Nonlinear structural behavior of a size-dependent MEMS gyroscope assuming a non-trivial shaped proof mass

This paper focuses on the influence of sudden drop tests on the nonlinear structural behavior of electrically actuated bi-table shallow microelectromechanical system (MEMS) arches. The assumed structure consists of an initially bell-shaped doubly clamped microbeam with a rectangular cross section. The Euler–Bernoulli beam theory is assumed to model the nonlinear structural behavior of the bistable system under the combined effect of both the direct current (DC) actuating load and the shaking waves. Moreover, the structural model takes into account both geometric midplane stretching and electric actuation nonlinear terms. A multimode Galerkin-based decomposition is used to discretize the beam equations to extract a reduced-order model (ROM). The convergence of the ROM simulations are first verified and furthermore compared to published experimental data. A thorough ROM parametric study showed that the effect of increasing the shallow arch initial rise alter drastically the system behavior from undergoing a uninterrupted snap-through motion to a sudden snap-through instability. Moreover, the arch rise relationship with its shock spectrum response (SSR) is investigated and it was concluded that as increasing the rise value can cause the system to collapse under the combined DC and shock wave loadings if the shock wave duration is lower or near the system fundamental natural period. All the presented graphs in this investigation represent some robust numerical approaches and design tools to help MEMS designers in improving both the reliability and efficiency of these bistable-based microdevices under shaking dynamic environments.

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Numerical and Experimental Analysis of a Nonlinear Vibrating MEMS

Microelectromechanical Systems ◽

10.1115/imece2005-81014 ◽

2005 ◽

Author(s):

Francesco Braghin ◽

Elisabetta Leo ◽

Ferruccio Resta

Keyword(s):

Nonlinear Vibrations ◽

Proof Mass ◽

Integration Method ◽

Resonance Peak ◽

Lumped Parameter Model ◽

Mems Gyroscope ◽

High Deformation ◽

Lumped Parameter ◽

Analytical Integration ◽

Nonlinear Hardening

When significantly displacing a proof mass, the nonlinear hardening characteristic of the supporting beams becomes visible. Thus, the resonance peak of the structure is no longer vertical but bends towards the higher frequencies. This property is useful to easily synchronise sense and drive resonances thus increasing the sensibility of the MEMS gyroscope. Through a test structure designed to investigate the high deformation range of the supporting beams, its nonlinear vibrations were investigated both experimentally and numerically. It is shown that a simple nonlinear lumped parameter model could be sufficient to schematise the system and that a semi-analytical integration method allows to quickly determine both stable and unstable branches of the system’s dynamic response and to design the supporting structure.

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A reduced order system ID approach to the modelling of nonlinear structural behavior in aeroelasticity

Journal of Fluids and Structures ◽

10.1016/j.jfluidstructs.2005.08.012 ◽

2005 ◽

Vol 21 (5-7) ◽

pp. 531-542 ◽

Cited By ~ 18

Author(s):

P.J. Attar ◽

E.H. Dowell

Keyword(s):

Structural Behavior ◽

Order System ◽

Reduced Order ◽

Nonlinear Structural

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Newton-raphson procedure for the sensitivity analysis of nonlinear structural behavior

Computers & Structures ◽

10.1016/0045-7949(88)90191-5 ◽

1988 ◽

Vol 30 (6) ◽

pp. 1263-1273 ◽

Cited By ~ 10

Author(s):

H.S. Gopalakrishna ◽

Lowell F. Greimann

Keyword(s):

Sensitivity Analysis ◽

Structural Behavior ◽

Nonlinear Structural ◽

Newton Raphson

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Nonlinear Vibration of Size Dependent Microresonators with an Electrostatically Actuated Proof Mass

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455418500578 ◽

2018 ◽

Vol 18 (04) ◽

pp. 1850057 ◽

Cited By ~ 4

Author(s):

Ehsan Sharifinsab ◽

Mahdi Mojahedi

Keyword(s):

Nonlinear Vibration ◽

Microelectromechanical Systems ◽

Proof Mass ◽

Multiple Scales ◽

Initial Conditions ◽

Couple Stress Theory ◽

Modified Couple Stress Theory ◽

System Response ◽

Stress Theory ◽

Size Dependent

In this paper, the dynamic and nonlinear vibration responses of a microresonator containing a microbridge with a proof mass located at its middle are studied. The proof mass of the microresonator is actuated by the electrostatic field in such a way that a direct voltage finds a certain equilibrium position and then be prompted to vibration under the alternative voltage. Due to the importance of the size dependency effect in analysis of the performance of microelectromechanical systems, the size dependent theory is used in the modeling of the microstructure. By adopting the modified couple stress theory and considering electrostatic actuation, the dynamic equation of motion is derived using the extended Hamilton’s principle. Further, with the approximation by Galerkin’s method, the governing equation for the static and oscillatory motion is reduced and the resultant equation is solved by analytical (multiple-scales) and numerical methods. In the analytical and numerical results, the effects of various parameters on the system response, including the midplane stretching and size dependent effects, and dependency of vibration response to initial conditions, are analyzed in detail.

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