Free vibration of tall buildings using Timoshenko beams with variable cross-section

摘要

The free vibration of Timoshenko beams with varying cross-section is reduced to an analytical solvable standard differential equation. This equation form depends on the specific moment of inertia, cross-section area and mass variation. The more accurate mode shapes and natural frequencies can be obtained by combining the effects of shear and flexural deformation. In this paper the main differential equation of vibration which involves flexural and shear effects (Timoshenko beam without rotary inertia effect) is obtained. The general solution of the main vibration equation has been derived by selecting suitable expressions such as power and exponential functions for the stiffness and mass distribution. Tall structures can be treated as cantilever beams with variable cross-section for their free vibrational analysis. The natural frequencies and mode shapes of tall buildings can be obtained by applying the proposed general solution of Timoshenko beams with varying cross-section. The calculated frequencies and mode shapes with the proposed method are compared with measured values and show high accuracy.