Reexamination of the Vibrational Period of Coupled Shear Walls by Differential Transformation

Abstract

In multistory buildings, coupled shear walls are frequently used as the main lateral load resisting system, the seismic design of which requires some knowledge of their periods of vibration. Although the vibrational characteristics of coupled shear walls have been extensively studied since the 1970’s, most of the studies were based on approximations resulting in varying degree of accuracies and complexities. Methods proposed by these studies ranged from the Rayleigh’s quotient to the Dunkerley’s formula, to the Galerkin’s method of weighted residuals, and to the solution of the Sturm-Louiville type differential equation. A review of the literature, including a recent publication, shows conflicting results regarding the accuracy and implementation of these methods. With this as motivation, this paper re-examines the vibrational characteristics of coupled shear walls and compares their periods of vibration with previous methods when available. The governing equation, established on the basis of replacing the coupling beams by an equivalent laminae medium, is solved as an eigenvalue problem using the recently developed technique of differential transformation. The convergence of solutions, which is important for numerical implementation, is investigated as part of this study.