Parametric analysis of the whole loading process of translation-torsion coupled vibration characteristics of the multi-layer bi-directional eccentric frame structure

Earthquake investigations confirm that irregular structures suffer more damage than their symmetric counterparts. The vibration mode of irregular structures is affected by the cou- pling of lateral and torsional vibration characteristics. The analysis of the lateral-torsional coupling effect is mainly limited to unidirectional eccentric structure or single-layer eccentric design. To fill this gap, this paper presents a parametric study of the whole loading pro- cess, exploring lateral-torsional coupling vibration characteristics of multi-layer bi-directional eccentric structures. The performed nonlinear static analysis revealed that the natural fre- quency of eccentric frames with different layers exhibited a general pattern with a three-stage evolution from elastic to elastic-plastic stages. Accordingly, three different elastic-plastic de- velopment stages of parametric analysis were defined. The effects of the uncoupled torsion-to- -lateral frequency ratios Ω and stiffness eccentricities on the translation-torsion coupled vi- bration characteristics in the above three stages were simulated via self-compiled programs on the MATLAB platform. The results obtained show that the range of Ω controlling the vibration characteristics was related to the eccentricities. Therefore, it was proposed to set different limit values of Ω in designing and analyzing the structures with different bi- directional eccentric degrees. At Ω = 1.1 ∼ 1.2, the coupling effect between bi-directional eccentricities led to transformation between the first- and second-order vibration modes, while the direction with the lowest lateral stiffness could not be directly judged as the structure first-order principal vibration direction. In the third stage, when the bi-directional eccentricities reached or even exceeded 0.3, the second and third modes transformed into each other.