Vibration analysis of doubly asymmetric, three-dimensional structures comprising wall and frame assemblies with variable cross-section

A global analysis approach to modelling doubly asymmetric, three-dimensional, multi-bay, multi-storey, wall–frame structures is presented in a form that enables the lower numbered natural frequencies to be determined approximately with the certain knowledge that none have been missed. It is assumed that the primary walls and frames of the original structure run in two orthogonal directions and that their properties may vary in a step-wise fashion at one or more storey levels. The structure therefore divides naturally into uniform segments between changes of section properties. A typical segment is then replaced by an equivalent shear–flexure–torsion coupled beam whose governing differential equations are formulated using a continuum approach and posed in the form of a dynamic member stiffness matrix. The original structure can then be re-modelled as a sophisticated stepped cantilever 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. A parametric study on a series of wall–frame structures of varying height with different plan configurations is given to compare the accuracy of the current approach with datum results from fully converged finite element analyses.