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Size-dependent asymmetric buckling of initially curved shallow nano-beam using strain gradient elasticity

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Abstract

We have investigated the size-dependency of symmetric and asymmetric buckling in an electrostatically actuated initially curved (arch) stress-free shallow nano-beam. Using the double-mode Galerkin projection method, we have converted the partial differential equation of motion of the arch, given in the framework of Euler–Bernoulli beam and the strain gradient elasticity, to a two-degree-of-freedom model which is capable of accounting for the symmetric and asymmetric instabilities as well as the size-dependencies. Analyzing the bifurcation diagrams of the obtained reduced-order model, we have shown that the symmetric snap-through, release and pull-in instabilities, as well as the asymmetric buckling of the arch are all size-dependent. Our studies show that, as the structure scales down, possibility of the snap-through and the symmetry breaking reduces. We have derived analytical necessary conditions for prediction of the size-dependent snap-through and symmetry breaking. We further have shown that the sufficient condition for the threshold snap-through, during which the asymmetric buckling occurs prior to the symmetric snap-through, is also size-dependent.

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Acknowledgements

Funding was provided by Natural Sciences and Engineering Research Council of Canada (Grant No. 129619).

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  1. Department of Electrical and Computer Engineering, Ryerson University, 350 Victoria St, Toronto, ON, M5B 2K3, Canada

    Kaamran Raahemifar

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  1. Kaamran Raahemifar
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Correspondence to Kaamran Raahemifar.

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Raahemifar, K. Size-dependent asymmetric buckling of initially curved shallow nano-beam using strain gradient elasticity. Microsyst Technol 23, 4567–4578 (2017). https://doi.org/10.1007/s00542-016-3249-9

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