Application of the reciprocity theorem to determine line-load-generated surface waves on an inhomogeneous transversely isotropic half-space

Free and forced time-harmonic surface waves are investigated for a half-space of transversely isotropic elastic material, where the axis normal to the free surface (the z-axis) is the axis of symmetry. In addition, the elastic constants and the mass density depend on the distance from the free surface. A surface wave is considered as being composed of a carrier wave that propagates over the free surface as it would over a membrane, while it carries along a system of depth-dependent motions. For free surface waves the analytical details, i.e., the calculation of the wave speed of the free surface waves, are worked out for the case that the elastic constants and the mass density vary exponentially with depth. For forced motion by a time-harmonic line load, the far-field surface wave motion is determined by an application of the reciprocity theorem for elastodynamics. Numerical results for displacements and stresses are graphically displayed. Fourier superposition has been used to determine the transient surface wave response to a pulse-type normal line-load.