<p>In this paper, a theoretical model is established for locally resonant plates with general resonators, and the corresponding governing equation is derived. The model provides a mathematical demonstration of the locally resonant effect, which contains two parts: the first part is induced by translation coupling, and the second part is induced by rotation coupling. The second part cannot be reflected by most existing theoretical models. The analytical solutions of the dynamic response are compared with the direct numerical simulation (DNS) results for two locally resonant plates with different resonator types, thereby validating the general applicability of the present model. The rotation coupling effect leads to the frequency-dependent effective rotational inertia density and anisotropic dispersion relation of the locally resonant plate, as well as the enhancement of the structural vibration suppression ability.</p>