Equivalent stiffness of the saturated poro-elastic half space interacting with an infinite beam to harmonic moving loads

Abstract

The expression of the equivalent stiffness of the saturated poro-elastic half space interacting with an infinite beam to harmonic moving loads is obtained via the Fourier transformation method in the frequency wave number domain. Based on the obtained equivalent stiffness, the frequency wave number domain solution of the beam-half-space system is obtained by the compatibility condition between the beam and the half space. Critical velocity of harmonic moving loads along an infinite Euler-Bernoulli elastic beam is determined. The time domain solutions for the beam and the saturated poro-elastic half space are derived by means of the inverse Fourier transformation method. Also, the influences of the load speed, frequency and material parameters of the poro-elastic half space on the responses of the beam are investigated. Numerical results show that the frequency corresponding to the maximum deflection and bending moment increases with increasing load speed. Moreover, it can be seen that at higher frequencies, the dynamic response is independent of the load speed. The present results also show that for a beam overlying a saturated poro-elastic half space, there still exist critical velocities even when the load velocity is larger than the shear wave speed of the medium.