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Journal of Computational and Nonlinear Dynamics | Volume 8 | Issue 1 | research-article
Research Papers

An Efficient Reduced-Order Model to Investigate the Behavior of an Imperfect Microbeam Under Axial Load and Electric Excitation

[+] Author and Article Information
Laura Ruzziconi

Department of Civil and Building Engineering, and Architecture,
Polytechnic University of Marche,
via Brecce Bianche, 60131 Ancona, Italy
e-mail: l.ruzziconi@univpm.it

Mohammad I. Younis

Department of Mechanical Engineering,
State University of New York at Binghamton,
Binghamton, NY 13902
e-mail: myounis@binghamton.edu

Stefano Lenci

Department of Civil and Building Engineering, and Architecture,
Polytechnic University of Marche,
via Brecce Bianche, 60131 Ancona, Italy
e-mail: lenci@univpm.it

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 15, 2011; final manuscript received May 11, 2012; published online July 23, 2012. Assoc. Editor: Carmen M. Lilley.

J. Comput. Nonlinear Dynam 8(1), 011014 (Jul 23, 2012) (9 pages) Paper No: CND-11-1217; doi: 10.1115/1.4006838 History: Received November 15, 2011; Revised May 11, 2012
Article
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Citing Articles

In this study an efficient reduced-order model for a MEMS device is developed and investigations of the nonlinear static and the dynamic behavior are performed. The device is constituted of an imperfect microbeam under an axial load and an electric excitation. The imperfections, typically due to microfabrication processes, are simulated assuming a shallow arched initial shape. The axial load is deliberately added with an elevated value. The structure has a bistable static configuration of double potential well with possibility of escape. We derive a single-mode reduced-order model via the Ritz technique and the Padé approximation. This model, while simple, is able to combine both a sufficient accuracy, which enables to detect the main qualitative features of the device response up to elevated values of electrodynamic excitation, and a remarkable computational efficiency, which is essential for systematic global nonlinear dynamic simulations. We illustrate the nonlinear phenomena arising in the device, such as the coexistence of various competing in-well and cross-well attractors, which leads to a considerable versatility of behavior. We discuss their physical meaning and their practical relevance for the engineering design of the microstructure, since this is an uncommon and very attractive aspect in applications.
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References

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Figures

Grahic Jump Location
Fig. 1

Schematic of the MEMS device

+Schematic of the MEMS device
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Schematic of the MEMS device
Grahic Jump Location
Fig. 5

Bifurcation diagram of the maximum static deflection vs(0.5) versus the electrostatic voltage VDC, at n=60. Stable and unstable branches are, respectively, the solid and dashed lines.

+Bifurcation diagram of the maximum static deflection vs(0.5) versus the electrostatic voltage VDC, at n=60. Stable and unstable branches are, respectively, the solid and dashed lines.
View Large  |  Save Figure  |  Download Slide (.ppt)
Bifurcation diagram of the maximum static deflection vs(0.5) versus the electrostatic voltage VDC, at n=60. Stable and unstable branches are, respectively, the solid and dashed lines.
Grahic Jump Location
Fig. 4

Bifurcation diagram of the maximum static deflection vs(0.5) versus the axial load n, at VDC=1.2 V. Stable and unstable branches are, respectively, the solid and dashed lines.

+Bifurcation diagram of the maximum static deflection vs(0.5) versus the axial load n, at VDC=1.2 V. Stable and unstable branches are, respectively, the solid and dashed lines.
View Large  |  Save Figure  |  Download Slide (.ppt)
Bifurcation diagram of the maximum static deflection vs(0.5) versus the axial load n, at VDC=1.2 V. Stable and unstable branches are, respectively, the solid and dashed lines.
Grahic Jump Location
Fig. 3

Analytical approximation of the static configurations: the stable and unstable ones are, respectively, the solid and dashed line

+Analytical approximation of the static configurations: the stable and unstable ones are, respectively, the solid and dashed line
View Large  |  Save Figure  |  Download Slide (.ppt)
Analytical approximation of the static configurations: the stable and unstable ones are, respectively, the solid and dashed line
Grahic Jump Location
Fig. 2

The total potential energy V(a)

+The total potential energy V(a)
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The total potential energy V(a)
Grahic Jump Location
Fig. 6

First mode shape around the upper (— —) and the lower (---) stable equilibrium and the unstable (------) equilibrium between the two wells

+First mode shape around the upper (— —) and the lower (---) stable equilibrium and the unstable (------) equilibrium between the two wells
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First mode shape around the upper (— —) and the lower (---) stable equilibrium and the unstable (------) equilibrium between the two wells
Grahic Jump Location
Fig. 7

(a) The total potential energy V(Y) and (b) the electric potential Ve(Y). The numerical evaluation is in gray dots and the analytical Padé approximation is the black line.

+(a) The total potential energy V(Y) and (b) the electric potential Ve(Y). The numerical evaluation is in gray dots and the analytical Padé approximation is the black line.
View Large  |  Save Figure  |  Download Slide (.ppt)
(a) The total potential energy V(Y) and (b) the electric potential Ve(Y). The numerical evaluation is in gray dots and the analytical Padé approximation is the black line.
Grahic Jump Location
Fig. 8

Frequency response diagram at VAC=3.5 V. Attractors A, B, and C are, respectively, the black, blue, and green line.

+Frequency response diagram at VAC=3.5 V. Attractors A, B, and C are, respectively, the black, blue, and green line.
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Frequency response diagram at VAC=3.5 V. Attractors A, B, and C are, respectively, the black, blue, and green line.
Grahic Jump Location
Fig. 10

Frequency response diagrams at VAC=14 V

+Frequency response diagrams at VAC=14 V
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Frequency response diagrams at VAC=14 V
Grahic Jump Location
Fig. 9

Attractor-basins phase portrait at Ω = 12 and VAC=3.5 V

+Attractor-basins phase portrait at Ω = 12 and VAC=3.5 V
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Attractor-basins phase portrait at Ω = 12 and VAC=3.5 V

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