# A Time-History Contact Force Model of the Dynamic Load of AERORail Structures
## 1 Introduction  
The AERORail Transportation System is a new type of transportation system in the form of a cable-supported rail combined structure composed of multi-span continuous string cables, rails, lower supports and related power supply and control systems [1]. The load bearing system of AERORail consists of two rails supported by prestressed cables. AERORail is advantageous for its reduced construction cost and time, which are attributed to its simplified structure and lightweight design. A full-scale model of AERORail was reported by [PERSON] et al. [2], who studied the full-scale model's acceleration and displacement response under a two-axle vehicle. Besides the structural responses during the vibration, the contact force between the vehicle and the structure is also an intriguing topic [3, 4]. Based on fundamental frequency analysis of the structure and the dynamic load test, the variation of the contact force in AERORail was studied and identified using the time domain identification method by [PERSON] et al. [5] in the previous study. It was proved that the occurrence time and frequency of the contact force are highly related to the passing time of the vehicle. However, the study was based on a limited number of experiments and was limited to low speed and 5-10 m spans. The vibration of large-span AERORail systems under high-speed vehicles is still open to discussion. Besides the absence of this knowledge, there is also a gap between the experiment data and a convincing model that depicts the variation of the contact force, which is essentially a load to the structure. Though a vehicle-structure model for the AERORail was reported by [PERSON] et al. [5], a load model applicable to static or dynamic analyses of AERORail is yet to be found. Due to the difference between the characteristics of the AERORail and conventional structures, it is necessary to investigate the contact force and devise a load model in order to promote the AERORail to its application.  
The traditional way to estimate the live load to a bridge is by survey or the weight-in-motion system [6; 7]. These methods are designed to obtain the probability density of distribution for multiple vehicle types. As was discussed by [PERSON] et al. [5], the force between the vehicle and structure shows dramatic fluctuation due to the vibration, therefore the axle weight of the vehicle cannot be regarded as the contact force. The weight-in-motion system is also inapplicable for the current study due to the no-deck design of AERORail. Thus, an alternative approach must be utilized to obtain the load model based on the history of the contact force.  
This paper used Bezier curves to establish a time-history load model of the AERORail structure by approximating the contact force from [PERSON] et al. [2]. The contact force was identified from the acceleration data of the structure during vehicle running. In order to validate the load model obtained, the displacement response of AERORail under the proposed load curves was compared to available experiment data. Furthermore, the structural response of large spans under high-speed vehicles was investigated via the proposed load model.