# Vibration Response Characteristics of Prefabricated Frame Structures Around the Subway
## 1 Introduction  
To meet the demands of urbanization, subway mileage has been increasing annually, and prefabricated structures have gained wider application. However, subway operations have exacerbated environmental vibration issues [1]. Existing studies on the vibration characteristics of prefabricated frame structures in subway environments are scarce. Long-term vibration exposure can severely degrade human comfort in adjacent areas, interfere with sensitive equipment operation, and accelerate structural fatigue failure [2]. Thus, understanding vibration response patterns of such structures under subway-induced excitations is imperative. Prefabricated concrete frame joints are categorized into three types according to their load-bearing performance: rigid connections, pinned connections, and semirigid connections. Current research on prefabricated frames with semirigid connections has yielded two primary outcomes: (1) developing simplified yet accurate semirigid joint models describing M-\(\theta\) relationships through extensive experimental data fitting and (2) investigating how semirigid joints influence global structural mechanical behavior [3]. However, most seismic performance studies of prefabricated structures remain at the component level. Evaluating the seismic behavior of prefabricated frames with semirigid joints requires finite element analysis of complete structures, demanding substantial computational resources. Under limited computational capacity, researchers frequently adopt simplified joint models for holistic structural simulations. A common approachinvolves implementing zero-length spring elements in finite element platforms to represent joint behavior. In addition to modeling moment transfer through rotational springs, the axial stiffness of semirigid joints constitutes an essential modeling parameter. [PERSON] et al. (2004) [4] experimentally investigated the seismic performance of precast concrete beam-column joints. Under multiple seismic scenarios, significant crack propagation occurred at beam-slab connections, demonstrating that joint models must account for both rotational and axial stiffness. [PERSON] et al. (2008) [5] demonstrated via pseudodynamic testing that the axial stiffness of bolted semirigid connections between beams and columns is governed by bolt shear stiffness, where initial axial stiffness closely matches the shear stiffness of bolt cross-sections. Based on previous experimental studies, [PERSON] et al. (2017) [6] developed a bilinear semirigid joint model employing separate axial and rotational springs to represent translational and bending stiffness, with SAP2000 verification confirming its engineering applicability. [PERSON] et al. (2013) [7] conducted quasidynamic tests on a three-story concrete frame, revealing that reduced joint stiffness prolongs structural natural periods and significantly alters lateral displacements under varying stiffness conditions. [PERSON] et al. (2016) [8] compared structural responses under seismic action with varying joint stiffnesses, demonstrating significant influence of joint stiffness on dynamic behavior. Although existing research addresses semirigid joint impacts on prefabricated frames during earthquakes, the distinct spectral characteristics, duration, and magnitude of subway-induced vibrations warrant dedicated studies on vibration response patterns of semirigid prefabricated frame systems under subway operational conditions. Variations in beam cross-sections, column sections, slab thicknesses, total stories, and spans alter the vibration response of prefabricated frame structures under subway environments. Structural parameter changes and semirigid joint modifications exhibit coupled effects on vibration behavior.