dc dynamic and static pull-in predictions and analysis for electrostatically actuated clamped circular micro-plates based on a continuous model

Abstract

This study develops a continuous model to analyze the 'pull-in' effect in the circular micro-plates used in capacitive-type micro-electro-mechanical systems (MEMS) sensors, actuators and microphones. In developing the model, the governing equation of motion of the deformed plate is established in the form of a partial different equation (PDE) which is then decomposed using the Galerkin method to create a coupled set of modal ordinary differential equations. By considering the first-order deflection mode only and using a fifth-order Taylor series expansion of the electrostatic force, closed-form solutions are obtained for both the position and the voltage of the static pull-in event. Applying an energy balance method and a finite-order approximation method, the solutions are then obtained for the position and voltage of the dynamic pull-in event. The theoretical results obtained for the pull-in phenomena are verified based on the comparison to available experimental data, and also numerically using a finite element analysis (FEA) approach. In general, the results indicate that the ratio of the dynamic to static pull-in voltages is approximately 92%. However, when the squeezed-film effect induced by the air gap between the two plates is taken into account, the value of this ratio increases slightly as a result of considering a higher dynamic pull-in voltage.

Effect of pressure on nonlinear dynamics and instability of electrically actuated circular micro-plates

“…In order to investigate the nonlinear dynamic behavior of the micro-plate in the bi-stable regime, we set the differential pressure to P = 3300 Pa. Moreover, 8 The normalized deflection of the micro-plate averaged over time as a function of applied DC voltage, while P = 3300 Pa, /ω 0 = 1. Straight line: stable solution, dotted line: unstable solution.…”

“…Particularly, at a critical combination of DC and AC voltages and also the excitation frequency, the motion of the flexible electrode becomes unstable, and then, the micro-plate falls on to the stationary one. This phenomenon is known as pull-in [7,8].…”

“…In that case, the only load parameter in assessment of stability is the applied DC voltage, and the critical stability appears as a 'fold' or a 'limit point' in the response of the system. Many studies have addressed the static pull-in phenomenon, and proposed analytical or numerical methods to estimate the pull-in voltage [6,[8][9][10][11][12][13]. A literature survey on this topic has been carried out in Ref.…”

“…In studying the stability of such a system, in addition to the DC voltage, the frequency and the amplitude of the AC voltage play influential roles. Many studies have addressed the dynamic pull-in phenomenon, and proposed analytical or numerical methods to estimate the pull-in voltage [7,8,16]. It has been reported that for micro-resonators, the dynamic pull-in can be triggered by dynamic instabilities, and therefore, it might occur at much lower voltages compared to the static pull-in voltage [17,18].…”

Bi-stability of micro-plates: A sensitive mechanism for differential pressure measurements

“…After pull-in, the contact between the electrodes causes failures including short circuits, sticking, and wear. 4,19 If the sensor employs a bi-stable flexible electrode (such as an arched plate), after reaching the pull-in voltage, the electrode snaps to another stable configuration which is not in contact with the other electrode, 20,21 and if the voltage is released, it snaps back to its original configuration. Hence, the contact between the electrodes is avoided, and multiple measurements can be performed without failure.…”