Dynamic Characteristics of Coupled Shear Walls

The first three natural frequencies and the corresponding mode shapes for fixed-base coupled shear walls are presented. The wall is modeled as a continuum of uniform properties and the resulting sixth-order homogeneous differential equation in terms of lateral displacement is solved exactly using appropriate numerical methods. The results are presented for various combinations of the two nondimensional parameters which between them incorporate all the geometric and material properties of the wall system. The mode shapes are presented in terms of the first three normal modes of a uniform slender cantilever. The nondimensional base shears appropriate for the response spectrum analysis of the walls under seismic loading are also given for the three modes and for the various combinations of the wall parameters referred to earlier. The results show that the coupled wall mode shapes cannot be adequately approximated by the corresponding shapes for a slender cantilever.