Dynamic coupling of asymmetric shear wall structures: an analytical solution

In this paper, a dynamic analysis is presented for coupled flexural-warping torsional vibration of asymmetric shear wall structures in tall buildings. Due to the asymmetry of the structure, the free vibration is a coupled one, where laterally flexural vibrations in two orthogonal directions are coupled by a warping torsional vibration. 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 wall 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 and associated mode shapes of the structure. The proposed analysis is less approximate, and the numerical investigation pertaining to coupled vibration analysis of a generally asymmetric shear wall building shows that the results from the proposed analytical method and FEM analysis agree well. It is expected that the proposed analytical method of solution would enlarge the content of coupled vibration in the theory of dynamics of structures from theoretical research's point of view. (C) 2001 Elsevier Science Ltd. All rights reserved.