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Semi-analytical method to determine frequency and damping of plate-mounted miniature resonators.Approach combines finite element models with Lamb wave theory.Numerical examples include cantilevers mounted on plates.Good agreement between obtained results and those from conventional transient FE simulations.A semi-analytical technique for estimating the energy loss in a resonator mounted to an infinite plate substrate is proposed in this paper. In a plate, only Lamb waves have to be considered, leading to a simplified characterization of the energy carried away from a vibrating source on the plate surface. Instead of employing absorbing elements at the boundaries of the plate-resonator finite element model, it is shown how the semi-analytical approach of stitching together analytical Lamb wave expressions to the finite element model can be utilized. The approach is demonstrated for single and double cantilever configurations on a plate. The results have excellent agreement with those of conventional transient finite element simulations.