Vibration characteristics of tall buildings braced by shear walls and thin‐walled open‐section structures

An analytical method is presented for the three‐dimensional frequency analysis of buildings braced by shear walls and thin‐walled open‐section structures. Owing to the asymmetry of the structure, the centre of gravity and the centre of flexural rigidity of the floor plan do not coincide, and hence the flexural vibration in two mutually perpendicular directions and the warping torsional vibrations are all coupled. Based on the continuum approach and D'Alembert's principle, the governing differential equation of free vibration and its corresponding eigenvalue problem for asymmetric shear walls and thin‐walled open‐section structures are derived. Based on the theory of differential equations, an analytical method of solution is proposed to solve the eigenvalue problem and a general solution is derived for determining the natural frequencies of the structures. Results obtained from the proposed method for the example structure show good agreement with those of finite element analysis. It is also shown that the proposed analysis is efficient and accurate enough to be used both at the concept design stage and for final analysis. Copyright © 2007 John Wiley & Sons, Ltd.