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Research Papers

Modeling and Analysis of an Optically-Actuated, Bistable MEMS Device

[+] Author and Article Information
Vijay Kumar

School of Mechanical Engineering, Birck Nanotechnology Center, and Ray W. Herrick Laboratories,  Purdue University, West Lafayette, IN 47907kumar2@purdue.edu

Jeffrey F. Rhoads1

School of Mechanical Engineering, Birck Nanotechnology Center, and Ray W. Herrick Laboratories,  Purdue University, West Lafayette, IN 47907jfrhoads@purdue.edu

1

Corresponding author.

J. Comput. Nonlinear Dynam 7(2), 021007 (Jan 06, 2012) (7 pages) doi:10.1115/1.4005080 History: Received January 11, 2011; Revised September 08, 2011; Accepted September 09, 2011; Published January 06, 2012; Online January 06, 2012

Bistable microsystems have drawn considerable interest from the MEMS/NEMS research community not only due to their broad applicability in commercial applications, such as switching, but also because of the rich dynamic behavior they commonly exhibit. While a number of prior investigations have studied the dynamics of bistable microsystems, comparatively few works have sought to characterize their transient behavior. The present effort seeks to address this through the modeling and analysis of an optically-actuated, bistable MEMS switch. This work begins with the development of a distributed-parameter representation for the system, which is subsequently reduced to a lumped-mass analog and analyzed through the use of numerical simulation. The influence of various system and excitation parameters, including the applied axial load and optical actuation profile, on the system’s transient response is then investigated. Ultimately, the methodologies and results presented herein should provide for a refined predictive design capability for optically-actuated, bistable MEMS devices.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagram of the bistable microsystem of interest

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Figure 2

Diagram of the simplified device representation used for modeling

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Figure 3

Static buckled mode shapes associated with the system of interest. The red (solid) and green (dotted) lines represent the first and second symmetric modes of the system, and the blue (dashed) line represent the first antisymmetric mode of the system.

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Figure 4

Static behavior of the beam at its first symmetric buckling mode. The beam shows a supercritical pitchfork behavior with the zero solution becoming unstable and two additional stable solutions arising as the axial load is increased beyond the critical Eulerian load. Solid lines represent stable solutions, while dashed lines represent the unstable solution of the system.

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Figure 5

Phase plane for the buckled beam in its first symmetric buckling mode, when the load is (a) 1% and (b) 5% higher than the critical load of the system. There are two stable spirals at (±1,0) and a saddle point at (0,0). Note that the following nominal values are used for all simulations unless otherwise stated. The mass of the actuator (M) is about 10 times the mass of the beam, K = 1000 and c = 0.1.

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Figure 6

Basins of attraction for the two stable configurations of the system buckled in its first mode when the load is (a) 1% and (b) 5% greater than the critical load. Note that the blue areas represent the basin of attraction for the stable point (-1,0) and the white area represents the basin of attraction for the stable point (1,0).

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Figure 7

Basins of attraction for the two stable configurations of the system buckled in its first mode when the load is 1% greater than the critical load. c = 0.01 and all other parameters are as in Fig. 5. Note that the blue areas represent the basin of attraction for the stable point (−1,0) and the white area represents the basin of attraction for the stable point (1,0).

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Figure 8

Basins of attraction for the two stable configurations of the system buckled in its first mode when the load is (a) 1% and (b) 5% greater than the critical load. The mass of the actuator is 1.5 times the nominal value used in Fig. 5, and all other parameters are the same. Note that the blue areas represent the basin of attraction for the stable point (−1,0), and the white area represents the basin of attraction for the stable point (1,0).

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Figure 9

Response of the system when actuated by a simple pulse input (5 mW) for 0.4 ms (red) and 0.8 ms (blue). The system is initially at the state (−1,0). It switches to the other stable state for the pulse of width 0.8 ms, but not for the pulse width of 0.4 ms.

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Figure 10

Response of the system when actuated by a half-sine pulse input (5 mW) for 0.4 ms (red) and 0.8 ms (blue). The system is initially at the state (−1,0). It switches to the other stable state for the pulse of width 0.8 ms but not for the pulse of width 0.4 ms.

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Figure 11

Relationship between switching times and pulse widths for a simple pulse input and a half-sine wave input for two different pulse amplitudes when the axial load is 0.5% higher than the critical load of the beam. The pulse amplitudesare designed such that both of the inputs are of equal energy. The switching time is defined to be the time taken by the system to settle in the stable state (1,0), starting from the (−1,0) configuration, after the removal of the pulse.

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Figure 12

Relationship between switching times and pulse widths for a simple pulse input and a half-sine wave input for two different values of critical load at the same excitation level (5 mW). The pulse amplitude are such that both the inputs are of equal energy. The switching time is defined here to be the time taken by the system to settle in the stable state (1,0), starting from the (−1,0) configuration, after the removal of the pulse.

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Figure 13

Relationship between switching times and pulse widths for a simple pulse input for different values of the actuator mass (note that in this figure, mass ratio is the ratio of the mass of the actuator to the nominal value of the actuator mass) when the axial load is 0.5% higher than the critical load of the beam at the same excitation level (5 mW). The switching time is defined to be the time taken by the system to settle in the stable state (1,0), starting from the (−1,0) configuration, after the removal of the pulse.

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