Surface Waves on a Half-Space Due to a Time-Harmonic Loading on an Inertial Strip Foundation

An analytical approach has been applied to obtain the solution of Navier's equation for a homogeneous, isotropic half-space under an inertial foundation subjected to a time-harmonic loading. Displacement potentials were used to change the Navier's equation to a system of wave-type equations. Calculus of variation was employed to demonstrate the contribution of the foundation's inertial effects as boundary conditions. Use of the Fourier transformation method for the system of Poisson-type equations and applying the boundary conditions yielded the transformed surface displacement field. Direct contour integration has been employed to achieve the surface waves. In order to clarify the foundation's inertial effects, related coefficients were defined and a parametric study was conducted. Final results revealed that increasing the mass per unit length of the foundation or the frequency of the applied harmonic load intensifies the inertial effect factors. On the other hand, an increase in strip width or Poisson's ratio would imply reduction in the inertial effect factors.