Eigenvalue Analysis of Multibody Models of Railroad Vehicles Including Track Flexibility

The stability analysis of railroad vehicles using eigenvalue analysis can provide essential information about the stability of the motion, ride quality or passengers comfort. The system eigenvalues are not in general a vehicle property but a property of a vehicle travelling steadily on a periodic track. Therefore the eigenvalue analysis follows three steps: calculation of steady motion, linearization of the equations of motion and eigenvalue calculation. This paper deals with different numerical methods that can be used for the eigenvalue analysis of multibody models of railroad vehicles that can include deformable tracks. Depending on the degree of nonlinearity of the model, coordinate selection or the coordinate system used for the description of the motion, different methodologies are used in the eigenvalue analysis. A direct eigenvalue analysis is used to analyse the vehicle dynamics from the differential-algebraic equations of motion written in terms of a set of constrained coordinates. In this case not all the obtained eigenvalues are related to the dynamics of the system. As an alternative the equations of motion can be obtained in terms of independent coordinates taking the form of ordinary differential equations. This procedure requires more computations but the interpretation of the results is straightforward.