# Dynamic Response Analysis of Mega-Sub Isolated Structures under Multiaxial Earthquakes
## 2 Mega-Sub Isolation Structural Model  
The model has 25 floors, with a total plan size of 30 m \(\times\) 48 m and a total height of 97.5 m, and each floor of the sub-frame is 3.9 m. The mega-beams are made of H-beams, with a total height of 3.9 m and a width of 6 m; the mega-columns are arranged at the four corners of the building plan and combined with the mega-beams to form a three-floor main frame structure. There are three sub-structures between the foundation and the mega-beam and between the mega-beam and the mega-beam, named subframes 1, 2, and 3, respectively, from the bottom up. The isolation joints between the main frame and the sub-structure are 400 mm wide. In the mega-sub isolated structure, the first sub-frames are only solidly connected to the foundation and have no connection with the surroundings and top of the main frame. Furthermore, the maximum displacement of the ground floor subframe under rare earthquakes is empirically calculated to be less than 400 mm, so the influence of the sub-structure is ignored in the following analysis, as shown in Figure 1. A seismic isolation layer formed by seismic isolation bearings is provided between the main and sub-structures. In this paper, using the model shown in Figure 1[32; 33], the vibration isolation substructure is simplified to a single mass point. In the calculation example: the main  
Figure 1: Simplified process for calculating the model: (**a**) Mega-sub isolation structural model; (**b**) Computational model. frame with three layers, as shown in Figure 1, \(m_{1}\) = 17.44 \(\times\) 10\({}^{5}\) kg, \(m_{2}\) = 17.96 \(\times\) 10\({}^{5}\) kg, \(m_{3}\) = 19.24 \(\times\) 10\({}^{5}\) kg; in the substructure, \(m_{4}\) = \(m_{5}\) = 19.24 \(\times\) 10\({}^{5}\) kg. The horizontal stiffness of the main frame from bottom to top is \(k_{1\text{x}}\) = 2.3 \(\times\) 10\({}^{8}\) N/m, \(k_{2\text{x}}\) = 2.8 \(\times\) 10\({}^{8}\) N/m, \(k_{3\text{x}}\) = 3 \(\times\) 10\({}^{8}\) N/m; the horizontal stiffness of isolation layer is provided by the horizontal stiffness of bearing, in which the horizontal stiffness of substructure isolation layer is: \(k_{4\text{x}}\) = 5.3 \(\times\) 10\({}^{7}\) N/m, \(k_{5\text{x}}\) = 4.6 \(\times\) 10\({}^{7}\) N/m. The vertical stiffness of the main frame is taken from the top to the bottom floor as, \(k_{1\text{z}}\) = 8.72 \(\times\) 10\({}^{9}\) N/m, \(k_{2\text{z}}\) = 10.72 \(\times\) 10\({}^{9}\) N/m, \(k_{3\text{z}}\) = 11.52\(\times\)10\({}^{9}\) N/m. The vertical stiffness of the sub-structure seismic isolation layer is, respectively, \(k_{4\text{z}}\) = 2.31 \(\times\) 10\({}^{9}\) N/m and \(k_{5\text{z}}\) = 1.96 \(\times\) 10\({}^{9}\) N/m. The damping ratio of the main frame was taken as 0.05. The peak displacement dynamic response was used as an indicator to study the variation law. The parameters of the seismically isolated structure in the horizontal direction are first investigated, followed by the analysis of the parameters in the vertical direction. [PERSON] et al. [34] carried out an earthquake dynamic time course analysis and found that: the earthquake response of main and sub-structures under the action of different seismic waves are different, and the dynamic response of the structure is largest under El Centro seismic wave. Meanwhile, [PERSON] et al. [35] summarized the main earthquake response time analysis methods and their characteristics. According to the above-simplified model, in order to better parameterize the mass, stiffness, and damping, the Newmark-\(\beta\) time integration method was finally used to study the influences of El Centro seismic wave, parameters, ground shaking excitation direction and other relevant parameters on the dynamic response of the main and substructure in conjunction with the research content of this paper.