Differential Equations (ODE) solver for free vibration analysis of tubular structures of tall buildings is developed, considering the deformation of the foundation soil as well as the interactions between the foundation and soil, by means of a three dimensional model with continuously distributed mass and stiffness. The nodal lines employed to discretize the computational model of the structures are one-variable functions defined on the nodal lines selected by the analyst to describe the dynamic behavior of the model. The unknown functions determined numerically herein are actual vibration modes that can be also recognized as the deformation functions of a set of conceptual structural components. 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 vibration modes with their corresponding boundary conditions. The desired frequencies and corresponding vibration modes can be obtained by numerically solving the ODEs with boundary conditions. The method is applied to the tubular structures of tall buildings. The results from the illustration example show that the method is rational and powerful for the free vibration analysis of tall buildings.