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

作者：Raahemifar Kaamran^*

来源：Microsystem Technologies, 2017, 23(10): 4567-4578.

DOI：10.1007/s00542-016-3249-9

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.

• 出版日期2017-10