This paper investigates electrostatically actuated resonator micro-sensor response near natural frequency. The Casimir effect is included. Both the electrostatic force and the Casimir force introduce nonlinearities in the system. Hamilton’s principle is used to derive the partial-differential equation of motion for the general case of nonuniform sensors. The method of multiple scales is then used in a direct approach of the problem. Two approximation problems resulting from the direct approach are solved. The phase-amplitude relationship is obtained. Numerical results for uniform capacitive resonator micro-sensors are provided.

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