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Anchor loss is a primary energy dissipation mechanism limiting the quality factor (Q) of micromechanical resonators. This study presents analytical relationships for the natural frequency and anchor loss quality factor of an elliptical micromechanical resonator with two horizontal supporting beams operating in the in-plane slapping vibration mode. The model was developed using Euler-Bernoulli beam theory, where equivalent stiffness and effective moment of inertia were derived from the kinetic energy of the bending beams. The analytical natural frequency (32.528 kHz) showed excellent agreement with ANSYS simulations (31.39 kHz), with an error of only 3.5%. Parametric analysis revealed that increasing beam length improves the quality factor, while increasing beam width or the major radius of the ellipse significantly degrades it. The proposed analytical model provides a validated, computationally efficient tool for designing high-Q elliptical Micro-Electro-Mechanical Systems (MEMS) resonators.
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