Coupled lateral–torsional frequencies of asymmetric, three-dimensional structures comprising shear-wall and core assemblies with stepwise variable cross-section

A simple and accurate model for asymmetric, three-dimensional wall-core structures is developed that enables any desired natural frequency to be determined by a method which guarantees that no natural frequencies can be missed. The model assumes that the primary walls and cores run in two orthogonal directions and that their properties may vary in a stepwise fashion at one or more storey levels. A vectorial approach is used to generate the governing differential equations for coupled flexural-torsional motion that are finally incorporated into an exact dynamic stiffness matrix (exact finite element) that can model any uniform segment of the structure. A model of the original structure can then be assembled in the usual way. Since the mass of each segment is assumed to be uniformly distributed, it is necessary to solve a transcendental eigenvalue problem, which is accomplished using the Wittrick–Williams algorithm. When the structure can be represented realistically by a uniform cantilever, solutions can be found easily, by hand. A parametric study comprising five, three-dimensional, asymmetric wall-core structures is given to compare the accuracy of the current approach with that of a full finite element analysis.