TY - JOUR

T1 - The equivalent dynamic stiffness of a visco-elastic half-space in interaction with a periodically supported beam under a moving load

AU - Lu, T.

AU - Metrikine, A.

AU - Steenbergen, M.J.M.M.

PY - 2020

Y1 - 2020

N2 - A periodically supported beam on a visco-elastic half-space is considered to model the vibration of railway tracks. The viscosity of the half-space is assumed to be of the Kelvin-Voigt type. Making use of the concept of equivalent dynamic stiffness, the reaction of the half-space to the sleepers is replaced by a system of identical spring located under each sleeper. The frequency-dependent equivalent stiffness of the springs is a function of the phase shift of vibrations of neighbouring supports. The equivalent stiffness is derived analytically employing the contour integration technique, resulting in a comprehensive expression for different phase velocities of the waves in the beam with respect to the wave speeds of the half-space. Apart from the Rayleigh type surface wave (quasi-elastic wave), an extra visco-elastic surface wave may exist in a visco-elastic half-space depending on the parameters of the half-space and the frequency range. The existence of this second surface wave has not been addressed within the field of train-induced ground vibration. The importance of this wave for the equivalent stiffness is analysed. An effective method to determine the frequency range for the visco-elastic surface wave to exist is proposed.

AB - A periodically supported beam on a visco-elastic half-space is considered to model the vibration of railway tracks. The viscosity of the half-space is assumed to be of the Kelvin-Voigt type. Making use of the concept of equivalent dynamic stiffness, the reaction of the half-space to the sleepers is replaced by a system of identical spring located under each sleeper. The frequency-dependent equivalent stiffness of the springs is a function of the phase shift of vibrations of neighbouring supports. The equivalent stiffness is derived analytically employing the contour integration technique, resulting in a comprehensive expression for different phase velocities of the waves in the beam with respect to the wave speeds of the half-space. Apart from the Rayleigh type surface wave (quasi-elastic wave), an extra visco-elastic surface wave may exist in a visco-elastic half-space depending on the parameters of the half-space and the frequency range. The existence of this second surface wave has not been addressed within the field of train-induced ground vibration. The importance of this wave for the equivalent stiffness is analysed. An effective method to determine the frequency range for the visco-elastic surface wave to exist is proposed.

KW - Equivalent stiffness

KW - Moving load

KW - Periodically supported beam

KW - Quasi-elastic surface wave

KW - Visco-elastic half-space

KW - Visco-elastic surface wave

UR - http://www.scopus.com/inward/record.url?scp=85087590161&partnerID=8YFLogxK

U2 - 10.1016/j.euromechsol.2020.104065

DO - 10.1016/j.euromechsol.2020.104065

M3 - Article

VL - 84

JO - European Journal of Mechanics A - Solids

JF - European Journal of Mechanics A - Solids

SN - 0997-7538

M1 - 104065

ER -