| Citation: |
Xiangshuo Liu, Lijun Zhang, Mingji Zhang. STUDIES ON PULL-IN INSTABILITY OF AN ELECTROSTATIC MEMS ACTUATOR: DYNAMICAL SYSTEM APPROACH[J]. Journal of Applied Analysis & Computation, 2022, 12(2): 850-861. doi: 10.11948/20210479
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STUDIES ON PULL-IN INSTABILITY OF AN ELECTROSTATIC MEMS ACTUATOR: DYNAMICAL SYSTEM APPROACH
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Abstract
The pull-in instability of an electrostatic microstructures is a common undesirable phenomenon which implies the loss of reliability of micro-electromechanical systems. It is important to better understand its mechanism and then to reduce the occurrence of such phenomenon. Our work is devoted to analyzing the pull-in instability of a typical electrostatic micro-electro-mechanical-system actuators with edge effects. The pull-in phenomenon and the dynamic threshold are examined via dynamical system approach and the qualitative theory of differential equations. Nonlinear interplays between the voltage and the initial positions are characterized, from which critical voltage values are identified. Those critical voltages play crucial roles in our analysis. Effects from other system parameters are also examined numerically. It turns out that most of the parameters involved in the MEMS oscillator have corresponding threshold values, beyond which the pull-in instability occurs.
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References
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Xiangshuo Liu, Lijun Zhang, Mingji Zhang. STUDIES ON PULL-IN INSTABILITY OF AN ELECTROSTATIC MEMS ACTUATOR: DYNAMICAL SYSTEM APPROACH[J]. Journal of Applied Analysis & Computation, 2022, 12(2): 850-861. doi: 10.11948/20210479
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- Figure 1. A single-degree-of-freedom model of a parallel-plate capacitor in a spring-mass system
- Figure 2. Phase portraits of system (2.3)
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Figure 3. Phase portrait and corresponding solution curves with physical parameters
$ w=1 $ ,$ m=k=\frac{\epsilon}{\pi} $ and$ V=1 $ -
Figure 4. Trajectories and corresponding solution curves with
$ x_0=0 $ and$ w=1 $ and$ m=k=\frac{\epsilon}{\pi} $ . Under the specific setup, one has$ V_c=0.4180909 $ and$ V^*=0.6764614 $ . We also point out that once the value of$ V $ is fixed, the corresponding values for$ x_2, x_c $ and$ x_t $ can be uniquely determined -
Figure 5. The solution curves of the equation 1.4 with
$ \epsilon=1 $ and$ V=0.1 $ for different setups: (a)$ m=1 $ and$ k=1 $ , (b)$ m=1 $ and$ w=1 $ , (c)$ w=1 $ and$ k=1 $