Active cloaking of flexural waves in thin plates

An active cloak consists of a set of discrete multipole sources distributed in space. When the source positions and amplitudes are carefully specified the active field destructively interferes with an incident time harmonic wave so as to nullify the total field in some finite domain and ensure that in the far field only the incident wave is present, i.e. the active field is non-radiating. Here it is shown how to efficiently determine the source coefficients explicitly in the context of flexural waves in thin plates. The work is carried out in the context of Kirchhoff plate theory, using the Rayleigh-Green theorem to derive the unique source amplitudes for a given incident flexural wave.