Non-classical continuum theories are able to capture the size-dependent behavior of microscale structures. Among them, strain gradient modeling is one of the most accurate ones. The objective of this paper is to develop for the first time a nonlinear strain gradient formulation for the vibrational analysis of electrostatically actuated shear deformable microarches. The normalized equations of motion and the corresponding boundary conditions are derived based on Hamilton’s principle. Novel closed form expressions are derived for the mode shapes of the system using the perturbation technique. These mode shapes are then utilized in a Galerkin projection method to reduce the partial differential equations of motion to time domain nonlinear ordinary differential equations. Multiple time scales perturbation technique is then employed to derive analytical solutions for the nonlinear vibration of the system resulting from a DC step voltage excitation. The analytical results are compared with numerical simulations, and excellent agreement is observed. The formulations and the results presented in this paper can be utilized for design, analysis and synthesis of microscale bistable structures with pre-deformed thick microbeams as their main operating element.

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