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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.


For α = 1 (solid line), α = 4 (dashed line), and μ = 0, variation with β of the pull-in voltage parameter λPIfor (a) square plate, and (b) rectangular plate with φ = 1/2.
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f8-sensors-08-01048: For α = 1 (solid line), α = 4 (dashed line), and μ = 0, variation with β of the pull-in voltage parameter λPIfor (a) square plate, and (b) rectangular plate with φ = 1/2.

Mentions: In the absence of van der Waals force, that is, for μ = 0, Figure 8 exhibits the variation with the prestress parameter β of the pull-in voltage λPI for a square plate, and a rectangular plate with p = 1/2, and also two values of α. We note that magnitudes of the compressive and tensile thermal stresses are limited, respectively, by the buckling instability of the MEMS and the tensile strength of the material of the MEMS.


Effects of van der Waals Force and Thermal Stresses on Pull-in Instability of Clamped Rectangular Microplates
For α = 1 (solid line), α = 4 (dashed line), and μ = 0, variation with β of the pull-in voltage parameter λPIfor (a) square plate, and (b) rectangular plate with φ = 1/2.
© Copyright Policy
Related In: Results  -  Collection

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

f8-sensors-08-01048: For α = 1 (solid line), α = 4 (dashed line), and μ = 0, variation with β of the pull-in voltage parameter λPIfor (a) square plate, and (b) rectangular plate with φ = 1/2.
Mentions: In the absence of van der Waals force, that is, for μ = 0, Figure 8 exhibits the variation with the prestress parameter β of the pull-in voltage λPI for a square plate, and a rectangular plate with p = 1/2, and also two values of α. We note that magnitudes of the compressive and tensile thermal stresses are limited, respectively, by the buckling instability of the MEMS and the tensile strength of the material of the MEMS.

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.