# Seismic Response Study of L-Shaped Frame Structure with Magnetorheological Dampers
## 1 Introduction  
Magnetorheological fluid (MRF) is a new kind of smart fluid whose rheological characteristics are related to the strength of the magnetic field under the action of the magnetic field; MRFs can restore to the initial liquid state without the magnetic field [1]. Magnetorheological dampers (MRDs), semi-active control devices using MRFs, become effective damping control devices for controlling structural vibration because of advantages such as quick response, low energy consumption, large damping force, and being continuously adjustable. Therefore, MRDs have shown good application prospects in civil engineering earthquake mitigation and disaster prevention [2; 3; 4; 5; 6; 7; 8]. The mechanical performance of the MRD is an important factor affecting the efficiency of suppressing vibration control of structures [9]. Therefore, the performance of the MRD should be experimentally studied before the MRD is installed on the structure [10; 11]. Since 1996, many important experimental studies on the performance of MRDs have been carried out. [PERSON] et al. [12] designed and tested an MRD that had a 200 kN damping force. In 2003, [PERSON] et al. [13] developed a 400 kN MRD for a real base-isolated building, whose dynamic characteristics were verified through tests. [PERSON] et al. [14] carried out tests on a multi-stage shear-valve mode MRD, and the test results showed that the energy dissipation and the damping force increased significantly with the current until magnetic saturation occurred. [PERSON] et al. [15] presented a large-scale MRD that had a 500 kN damping force and carried out its performance experiments; the results showed that the damping forceincreased obviously with the increase of current, and when the current was 1.0 A, the maximum damping force provided by the MRD was 537 kN. The trends of the irregular plane frame structure [16; 17; 18; 19] have rapidly increased due to flexible column grid layouts and large practical spaces. However, the building structures with irregular planes are more susceptible to seismic forces than regular ones. The reason is that the center of mass has different positions from the center of rigidity in the irregular frame structure, and the torsional deformation of the structure caused by eccentricity is more likely to lead to structural failure. To reduce the torsional response of irregular structures, many experimental studies on the multi-dimensional seismic response of the irregular structure with MRDs have been carried out, and the results demonstrate that setting MRDs in the structure can efficaciously decrease the structural torsion response and the multi-dimensional dynamic response [20; 21; 22; 23; 24; 25; 26][PERSON]  
[PERSON] et al. [27] studied a three-story model structure with MRDs through tests and concluded that MRDs had a significant weakening effect on the peak and RMS responses caused by seismic excitations. [PERSON] et al. [28] conducted experimental research on a two-story structure model with an irregular column distribution and concluded that the responses of the structure were greatly reduced after adopting the semi-active controller. Although the analysis of the structure with MRDs has the advantages of obtaining accurate results and high reliability, it also has the disadvantages of high costs and being time-consuming. Moreover, numerical simulation analysis of the structure with MRDs is an effective and economical method to study the effect of structural torsion and multi-dimensional dynamic responses. Therefore, many scholars have used MATLAB programming to establish various models of the structures with MRDs. [PERSON] et al. [29] carried out the time history analysis on the elastic-plastic for the plane structure with MRDs, and the results showed that the amount of the yielding point and cracking point of the controlled structure obviously decreased and that MRDs can improve the seismic performance of the structure. [PERSON] et al.