## 1 Introduction
Field tests and laboratory experiments have been conducted to identify modal properties and detect bridge damage [28; 29; 30; 31]. Despite the great efforts that have been accomplished, the pollution of recorded signals is still an obstacle to implementing an indirect method [13]. This corruption of signals may occur due to the vehicle's own vibration frequency or due to road irregularities. One of the recent methods proposed to obtain more accurate results from a scanning vehicle is the contact-point response calculation approach which was proposed by [PERSON] and [PERSON] [32]. The contact point refers to the point on the underside of the vehicle tire which is in direct contact with the bridge. The accelerometer mounted on the vehicle measures the vertical vibration of the vehicle during its passage over the bridge; however, this response is distorted by the vehicle frequency, which corrupts the acceleration signal. As such, it is more accurate to use the contact-point response instead of the vehicle response. Contact-point response has the advantage of being free of the vehicle frequency which may overshadow the bridge frequency. [PERSON] and [PERSON] [32] proposed a method to calculate the contact-point response of the moving vehicle. The contact-point response of a moving vehicle has exhibited promising results for crack identification when performing numerical simulation for a bridge model [33; 34]. The scanning vehicle can be used in moving or stationary conditions. Previous work has been carried out for a moving vehicle and this paper instead addresses the contact-point response for a stationary vehicle when a bridge is excited by a moving vehicle. Recently, [PERSON] and [PERSON] [35] proposed an approach which utilized the response of a stationary vehicle to overcome the issue of road roughness; however, in their study, the stationary vehicle response does not reflect the true vibration of the bridge because the stationary vehicle response is distorted by its own frequency. Few studies have been dedicated to the analysis of stationary vehicle vibration due to excitation from moving vehicles. [PERSON] and [PERSON] [36] and [PERSON] and [PERSON] [37] employed stationary vehicle responses for bridge damage identification; however, they considered the stationary vehicle as a lumped mass, which is not realistic. [PERSON] and [PERSON] [17] demonstrated how the response of a stationary vehicle is different from the true response of the bridge in a field test experiment. [PERSON] and [PERSON] [38] employed stationary vehicle vibration for mode shape identification in bridges; however, their bridge was excited by ambient vibrations, such as wind. Very recently, [PERSON] and [PERSON] [39] compared the response of a moving vehicle and a stationary vehicle (the vehicle in a non-moving state) in a field experiment. They found that the response of the stationary vehicle could detect more bridge frequencies than the moving vehicle; however, they used an arbitrary source of excitation to excite the stationary vehicle, such as people jumping on the bridge. Also, they only considered one location in the bridge's span. The numerical investigations that have been carried out on the vibration of a stationary vehicle over a bridge still lack several aspects, such as the effects of the vehicle's frequency, damping effects, stationary vehicle's location, and road roughness effects. Also, the properties of the source of excitation (moving vehicle), such as the speed and mass, have not been discussed by previous studies. As such, more research is required to confirm the behavior of a stationary vehicle when parked on a bridge. This study is dedicated to investigating the response of a stationary vehicle and the contact-point response via the use of a finite element (FE) model of the stationary vehicle when parked on a bridge that is traversed by a moving vehicle. First, a vehicle bridge interaction formulation is presented and used to validate the FE model. Then, the response of the stationary vehicle is obtained from the FE model.