Modeling electrostatic field in mems devices using artdticial springs in rayleigh-ritz method
Keywords:Eigenvalues and eigenfunctions, Electrostatics, MEMS, Stiffness, Boundary characteristics, Boundary conditioning, Eigenvalues, Elastic foundation, Elastic properties, Electrostatic effect, Electrostatic field, Gram-schmidt, MEMSDevices, Micro devices, Microelectromechanical systems, Mode shapes, Orthogonal polynomial, Per unit, Plate-Type, Rayleigh-Ritz methods, Softening effect, Static equilibrium, Static equilibrium conditions, Structural stiffness, Vibration problem
AbstractBoundary characteristic orthogonal polynomials were used in the Rayleigh-Ritz method to model and analyze electrostatic field in micro electro mechanical system (MEMS) devices. These orthogonal polynomials were generated using Gram-Schmidt process to conduct the investigations. The vibration problem was formulated at the static equilibrium condition by including an elastic foundation stiffness to represent the electrostatic field effects. The problem was formulated to obtain the modeshapes and the eigenvalues of the plate type microdevice at the static equilibrium position. The electrostatic field had a softening effect on the elastic property of the system, as it acted in opposition to the structural stiffness. The softening effect was introduced in terms of distributed springs or an elastic foundation with stiffness per unit area of 'Ke' to apply the boundary conditioning to represent the electrostatic effect.
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