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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.


Normalized fundamental frequency versus A for μ = 0 (solid curve), μ ⋍ 0.3μcr (dashed curve), α = 4 and β = 0; (a) φ = 1 and (b) φ = 1/2.
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f9-sensors-08-01048: Normalized fundamental frequency versus A for μ = 0 (solid curve), μ ⋍ 0.3μcr (dashed curve), α = 4 and β = 0; (a) φ = 1 and (b) φ = 1/2.

Mentions: In Figure 9, we report, for two different values of μ, the fundamental frequency w0 of the deflected microplate versus A for α = 4 and β = 0 and for a square and a rectangular plate. The natural frequency is normalized with respect to the value w̅0 corresponding to λ = 0; values of non-dimensional w̅0 for Figures 9 and 10 are reported in Table 1. The corresponding dimensional frequencies equal . As reported in [56], for μ = 0 and λ = 0, the values of the non-dimensional frequency w̅0 equal 36.108 and 98.592 for the square and the rectangular plate with φ = 1/2, respectively.


Effects of van der Waals Force and Thermal Stresses on Pull-in Instability of Clamped Rectangular Microplates
Normalized fundamental frequency versus A for μ = 0 (solid curve), μ ⋍ 0.3μcr (dashed curve), α = 4 and β = 0; (a) φ = 1 and (b) φ = 1/2.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3927533&req=5

f9-sensors-08-01048: Normalized fundamental frequency versus A for μ = 0 (solid curve), μ ⋍ 0.3μcr (dashed curve), α = 4 and β = 0; (a) φ = 1 and (b) φ = 1/2.
Mentions: In Figure 9, we report, for two different values of μ, the fundamental frequency w0 of the deflected microplate versus A for α = 4 and β = 0 and for a square and a rectangular plate. The natural frequency is normalized with respect to the value w̅0 corresponding to λ = 0; values of non-dimensional w̅0 for Figures 9 and 10 are reported in Table 1. The corresponding dimensional frequencies equal . As reported in [56], for μ = 0 and λ = 0, the values of the non-dimensional frequency w̅0 equal 36.108 and 98.592 for the square and the rectangular plate with φ = 1/2, respectively.

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.