Natural Periods of Coupled Shear Walls via Differential Transformation

Abstract eng:
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 period 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 used in these studies range 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. Motivated by conflicting results in the literature, particularly inaccuracies in a recent study, this paper re-examines the vibrational characteristics of coupled shear walls. The governing equation, established on the basis of replacing the coupling beams by equivalent laminae, is solved using the technique of differential transformation, which has been shown to provide rather accurate solution for eigenvalue problems. Solutions are shown to compare well with experimental results of model coupled shear walls published in the literature.

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