Improved lateral-dynamics-intended railway vehicle model involving nonlinear wheel/rail interaction and car body flexibility

To study the vehicle hunting behavior and its coupling with car body vibrations,a simplified lateral-dynamics-intended railway vehicle model is developed.A two-truck vehicle is modeled as a 17 degrees-of-freedom rigid system,into which the car body flexural vibrations of torsion and bending modes are further integrated.The wheel/rail interaction employs a real-time calculation for the Hertzian normal contact,in which the nonlinear curvatures of wheel and rail profiles are presented as functions of wheelset lateral movement and/or yaw rotation.Then the tangential/creep forces are analytically expressed as the Hertzian contact patch geometry,and lead to a continuous and fast calculation compared to a look-up table interpolation.It is shown that the hunting frequencies of the vehicle model and a truck model differ significantly,which verifies the necessity of the whole vehicle model.In the case of low wheel/rail conicity,the hunting frequency increases linearly with vehicle speed,whereas it rises slowly at high speed for a large conicity.Comparison of hunting frequency and damping ratio between various conicities shows that first hunting(car body hunting)may occur when the vehicle is operated at a low speed in a small conicity case,while a second hunting(truck hunting)appears when the vehicle is operated at a high speed in a large conicity case.Stability analysis of linear and nonlinear vehicle models was carried out through coast down method and constant speed simulations.Results tell that the linear one overestimates the lateral vibrating.Whereas the structural vibrations of car body can be ignored in the stability analysis.Compared to existing simplified models for hunting stability study,the proposed simplified vehicle model released limitations in the nonlinear geometries of wheel/rail profiles,and it is suitable for a frequency-domain analysis by deriving the analytical expressions of the normal and tangential wheel/rail contact forces.

Exact free vibration analysis of open circular cylindrical shells by the method of reverberation-ray matrix

This paper is concerned with the free vibration analysis of open circular cylindrical shells with either the two straight edges or the two curved edges simply supported and the remaining two edges supported by arbitrary classical boundary conditions. Based on the Donnell-Mushtari-Vlasov thin shell theory, an analytical solution of the traveling wave form along the simply supported edges and the modal wave form along the remaining two edges is obtained. With such a unidirectional traveling wave form solution, the method of the reverberation-ray matrix is introduced to derive the equation of natural frequencies of the shell with different classical boundary conditions. The exact solutions for natural frequencies of the open circular cylindrical shell are obtained with the employment of a golden section search algorithm. The calculation results are compared with those obtained by the finite element method and the methods in the available literature. The influence of length, thickness, radius, included angle, and the boundary conditions of the open circular cylindrical shell on the natural frequencies is investigated. The exact calculation results can be used as benchmark values for researchers to check their numerical methods and for engineers to design structures with thin shell components.