# Experimental and Mathematical Study of Flexible-Rigid Rail Vehicle Riding Comfort and Safety
## 1 Introduction
[9], the suspended equipment divides the first bending frequency into two frequencies with lesser amplitudes. This equipment includes traction transformers, power converter units, fan systems, etc. The active control of the suspended mass is an improvement that may be made using this method. [PERSON] et al. [10] researched the impact of regulating a suspended group placed on a beam-like car body model using an electromagnetic actuator. [PERSON] et al. [11] stated this method's benefits when used for semi-active suspensions. Despite their efficacy in regulating flexible body modes, the approaches described above have marginal influence on controlling stiff body modes, which still affect ride comfort. The method of control used most often falls into the second group. With this configuration, traditional dampers are replaced by actuators [12] situated between the bogies (also known as wheelsets) and the car body in vertical and lateral directions. Inter-vehicle actuators (and lateral-vertically linked actuators) are not included in these designs [13]. A lower-weight design of railway vehicles aims to achieve higher speeds with lesser power requirements. It also results in a decrease in ground vibration and a reduction in construction costs. It is also recommended that the car body's lightweight design fulfils other objectives such as crashworthiness, strength and wear. Researchers have conducted extensive analyses on car body structural vibrations that seriously affect the vehicle ride comfort, and the influences of active and semi-active secondary suspensions on vehicle vibration isolation, considering the flexibility of the car body [14]. Researchers have also determined the influences of active secondary suspensions and an active DVA attached to the car body to attenuate flexible and rigid mode vibration [15; 16; 17]. Increasing the vehicle speed significantly increases the energy and frequency range of the track inputs, which induces the flexural vibrations in the car body. It has also been found that typical track excitation frequencies and vehicle speeds extensively boost the car body vibration modes [13]. In recent years, much theoretical research has been conducted to identify effective strategies for reducing the flexible vibrations that cause discomfort in railway vehicle passengers. Numerical simulation programs have been utilized to analyze and assess the comfort performance of railway vehicles based on specific theoretical models of the vehicles. The accuracy of these models largely depends on the quality of the car body modelling. One such theoretical model is the \"stiff car body\", which provides insights into the fundamental features of vibration behaviors in railway vehicles. The findings from these models suggest that the ends of the car body are the most critical areas in ride comfort. However, in reality, there are instances in which the level of vibrations measured at the center of the car body is equivalent to the level recorded at either end, despite the importance of the ends [7]. It is important to note that passenger comfort is a significant factor in this research. Passengers experience heightened discomfort at specific vibration frequencies and for particular durations. Therefore, reducing these flexible vibrations is crucial for enhancing passenger comfort and satisfaction during train journeys. This paper investigates a dynamics analysis of rail vehicle behaviors using experimental and numerical techniques. The focus is on investigating the impact of elastic vibrations on rail vehicle dynamics. Mathematical models are developed for the car body, bogie frame, and wheel axle using rigid-flexible and multi-rigid formulations. For the rigid body analysis, the car body is considered rigid, while a flexible car body is considered for the flex-rigid analysis. ANSYS is used to build a finite element model for the car body, and substructure and modal analyses are carried out. The dynamic simulation and numerical analysis are then validated using experimental results.