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Free vibration analysis of coupled shear walls with axial force effects

In this article, an approximate method of determining the vibrational frequencies of coupled shear walls with inclusion of axial force effects is presented. For this purpose, first the continuum approach is adopted for modelling linked beams. Then by applying force equilibrium conditions to each of the walls, and enforcement of displacement compatibility relations for the inflection point of linked beams subjected to bending, the governing differential equation of a statically loaded structure is formed. Using D'Alembert's principle, this equation is converted to a structural dynamics equation. The obtained model is a partial differential equation in space and time. Using separation of variables, two independent differential equations are further obtained, one of which, depends on time and the other on position. Finally, a new method of determining natural frequencies of coupled shear wall structures with axial force effect is presented. Also comparisons between the proposed method, finite element analysis and published results are presented.