Journal: |
Engineering with Computers
Springer-Verlag London Ltd., part of Springer Nature
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Volume: |
22
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Abstract: |
Because of fasttechnological development, electrostatic nanoactuator devices like nanosensors, nanoswitches, and nanoresonators are highly considered by scientific community. Thus, this article presents a new solution technique in solving highly
nonlinear integro-differential equation governing electrically actuated nanobeams made of functionally graded material. The
modified couple stress theory and Gurtin–Murdoch surface elasticity theory are coupled together to capture the size effects
of the nanoscale thin beam in the context of Euler–Bernoulli beam theory. For accurate modelling, all the material properties of the bulk and surface continuums of the FG nanoactuator are varied continuously in thickness direction according to
power law. The nonlinearity arising from the electrostatic actuation, fringing field, mid-plane stretching effect, axial residual
stress, Casimir dispersion, and van der Waals forces are considered in mathematical formulation. The nonlinear nonclassical
equilibrium equation of FG nanobeam-based actuators and associated boundary conditions are exactly derived using Hamilton
principle. The new solution methodology is combined from three phases. The first phase applies Galerkin method to get an
integro-algebraic equation. The second one employs particle swarm optimization method to approximate the integral terms
(i.e. electrostatic force, fringing field, and intermolecular forces) to non-integral cubic algebraic equation. Then, solved the
system easily in last phase. The resulting algebraic model provides means for obtaining critical deflection, pull-in voltage,
detachment length, minimum gap, and freestanding effects. A reasonable agreement is found between the results obtained
from the present method and those in the available literature. A parametric study is performed to investigate the effects of
the gradient index, material length scale parameter, surface energy, intermolecular forces, initial gap, and beam length on
the pull-in response and freestanding phenomena of fully clamped and cantilever FG nanoactuators.
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