Dynamic properties of planar, coupled shear walls

The paper is a study of the natural frequencies and mode shapes of planar, coupled shear walls, a common lateral resistive element in building construction. The equations of motion are derived for the general case, and the eigenvalue problem associated with free vibrations of equal, constant shear walls is solved, both with and without the inclusion of the inertia of vertical motion. Explicit solutions are presented for the characteristic equation and the mode shapes and the results are illustrated with figures, including an example calculation based on the shear walls of the Mt. McKinley Building, damaged by the Alaskan earthquake of 1964. The results affirm the necessity of including vertical displacement of the shear walls in the analysis of such systems, and suggest that the inertia of vertical motion also must be considered in the analysis for certain ranges of the parameters.