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Effects of van der Waals Force and Thermal Stresses on Pull-in Instability of Clamped Rectangular Microplates

View Article: PubMed Central - PubMed

ABSTRACT

We study the influence of von Kármán nonlinearity, van der Waals force, and thermal stresses on pull-in instability and small vibrations of electrostatically actuated microplates. We use the Galerkin method to develop a tractable reduced-order model for electrostatically actuated clamped rectangular microplates in the presence of van der Waals forces and thermal stresses. More specifically, we reduce the governing two-dimensional nonlinear transient boundary-value problem to a single nonlinear ordinary differential equation. For the static problem, the pull-in voltage and the pull-in displacement are determined by solving a pair of nonlinear algebraic equations. The fundamental vibration frequency corresponding to a deflected configuration of the microplate is determined by solving a linear algebraic equation. The proposed reduced-order model allows for accurately estimating the combined effects of van der Waals force and thermal stresses on the pull-in voltage and the pull-in deflection profile with an extremely limited computational effort.

No MeSH data available.


Variation of μcr with the aspect ratio φ for (a) α = 1 and β = 0 and (b) α = 4 and β = 0.
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f2-sensors-08-01048: Variation of μcr with the aspect ratio φ for (a) α = 1 and β = 0 and (b) α = 4 and β = 0.

Mentions: Figure 2 shows the variation of the critical van der Waals force parameter μcr with respect to the aspect ratio φ for two values of and for λ = 0 and β = 0. Numerical data in Figure 2 are interpolated with(40)μcr=f(α)(1+∑k=24φ−k),where the function f(α), plotted in Figure 3, is given by(41)f(α)=3.91α+36.7.


Effects of van der Waals Force and Thermal Stresses on Pull-in Instability of Clamped Rectangular Microplates
Variation of μcr with the aspect ratio φ for (a) α = 1 and β = 0 and (b) α = 4 and β = 0.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3927533&req=5

f2-sensors-08-01048: Variation of μcr with the aspect ratio φ for (a) α = 1 and β = 0 and (b) α = 4 and β = 0.
Mentions: Figure 2 shows the variation of the critical van der Waals force parameter μcr with respect to the aspect ratio φ for two values of and for λ = 0 and β = 0. Numerical data in Figure 2 are interpolated with(40)μcr=f(α)(1+∑k=24φ−k),where the function f(α), plotted in Figure 3, is given by(41)f(α)=3.91α+36.7.

View Article: PubMed Central - PubMed

ABSTRACT

We study the influence of von Kármán nonlinearity, van der Waals force, and thermal stresses on pull-in instability and small vibrations of electrostatically actuated microplates. We use the Galerkin method to develop a tractable reduced-order model for electrostatically actuated clamped rectangular microplates in the presence of van der Waals forces and thermal stresses. More specifically, we reduce the governing two-dimensional nonlinear transient boundary-value problem to a single nonlinear ordinary differential equation. For the static problem, the pull-in voltage and the pull-in displacement are determined by solving a pair of nonlinear algebraic equations. The fundamental vibration frequency corresponding to a deflected configuration of the microplate is determined by solving a linear algebraic equation. The proposed reduced-order model allows for accurately estimating the combined effects of van der Waals force and thermal stresses on the pull-in voltage and the pull-in deflection profile with an extremely limited computational effort.

No MeSH data available.