TY - JOUR
T1 - Dynamic response of an infinite beam periodically supported by sleepers resting on a regular and infinite lattice
T2 - Semi-analytical solution
AU - de Oliveira Barbosa, João Manuel
AU - van Dalen, Karel N.
N1 - Accepted Author Manuscript
PY - 2019
Y1 - 2019
N2 - In this work we propose a model for the analysis of the dynamic behaviour of a ballasted track that combines discrete and continuous elements. The rail is modelled via an Euler-Bernoulli beam, the periodically spaced sleepers are represented with lumped masses, and the ballast is simulated using a lattice (regular network of elastically connected lumped masses). All elements are assumed to behave linearly, and the lattice can be supported by a flexible or a rigid foundation, simulating soil or a hard rock. The equations of motion of each component are presented and the coupled system is solved semi-analytically in the frequency domain. The time domain response can be calculated afterwards by means of a numerical inverse Fourier transform. Dispersion curves and time responses are produced for the case of a ballasted track on a stiff soil. These responses are compared with the scenario in which ballast is modelled as lumped supports, and the scenario in which the force is applied directly to the ballast (no superstructure). It is observed that the simpler models fail to capture the vibration modes in which energy is concentrated in the ballast, and that the superstructure significantly alters the response of the track, increasing its critical velocity and changing the deformed shape of the ballast. The model herein proposed can be used to assess the dynamic characteristics of the track (critical speeds, energy propagation, vehicle-track interaction, etc.) and will serve as framework for a development of a tool for assessment of the settlement behaviour of ballast.
AB - In this work we propose a model for the analysis of the dynamic behaviour of a ballasted track that combines discrete and continuous elements. The rail is modelled via an Euler-Bernoulli beam, the periodically spaced sleepers are represented with lumped masses, and the ballast is simulated using a lattice (regular network of elastically connected lumped masses). All elements are assumed to behave linearly, and the lattice can be supported by a flexible or a rigid foundation, simulating soil or a hard rock. The equations of motion of each component are presented and the coupled system is solved semi-analytically in the frequency domain. The time domain response can be calculated afterwards by means of a numerical inverse Fourier transform. Dispersion curves and time responses are produced for the case of a ballasted track on a stiff soil. These responses are compared with the scenario in which ballast is modelled as lumped supports, and the scenario in which the force is applied directly to the ballast (no superstructure). It is observed that the simpler models fail to capture the vibration modes in which energy is concentrated in the ballast, and that the superstructure significantly alters the response of the track, increasing its critical velocity and changing the deformed shape of the ballast. The model herein proposed can be used to assess the dynamic characteristics of the track (critical speeds, energy propagation, vehicle-track interaction, etc.) and will serve as framework for a development of a tool for assessment of the settlement behaviour of ballast.
KW - Infinite beam
KW - Infinite lattice
KW - Moving load
KW - Periodic structures
UR - http://www.scopus.com/inward/record.url?scp=85068106884&partnerID=8YFLogxK
U2 - 10.1016/j.jsv.2019.06.014
DO - 10.1016/j.jsv.2019.06.014
M3 - Article
AN - SCOPUS:85068106884
SN - 0022-460X
VL - 458
SP - 276
EP - 302
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
ER -