## 3 Prediction of Carriage Vibration Based on Rigid-Flex Coupled Dynamics Model  
The full-trimmed carriage FE model of the CRH380 series high-speed train was adopted from [6], which was verified by a modal test. The full-trimmed carriage FE model was generally divided into two parts: BIW (body-in-white) part and trim part. The BIW FE model was discretized by quadrangular and triangular elements consisting of approximately 446,000 elements and 350,000 nodes, as shown in Figure 4a. In the direction from bottom to top, the trim parts included thermal insulation layer, draining board, sound absorption layer, floorboard system, chairs, doors, windows, wooden dividing-walls, glass dividing walls, sidewall panels, luggage racks, and ventilation system. The FE model of the trim part was mainly discretized by hexahedral units consisting of about 320,000 units and 440,000 nodes, as shown in Figure 4b. The BIW body was mainly composed of 7N01 aluminum alloy material. The density of the aluminum alloy material was 2685 kg/m\({}^{3}\), the elastic modulus was 72.4 Gpa, and the Poisson's ratio was 0.3. The material parameters of each component of the trim part were chosen from [6]. The full-trimmed carriage FE model is displayed in Figure 4c. Figure 3: \(Z\)-direction acceleration measured at the seat pan. (**a**) Signals in time domain; (**b**) power spectral density. Figure 2: \(Z\)-direction acceleration measured at the carriage floor. (**a**) Signals in time domain; (**b**) power spectral density. As the dynamic characteristics of a high-speed train can be analyzed based on rigid-flex coupled model, the elastic processing of the train-rail coupled multibody dynamics model requires the substructure analysis of the carriage. In order to maintain the accuracy of the FE model of the carriage as well as simplify the calculation burden, the main nodes of the substructure were selected as follows. 1. The position with large rigidity of BIW was evenly spaced to select the main nodes. 2. In order to maintain the outline of the carriage, the main nodes were selected in the center of the walls and top and bottom on both sides of the carriage. 3. The main nodes were selected for the suspension installation positions of the two series of pillow beams at the bottom of the carriage for subsequent connection with the bogie. 4. The position where the floor and side walls of the carriage were connected to the seat was selected as the main node for subsequent connection to the seat model. According to the above selection rules, 244 master nodes (marked yellow) were selected during the substructure analysis, and each node retained full degrees of freedom, so the degrees of freedom of the substructure model were 1464, as shown in Figure 4d. The train-track coupled rigid multibody dynamics model of the CRH380 series high-speed train was adopted from [17], as shown in Figure 5. The rigid carriage in the model was replaced with the elastic substructure model to form a train-track rigid-flex coupled dynamics model. As the carriage was connected to the wheel-rail system through the suspension force of the second series, the influence of the elastic deformation of the carriage on the wheel-rail contact was small, so the influence of the elastic treatment of the carriage on the wheel-rail interaction force could be ignored. Figure 4: FE model of the carriage. (**a**) FE model of BIW; (**b**) trim parts; (**c**) full-trimmed carriage assembly; (**d**) main node of the carriage substructure. In order to verify the accuracy of the train-track rigid-flex coupled dynamics model, a vibration point was set on the carriage floor at the same position in the test. Simulation with the proposed model at the condition of 350 km/h acquired a 5 s result in the \(X\)-, \(Y\)-, and \(Z\)-directions, which were compared with the test results, as shown in Figure 6.  
As the ride comfort is mainly determined by vibrations within 20 Hz, the accuracy of the predicted vibrations within 20 Hz is very important for ride comfort evaluation.