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In Part 2 of the two-paper series, the asymmetrically laminated piezoelectric shell subjected to distributed bias voltage as modeled in Part 1 is analytically and numerically investigated. Three out-of-plane degrees-of-freedom (DOFs) and a number of in-plane DOFs are retained to study the shell's snap-through phenomenon. A convergence study first confirms that the number of the in-plane DOFs retained affects not only the number of predicted equilibrium states when the bias voltage is absent but also the prediction of the critical bias voltage for snap-through to occur and the types of snap-through mechanisms. Equilibrium states can be symmetric or asymmetric, involving only a symmetric out-of-plane DOF, and additional asymmetric out-of-plane DOFs, respectively. For symmetric equilibrium states, the snap-through mechanism can evolve from the classical bidirectional snap-through and latching to a new type of snap-through that only allows snap-through in one direction (i.e., unidirectional snap-through), depending on the distribution of the bias voltage. For asymmetric equilibrium states, degeneration can occur to the asymmetric bifurcation points when the radii of curvature are equal. Finally, the unidirectional snap-through renders an explanation to the experimental findings in Part 1.

journal of vibration and acoustics

Voltage-Induced Snap-Through of an Asymmetrically Laminated, Piezoelectric, Thin-Film Diaphragm Micro-Actuator—Part 2: Numerical and Analytical Results