Coupled lateral–torsional frequencies of asymmetric, three-dimensional frame structures

Abstract

This paper presents a global analysis approach to the calculation of the natural frequencies of asymmetric, three-dimensional frame structures in which the primary frames run in two orthogonal directions and whose properties may vary through the height of the structure in a step-wise fashion at one or more storey levels. The governing differential equations of a substitute system are formulated using a continuum approach and posed in the form of a simple dynamic member stiffness matrix. Such a formulation allows for the distributed mass and coupled shear-torsion stiffness of the member and thus necessitates the solution of a transcendental eigenvalue problem. The required natural frequencies are finally determined using a stepped cantilever model in conjunction with the Wittrick-Williams algorithm, which ensures that no natural frequencies are missed. When the structure can be represented realistically by a uniform cantilever, solutions can be found easily by hand. A parametric study comprising four, three-dimensional, asymmetric frame structures is given to compare the accuracy of the current approach with that of a full finite element analysis.

Enhanced reduced model for elastic earthquake response analysis of a class of mono-symmetric shear building structures with constant eccentricity

“…Substitution of Eqs. (10) and (11) into Eqs. (8) and (9) leads to the solution of 1 k and 1 K to the inverse eigenmode problem.…”

“…Lateral-torsional coupling in earthquake response of building structures with eccentricity is one of the key issues in the field of earthquake structural engineering (for example [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]). This is because such response has complicated properties and is difficult to tackle.…”

Coupled axial-flexural-torsional vibration of Timoshenko frames

“…A few of them have dealt with the shear and rotatory inertia effects (Howson and Williams, 1973;Antes et al, 2004;Lin and Wu, 2005). The inclusion of the foregoing effects and out-of-plane flexure and/or torsion in the analysis is more rarely encountered (Mead, 2002;Heppler et al, 2003;Rafezy et al, 2007). The present paper is concerned with the more general problem of coupled axial-flexural-torsional free vibrations of a planar two-beam open frame that takes into account the axial extension, transverse shear and rotatory inertia effects.…”

Vibration Analysis of Asymmetric-Plan Frame Buildings Using Transfer Matrix Method

“…The continuum model is very simple and efficient method used in static and dynamic analysis of buildings. There are numerous studies [1][2][3][4][5][6][7][8][9][10][11][12] on asymmetric structures in the literature regarding continuum method. Kuang and Ng [4] considered the problem of doubly asymmetric structures; in which the motion is dominated by shear walls.…”

“…For the analysis, the structure was replaced by an equivalent uniform cantilever whose deformation was coupled in flexure and warping torsion. Rafezy and Howson [8] proposed a global approach to the calculation of natural frequencies of doubly asymmetric, three dimensional, multi bay, and multi storey frame structures. It was assumed that the primary frames of the original structure ran in two original directions and that their properties may have varied in a step-wise fashion at one or more storey levels.…”