  We propose an analytical framework to model the effect of single and multiple
mechanical surface oscillators on the dynamics of vertically polarized elastic
waves propagating in a semi-infinite medium. The formulation extends the
canonical Lamb's problem, originally developed to obtain the wavefield induced
by a harmonic line source in an elastic half-space, to the scenario where a
finite cluster of vertical oscillators is attached to the medium surface. In
short, our approach utilizes the solution of the classical Lamb's problem as
Green's function to formulate the multiple scattered fields generated by the
resonators. For an arbitrary number of resonators, arranged atop the elastic
half-space in an arbitrary configuration, the displacement fields are obtained
in closed-form and validated with numerics developed in a two-dimensional
finite element environment.
