Affiliations: Koszalin University of Technology, Department of Civil
and Environmental Engineering, Sniadeckich 2, 75-453 Koszalin, Poland | Brunel University, School of Engineering and Design,
Uxbridge, Middlesex, UB8 3PH, UK
Abstract: This paper analyses theoretically the response of a solid for fast
moving trains using models related to real situations: a load moving in a
tunnel and a load moving on a surface. The mathematical model is described by
Navier's elastodynamic equation of motion for the soil and Euler-Bernoulli
equation for the beam with appropriate boundary conditions. Two modelling
approaches are investigated: the model with half space under the beam and the
model with finite thickness of supporting medium. The problem of singularities
for displacements calculation is discussed in relation with boundary conditions
and types of considered loads: harmonic and constant, point and distributed
moving loads. The analysis in frequency-time and frequency-velocity domains is
presented and discussed with regard to critical velocities. A wavelet approximation method based on application of coiflet filters is used for the
derivation of displacements in physical domain. A new, modified filter is used
in numerical calculations allowing to alleviate numerical difficulties related
to the form of approximating sequences based on classical filters, formulated
in previous publications. The effectiveness of the coiflet approach is
discussed for filter coefficients with different order of accuracy. This
methodology is very efficient for the analysis in the range of relatively high
and low load frequencies (treated as an approximation of a constant load) which
are especially important for the analysis of vibrations generated by trains
moving with velocities near critical values. Results of numerical simulations
are presented, demonstrating their utility for modelling and preliminary
analysis of complex models.
