Free Vibration and Frequency Calculation in Tall Buildings with Stepped Tube-in-Tube Systems

Abstract

This study investigates the free vibration and frequency analysis of tall buildings with stepped cross-sections for stepped tube-in-tube structures. Dynamic equations were presented in accordance with the stepped structural system for free vibration and the differential equations were solved according to the application of boundary conditions and flexural and shear stiffness and stepped cross-section of different steps. The answer was converted to an 8x8 matrix and was obtained using the determinants of matrix and mathematical calculations of frequency. Nine mathematical computational models were designed for stepped tube-in-tube structures for a 50-story tube-in-tube building by increasing the height of the outer tube by 15 meters. Finally, the heights of the inner and outer tubes were equalized by increasing the height of the outer tube and then compared with the results of free vibration in the articles with the tube-in-tube structural system with equal height and characteristics. Using this method, the frequency of structures was calculated correctly and the obtained results from finite element analysis showed that this mathematical method accurately calculated the frequency. It was found that this method was accurate enough and the obtained computational error was very small. The results showed that the frequency decreases by adding to the outer tube and increasing its height.