**1. Introduction**

With the recent continuous development of long-span spatial structures, the string dome, as a roof structure boasting light weight, high rigidity, good stability and strong spanning capability, has been widely adopted in large gymnasiums, opera houses and other public buildings such as the Tianbao Center Lobby, the 2008 Olympic Badminton Stadium, and the Jinan Olympic Sports Center Gymnasium [1,2]. The new square loops-string (SL-S) structure is one with pre-tensioned square ring cables and stay cables, in which struts bear axial compression and form a reliable support to arch up the lattice cylindrical shell. Compared with the traditional large-scale string dome structure, the square loops-string structure is simpler in lines, clearer in force transmission paths and better in force-bearing and antideformation performance of the roof grid beam structure. Such a structure has been integrated into the canopies of Shenzhen North Railway Station and the Fuzhou Strait Olympic Sports Center Gymnasium [3,4].

**Citation:** Lin, Z.; Zhang, C.; Dong, J.; Ou, J.; Yu, L. Dynamic Response Analysis of a Multiple Square Loops-String Dome under Seismic Excitation. *Symmetry* **2021**, *13*, 2062. https://doi.org/10.3390/sym13112062

Academic Editors: Yang Yang, Ying Lei, Xiaolin Meng and Jun Li

Received: 26 September 2021 Accepted: 21 October 2021 Published: 1 November 2021

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In addition to exhibition competitions and large-scale mass activities, the domestructure gymnasium can also serve as an earthquake refuge. Collapse of buildings during earthquakes causes serious casualties and economic losses. Much research has been carried out on recent years carried out by Chinese and foreign experts on the mechanical properties and stability of the string dome structure, such as seismic response and anti-seismic analysis [5–8], buckling and dynamic response under friction [9], model optimization design based on artificial neural networks [10], elastoplastic dynamic response [11], structural optimization algorithm and design [12–14], long-span discontinuous mechanical properties [15], initial geometric defect analysis [16], cable tension estimation [17], static and the dynamic analysis by finite element method [18,19], and thrust line analysis of masonry domes [20]. Gong, S.Y. [21] summarized the research on shape selection, statics and stability, dynamic and seismic resistance, prestress and optimization of the string dome. Li, X.Y. [22] used a simplified soil model through a modified SR method to analyze the dynamic characteristics and seismic response of a string dome structure under soil-structure interaction (SSI). Jiang, Z.R. [23] studied the nonlinear dynamic buckling of a long-span elliptic paraboloid string dome by introducing such factors as geometric nonlinearity, initial geometric defects, material elastoplasticity, and half-span live load distribution. Ruggieri, S. [24,25] developed a new numerical practical procedure to investigate the evaluation of floor deformability in the performance of a simple linear analysis on 3D numerical models by removing the rigid floor hypothesis and adopting a simple floor model, and defined a new approach for predicting the fundamental period of vibration for reinforced concrete buildings through regression analysis procedures of 40 new buildings using a numerical model with elastic dynamic parameters.

However, most of the current seismic response analyses on string structures are limited to the traditional string dome structure, without enough research on the dynamic characteristics of the latest string dome structure, i.e., the Multiple Square Loops-String (MSL-S) structure. Thus, a project adopting the MSL-S dome structure with the Fuzhou Strait Olympic Sports Center Gymnasium as the object of study, we used the time history method to analyze the internal force of cables and grid beams and the displacement response of grid beams under seismic excitation to provide a favorable reference for antiseismic responses of the MSL-S. The influence of two factors, namely, the near and far seismic fields and the seismic pulse, on the dynamic response of this structure was analyzed.
