PSI - Issue 22

B.R. Miao et al. / Procedia Structural Integrity 22 (2019) 102–109 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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vertical vibration characteristics of the vehicle (Mrzyglod, M. et al., 2014). Assuming that the carbody is an elastic body (considering the influence of internal damper damping), the Euler beam with a free homogenizing section at both ends is used. The force on the elastic body. If the vertical elastic vibration displacement of the carbody is   , z x t , the partial differential equation of the carbody elastic vibration is:           4 5 2 2 4 4 4 2 1 3 , , , si i ei i i i z x t z x t z x t EI I A F x x F x x x t x t                      (1) i e F is the suspension function at the under-vehicle equipment. EI is Equivalent bending stiffness of carbody section ， I  is damping Where i s F is the force of the second suspension of the first bogie acting on the elastic carbody. In order to numerically integrate equation (1), the equation (1) needs to be transformed into a second-order system of ordinary differential equations using the Ritz method. Assume that the first order of the carbody has a formation function of   i Y x and the corresponding modal coordinate is   i q t . If the vibration displacement of the carbody includes the rigid body motion of the carbody, then the carbody floating and sinking motion can be regarded as the first-order formation type, the formation function is   1 1 Y x  , the nodding motion of the carbody is used as the second-order formation type, and the formation function is   2 / 2 Y x x L   . The vibration displacement equation of the carbody can be obtained by taking the pre-mode modal superposition: (2) Combining the rigid body motion equation of the carbody, the overall motion equation expression of the carbody can be obtained as:               3 1 2 4 2 2 i i i i Y x Y x Y x Y x q t q t q t F F F F             ,          t     3 2 L N  c z t c  i i i z x t x Y x q t       coefficient ， A  is carbody Equivalent mass ，  is Dirac function, 1( 0(     ) ( )    ) j j j x x x x x x  .

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2.2. Rigid-flexible coupled vehicle system MBS dynamics model The high-speed train is a complex multi-body system (MBS) with strong nonlinearity. Not only the interaction between the various components of the vehicle, but also the interaction between the wheel and the rail. And these interactions usually manifest as nonlinear and coupled vibration effects. In order to facilitate the analysis of dynamics, it is necessary to make some reasonable simplifications and assumptions in vehicle dynamics modeling. The dynamics parameters of one EMU vehicle can be seen in Table 1. Some simplifications are made to the nonlinear elements of the EMU train. For the suspension system, the force is simulated by springs and damp. In order to analyze the influence of the vehicle's elastic vibration, a multi-body system analysis software is used to establish a vehicle system dynamics model considering the carbody elasticity. The whole rigid-flexible coupled dynamics model modeling process is shown in Fig. 1.