Dynamic Analysis of Coupled Shear Walls and Sandwich Beams

A study is made of the free vibration of planar coupled shear walls, a common lateral load-resisting configuration in building construction where two walls are coupled together by a system of discrete spandrel beams. The differential equations and boundary conditions are obtained by the variational method, and by assuming that the spandrels can be replaced by a continuous system of laminae, or small beams. Natural frequencies and mode shapes are determined, and the results are presented in a number of figures from which the natural frequencies of any coupled shear wall can be extracted. The importance of including vertical displacement in the analysis is discussed, and a study of the effect of neglecting the vertical inertia term is given. These cases are illustrated with graphs and with one specific example. Investigations are also made of the asymptotic behavior of the system as the spandrels become weak, as they become stiff, and as the frequencies become large. Finally, the theory of sandwich beams is presented and compared to that for coupled shear walls. It is observed that for most cases of constant properties, the differential equations (and boundary conditions) reduce to the same mathematical form for both theories.