Electromechanical Model of Electrically Actuated Narrow Microbeams

• Published in: Journal of microelectromechanical systems 2006-10, Vol.15 (5), p.1175-1189
• Main Authors: Batra, R.C., Porfiri, M., Spinello, D.
• Format: Article
• Language: English
• Subjects: Approximation; Boundary conditions; Clamps; Computer simulation; Differential equations; Electrostatics; Exact sciences and technology; Finite element method; Finite element methods; Fringing fields; Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Kinematics; Lagrangian functions; Mathematical analysis; Mathematical models; Mechanical instruments, equipment and techniques; meshless local Petrov-Galerkin (MLPG) method; Methods; microactuators; Microbeams; microelectromechanical systems (MEMS); microelectromechanical systems (MEMS) modeling; Micromechanical devices and systems; microsensors; microstructures; Moment methods; Nonlinear equations; Nonlinear systems; Physics; pull-in instability; pull-in voltage; reduced order models; Studies; Testing
• ISSN: 1057-7157; 1941-0158
• DOI: 10.1109/JMEMS.2006.880204

A consistent one-dimensional distributed electromechanical model of an electrically actuated narrow microbeam with width/height between 0.5-2.0 is derived, and the needed pull-in parameters are extracted with different methods. The model accounts for the position-dependent electrostatic loading, the fringing field effects due to both the finite width and the finite thickness of a microbeam, the mid-plane stretching, the mechanical distributed stiffness, and the residual axial load. Both clamped-clamped and clamped-free (cantilever) microbeams are considered. The method of moments is used to estimate the electrostatic load. The resulting nonlinear fourth-order differential equation under appropriate boundary conditions is solved by two methods. Initially, a one-degree-of-freedom model is proposed to find an approximate solution of the problem. Subsequently, the meshless local Petrov-Galerkin (MLPG) and the finite-element (FE) methods are used, and results from the three methods are compared. For the MLPG method, the kinematic boundary conditions are enforced by introducing a set of Lagrange multipliers, and the trial and the test functions are constructed using the generalized moving least-squares approximation. The nonlinear system of algebraic equations arising from the MLPG and the FE methods are solved by using the displacement iteration pull-in extraction (DIPIE) algorithm. Three-dimensional FE simulations of narrow cantilever and clamped-clamped microbeams are also performed with the commercial code ANSYS. Furthermore, computed results are compared with those arising from other distributed models available in the literature, and it is shown that improper fringing fields give inaccurate estimations of the pull-in voltages and of the pull-in deflections. 1641