Coupling of physical and modal components for analysis of moving non‐linear dynamic systems on general beam structures

Abstract

SUMMARYA general, well-structured and efficient method is advanced for the solution of a large class of dynamic interaction problems including a non-linear dynamic system running at a prescribed time-dependent speed on a linear track or guideway. The method uses an extended state-space vector approach in conjunction with a complex modal superposition. It allows for the analysis of structures containing both physical and modal components. The physical components studied here are vehicles modelled as linear or non-linear discrete mass-spring-damper systems. The modal component studied is a linear continuous model of a track structure containing beam elements which can be generally damped and which can be embedded in a three-parameter damped Winkler-type foundation. The complex modal parameters of the track structure are solved for. Algebraic equations are established which impose constraints on the transverse forces and accelerations at the interfaces between the moving dynamic systems and the track. An irregularity function modelling a given non-straight profile of the non-loaded track or a non-circular periphery of the wheels is also accounted for. Loss of contact and recovered contact between a vehicle and the track can be treated. The system of coupled first-order differential equations governing the motion of the vehicles and the track and the set of algebraic constraint equations are together compactly expressed in one unified matrix format. A time-variant initial-value problem is thereby formulated such that its solution can be found in a straightforward way by use of standard time-stepping methods implemented in existing subroutine libraries. Examples for verification and application of the proposed method are given. The present study should be of particular value in railway engineering.

Wheel/Rail Contact Forces for Flexible versus Solid Wheels due to Tread Irregularities

“…Complex-valued modal parameters are calculated by solving the eigenvalue problem pertaining to the nonloaded track model. The decoupled equations of motion are then obtained as [2] Downloaded by [Stanford University Libraries] at 07:29 02 October 2012…”

“…One objective was to clarify the influence of vehicle speed and axle load on dynamic responses in the vehicle and in the track. Another objective was to assemble experimental data in order to verify an existing theoretical model and numerical technique for solving dynamic interaction problems [2].…”

The dynamic code HSR-dyna: an efficient tool for the assessment of vibrations induced by high speed rail lines

“…The rolling surface of the rail is supposed to be rough on a total length of 25 m; the amplitude and wavelength of this harmonic irregularity are taken successively a t =0.5 mm and λ t =1 m. Figures 3(a) and 3(b) show the dynamic response of the contact point on the mobile wheel-rail interface expressed on the time and Figure 4(a) shows the contact force f w1 diagram calculated according to eqn (9). Fig.…”

“…K H denotes the Hertizian spring constant. According to the recommendation by Nielsen and Abrahamsson [9], the track irregularity profile can be written in terms of a sinusoidal function as follows: 2 sin…”

Dinámica estructural de cuerpos de revolución rotatorios: aplicación al eje de un vehículo ferroviario.

“…Tal como se señala en [59], la principal desventaja del uso de estos modelos es el coste computacional al considerar un número muy elevado de coordenadas. El MEF también ha sido empleado para obtener las FRF, tal como se propone en las referencias [57][58][59]78].…”