Effects of van der Waals force and thermal stresses on pull-in instability of clamped rectangular microplates

Romesh C. Batra, Maurizio Porfiri, Davide Spinello

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1048-1069
Number of pages22
JournalSensors (Switzerland)
Volume8
Issue number2
StatePublished - Feb 2008

Fingerprint

Van der Waals forces
thermal stresses
Thermal stress
Hot Temperature
Vibration
vibration
Galerkin method
Electric potential
electric potential
linear equations
Galerkin methods
Linear equations
Nonlinear equations
Ordinary differential equations
boundary value problems
Boundary value problems
nonlinear equations
deflection
estimating
differential equations

Keywords

  • Microelectromechanical systems
  • Microplate
  • Microsensor
  • Pull-in instability
  • Van der Waals force

ASJC Scopus subject areas

  • Analytical Chemistry
  • Biochemistry

Cite this

Effects of van der Waals force and thermal stresses on pull-in instability of clamped rectangular microplates. / Batra, Romesh C.; Porfiri, Maurizio; Spinello, Davide.

In: Sensors (Switzerland), Vol. 8, No. 2, 02.2008, p. 1048-1069.

Research output: Contribution to journalArticle

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