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Updated: Feb 22, 2026

Fabrication and Characterization of Superconducting Resonators
Published on: May 21, 2016
Semi-analytical modeling of anchor loss in plate-mounted resonators
Christoph Schaal1, Robert M'Closkey2, Ajit Mal2
1Department of Mechanical Engineering, California State University, Northridge, CA, USA; Mechanical and Aerospace Engineering Department, University of California, Los Angeles, CA, USA.
Abstract:
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.
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