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Research Papers

Asymmetric Bifurcation of Initially Curved Nanobeam

[+] Author and Article Information
X. Chen

Mechanics and Aerospace Design Laboratory,
Department of Mechanical
and Industrial Engineering,
University of Toronto,
5 King's College Road,
Toronto, ON M5S 3G8, Canada

S. A. Meguid

Fellow ASME
Mechanics and Aerospace Design Laboratory,
Department of Mechanical
and Industrial Engineering,
University of Toronto,
5 King's College Road,
Toronto, ON M5S 3G8, Canada
e-mail: meguid@mie.utoronto.ca

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received April 13, 2015; final manuscript received May 14, 2015; published online June 16, 2015. Assoc. Editor: Taher Saif.

J. Appl. Mech 82(9), 091003 (Sep 01, 2015) (8 pages) Paper No: JAM-15-1192; doi: 10.1115/1.4030647 History: Received April 13, 2015; Revised May 14, 2015; Online June 16, 2015

In this paper, we investigate the asymmetric bifurcation behavior of an initially curved nanobeam accounting for Lorentz and electrostatic forces. The beam model was developed in the framework of Euler–Bernoulli beam theory, and the surface effects at the nanoscale were taken into account in the model by including the surface elasticity and the residual surface tension. Based on the Galerkin decomposition method, the model was simplified as two degrees of freedom reduced order model, from which the symmetry breaking criterion was derived. The results of our work reveal the significant surface effects on the symmetry breaking criterion for the considered nanobeam.

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Figures

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Fig. 1

Schematics of instability behaviors of arch

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Fig. 2

Initially curved double-clamped nanobeam under distributed transverse load

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Fig. 3

Initially curved nanobeam actuated by Lorentz force. The directions of the magnetic flux, electric current, and Lorentz force are indicated.

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Fig. 4

Bifurcation diagram of nanobeam actuated by Lorentz force. ② and ③ are bifurcation points. The stretching parameter α = 96 and the residual surface tension parameter λs = 2. The inset in (b) shows the evolutions of the deformed beam.

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Fig. 5

Minimum allowable ratio (r/h)min between the initial arch rise r and the beam thickness h for the asymmetric bifurcation at different levels of h (normalized as h/(Es/E*)) and residual surface tension τ0 (normalized as τ0/Es). The beam length-to-thickness ratio L/h = 25.

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Fig. 6

Initially curved nanobeam actuated by electrostatic force (direction indicated by arrow)

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Fig. 7

Bifurcation diagram of nanobeam actuated by electrostatic force. ② and ③ are bifurcation points. The stretching parameter α = 600 and the residual surface tension parameter λs = 2.

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Fig. 8

Evolutions of asymmetric bifurcation points with dimensionless initial arch rise at different levels of the stretching parameter α. The dimensionless residual surface tension λs = 2.

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Fig. 9

Minimum allowable ratio (r/h)min between the initial arch rise r and the beam thickness h for the asymmetric bifurcation at different levels of h (normalized as h/(Es/E*)) and residual surface tension τ0 (normalized as τ0/Es). The beam length-to-thickness ratio L/h = 25.

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