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Abstract:
In this study, the size-dependent bistable behavior of a micro-electro-mechanical curved beam under the piezoelectric actuation is investigated. The system is modeled as a clamped slightly curved Euler–Bernoulli beam sandwiched with two piezoelectric layers along its length and suspended over a curved fixed electrode. Employing the strain gradient theory, the nonlinear governing equilibrium equation is derived using the principle of minimum total potential energy. A multi-mode Galerkin’s weighted residual method with the linear undamped mode-shapes of the straight beam as the approximating functions is then utilized to solve the higher-order governing equilibrium equation. The instability thresholds of the system are then obtained by vanishing the determinant of the Jacobian of the reduced equations. It is found that the present solutions are completely converged when three eigenmodes are included in the reduced order model (ROM), while hiring a single mode solution predicts the position of the snap-through and pull-in points with errors of at most 13% and 1.4%, respectively. The accuracy of the converged results is also validated by the available experimental observations in the literature. Moreover, snapping criteria which provide the required combination of the system properties for prompting snap-through instability is introduced in this study. A detailed parametric study is finally conducted to investigate the combined effects of the fixed electrode curvature and the piezoelectric actuation on the size-dependent bistability of electrically actuated curved micro-beams. Results reveal that the position of the snapping zone in the limit points map can be controlled by the input piezoelectric voltage as well as the initial rise of the fixed electrode.

Keywords:
Bistability, Initially curved micro-beam, Curved fixed electrode, Piezoelectric actuation, Strain gradient theory