# Study on Passenger Comfort Based on Human-Bus-Road Coupled Vibration
## 1 Introduction  
Nowadays, much attention has been drawn to the comfort of drivers and passengers. The interaction between vehicles and asphalt road can cause coupled vibration due to the road surface roughness, which will reduce the comfort of passengers. Therefore, the research on human-vehicle-road coupled vibration and the comfort of passengers is of great importance. Regarding the study of human-vehicle-road coupled vibration, most researchers mainly consider the vehicle-road coupled model and focus on the dynamic responses of the pavement [1; 2; 3]. [PERSON] [1] established the coupled model of vehicle and concrete pavement, considering the transverse shear and bending deformation, and analyzed the dynamic response of pavement considering the influence of slab thickness, soil modulus, and vehicle speed. [PERSON] et al. [2] analyzed the effects of a heavy-duty truck with different speeds and axle weights on the vibration of the subgrade. The vertical stress and acceleration of subgrades in different depths were analyzed, and the simulation results were in good agreement with field measurements. [PERSON] [3] presented an integrated model for the computation of vehicle-track interaction and ground vibration of passing trains. A combination of the finite elementmethod and boundary element method was used to calculate the dynamic compliance of the track on real soil. In order to study the human response, a few human biomechanical models have been proposed [4; 5]. [PERSON] et al. [4], according to 31 active markers on humans, proposed a biomechanical model of human front motion, which was used to study the mechanism of human-structure interaction and explained the characteristics of human balance response to the base excitation. The experiment was validated by the humans-oscillating treadmill interaction. [PERSON] et al. [5] proposed a 5-degrees-of-freedom (DOF) model with 23 parameters to describe the human-seat interaction. The resonant frequencies yielded by the model yielded are close to experimental observations. In general, the existing research has rarely considered the human body effect in the case of human-vehicle-road coupled vibration. Therefore, the present study proposes a three-dimensional (3D) human-bus-road coupled model, including 2 DOF human biomechanical model, a 3D bus model, and a 3D road model that was considered the interlayer bonding condition. Passenger comfort is mostly evaluated based on the evaluation standard, i.e., the International Organization for Standardization (ISO) 2631-1:1997 [6; 7; 8; 9]. [PERSON] [6] used the Lagrangian method to formulate the vertical-lateral coupled mathematical models of rail/road vehicles, and used the ISO 2631 normative method to analyze the vehicle ride quality and human comfort. [PERSON] and [PERSON] [7] established a vehicle model with 7 DOF and used the ISO 2631-1:1997 evaluation standard to study human comfort, considering factors such as the vehicle speed and vehicle weight. [PERSON] and [PERSON] [8] evaluated the driver comfort of haul trucks exposed to long-term vibration. Thirty-two whole-body vibration measurements were obtained from haul trucks under a range of normal operating conditions, and the health risk assessment of drivers was carried out according to the health guidance caution zone defined by ISO 2631-1. [PERSON] and [PERSON] [9] focused their study on the influence of road type and vehicle speed on the measured whole-body vibration (WBV) level, by considering three different types of vehicles driving on two different types of roads (i.e., asphalt and stone-paved roads). The recommended health and safety values in ISO 2631-1:1997 was used to study the impact of vehicle WBV on human health and comfort in a controlled environment. However, the ISO 2631-1:1997 does not consider the randomness of human body vibration and the fuzziness caused by the unclear judgment standard. Therefore, the uncertainty of human body vibration is considered, and an evaluation index of annoyance rate is proposed in this paper.