Determination by analytical approach of the characteristics in free vibration of a complex asymmetric structure

In this paper, a new analytical calculation method is presented to study the free vibration behavior of a tall building structure with constant properties over its entire height. The proposed calculation method is based on Alembert's principle, and the continuum approach of a structure composed of walls, frames, and structural cores arranged asymmetrically according to the plane of the floor. The main idea of the present model is to associate both the coupling effect of the flexural stiffness and the shear stiffness in the differential equations governing the free vibration behavior of the structure. The analysis focuses on the determination of the free coupled vibration characteristics. According to the two orthogonal directions, the lateral bending-shear vibrations are coupled to the torsional vibrations of St-Venant. A generalized solution method is proposed using the Galerkin approach to determine the frequencies and associated mode shapes of coupled free vibration structures. The obtained results were in good agreement with those found in the literature