Solution of moving-load-induced soil vibrations based on the Betti–Rayleigh Dynamic Reciprocal Theorem

Lamb, 1904, On the propagation of tremors over the surface of an elastic solid, Philosophical Transactions of the Royal Society, A203, 1, 10.1098/rsta.1904.0013 Lombaert G. Development and experimental validation of a numerical model for the free field vibrations induced by road traffic. PhD thesis, K.U. Leuven, Belgium, 2001. Auersch, 2008, The effect of critical moving loads on the vibrations of soft soils and isolated railway tracks, Journal of Sound and Vibrations, 310, 587, 10.1016/j.jsv.2007.10.013 Steenbergen, 2007, The effect of the interface conditions on the dynamic response of a beam on a half-space to a moving load, European Journal of Mechanics A/Solids, 26, 33, 10.1016/j.euromechsol.2006.03.003 Xu, 2007, Dynamic response of an infinite beam overlying a layered poroelastic half-space to moving loads, Journal of Sound and Vibrations, 306, 91, 10.1016/j.jsv.2007.05.031 Celebi, 2005, Investigation of ground vibrations induced by moving loads, Engineering Structures, 27, 1981, 10.1016/j.engstruct.2005.05.011 Bian, 2007, Characteristics of layered ground responses under train moving loads, Chinese Journal of Rock Mechanics and Engineering, 26, 182 Eason, 1965, The stresses produced in a semi-infinite solid by a moving surface force, Engineering Science, 2, 581, 10.1016/0020-7225(65)90038-8 Gakenheimer, 1969 Frýba, 1999 Alabi, 1992, A parametric study on some aspects of ground-borne vibrations due to rail traffic, Sound and Vibration, 153, 77, 10.1016/0022-460X(92)90628-B De Barros, 1994, Response of a layered visco-elastic half-space to a moving point load, Wave Motion, 19, 189, 10.1016/0165-2125(94)90066-3 Luco, 1983, On the Green's functions for a layered half-space, Part I. Bulletin of the Seismological Society of America, 73, 909 Grundmann, 1999, The response of a layered half-space to traffic loads moving along its surface, Archive Applied Mechanics, 69, 55, 10.1007/s004190050204 Lieb, 1998, A fast algorithm for soil dynamics calculations by wavelet decomposition, Archive Applied Mechanics, 68, 147, 10.1007/s004190050152 Hung, 2001, Elastic waves in visco-elastic half-space generated by various vehicle loads, Soil Dynamics and Earthquake Engineering, 21, 1, 10.1016/S0267-7261(00)00078-6 Andersen, 2007, Numerical methods for analysis of structure and ground vibration from moving loads, Computers and Structures, 85, 43, 10.1016/j.compstruc.2006.08.061 Bierer, 2007, A semi-analytical model in time domain for moving loads, Soil Dynamic and Earthquake Engineering, 27, 1073, 10.1016/j.soildyn.2007.03.008 Martínez-Castro, 2006, Semi-analytic solution in the time domain for non-uniform multi-span Bernoulli–Euler beams traversed by moving loads, Journal of Sound and Vibration, 294, 278, 10.1016/j.jsv.2005.11.009 Cai, 2007, Steady state responses of poroelastic half-space soil medium to a moving rectangular load, International Journal of Solids and Structures, 44, 7183, 10.1016/j.ijsolstr.2007.04.006 Zhou, 2007, Dynamics responses of viscoelastic half-space under moving loads, Chinese Journal of Theoretical and Applied Mechanics, 39, 545 Cao, 2008, Analysis of Green's functions in wavenumber–frequency domain for surface displacements of elastic layered half-space soil, Chinese Journal of Computer Mechanics, 25, 283, 10.3901/JME.2008.11.283 Yang, 2003, Train-induced wave propagation in layered soils using finite/infinite element simulation, Soil Dynamics and Earthquake Engineering, 23, 263, 10.1016/S0267-7261(03)00003-4