Independent tuning of the linear and nonlinear stiffness coefficients of a micromechanical device

Adams, Scott G.; Bertsch, F.M.; MacDonald, N.C.

doi:10.1109/memsys.1996.493825

Cited by 15 publications

(12 citation statements)

References 10 publications

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“…The first is the mechanical modelling [2], required to fill the lack of knowledge of these relatively new systems. Examples of phenomena which have been specifically considered are various kinds of nonlinearities [3], such as nonlinear stiffness [4], thermoelastic damping [5], micro-impacts [6], complex (Cosserat) models for microbeam [7,8], atomic forces [9], and so on.…”

Section: Introductionmentioning

confidence: 99%

Control of pull-in dynamics in a nonlinear thermoelastic electrically actuated microbeam

Lenci

Rega

2006

J. Micromech. Microeng.

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This work deals with the problem of controlling the nonlinear dynamics, in general, and the dynamic pull-in, in particular, of an electrically actuated microbeam. A single-well softening model recently proposed by Gottlieb and Champneys [1] is considered, and a control method previously proposed by the authors is applied. Homoclinic bifurcation, which triggers the safe basin erosion eventually leading to pull-in, is considered as the undesired event, and it is shown how appropriate controlling superharmonics added to a reference harmonic excitation succeed in shifting it towards higher excitation amplitudes. An optimization problem is formulated, and the optimal excitation shape is obtained. Extensive numerical simulations aimed at checking the effectiveness of the control method in shifting the erosion of the safe basin are reported. They highlight good performances of the control method beyond theoretical expectations.

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Section: Introductionmentioning

confidence: 99%

Control of pull-in dynamics in a nonlinear thermoelastic electrically actuated microbeam

Lenci

Rega

2006

J. Micromech. Microeng.

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“…Substituting equations (3) and (4) into equation (2) and equating coefficients of like powers of one obtains…”

Section: Formulation Of the Problem And Perturbation Analysismentioning

confidence: 99%

“…Nonlinearities in micro-electro-mechanical systems (MEMS) can arise from various sources such as spring and damping mechanisms [1,2] and resistive, inductive, and capacitive circuit elements [3]. Surface and fluids forces [4,5] can also be other sources of nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

Harmonic and sub-harmonic resonance of MEMS subjected to a weakly non-linear parametric and external excitations

Mosa

El-Naggar

El-Bassiouny

2013

International Journal of Applied Mathematical Research

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This paper presents a simplified mathematical model for the purpose of studying the resonant responses of a nonlinear dynamical system, (micro -electro -mechanical systems (MEMS)), which represented by a Van-der Pol equation subjected to a weakly non-linear parametric and forcing excitations. Using Multiple scales method, the Van-der Pol equation is transformed to a system of second order differential equation up to first order of small parameter ε. Three types of resonances are studied (harmonic resonance and subharmonic resonances of even order (onehalf and one -fourth )). The modulation equations for each resonances, steady state solutions, frequency-response equations, stability analysis are determined. Numerical analysis for frequency-response equations and stability conditions are carried out. Results are presented graphically by group of figures. Finally discussion for these figures are given.

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“…Recently, a fringe ÿeld comb drive and a linearly varied length comb drive have been fabricated for electrostatic tuning by Adams et al [17], and Lee et al [18], respectively. In the device of Adams, the operation range of this device is limited to only within 2-5 m, while, in Lee's device, only the linear sti ness can be tuned.…”

Section: Introductionmentioning

confidence: 99%

Optimal shape design of three-dimensional MEMS with applications to electrostatic comb drives

Mukherjee

1999

Int. J. Numer. Meth. Engng.

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SUMMARYA comb drive is one of the most important microactuators in Microelectromechanical (MEM) systems. In a standard comb drive, the capacitance varies linearly with displacement, resulting in an electrostatic driving force which is independent of the position of the moving ÿngers (relative to the ÿxed ones) except at the ends of the range of travel. It is of interest in some applications to have force proÿles such as linear, quadratic or cubic. Such shaped comb drives could be useful, for example, for electrostatic tuning or to get actuators with longer ranges of travel than those of standard comb drives. This paper presents a methodology for solving three-dimensional design (inverse) problems in MEM systems. Design of variable shape comb drives (shape motors) is presented as an application of the general methodology. It addresses issues of simulation, sensitivity analysis and then design of three-dimensional comb drives. Direct simulation is carried out by the exterior, indirect boundary element method and shape sensitivities are obtained by the direct di erentiation approach. The inverse problem determines the height proÿle of the moving ÿngers of a comb drive such that the driving force is a desired function of its travel distance. An available optimization code ('E04UCF' from the NAG package) is used to solve the inverse problem. Numerical results are presented for shape motors that produce linear or cubic force proÿles as functions of travel of the moving ÿngers.

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Independent tuning of the linear and nonlinear stiffness coefficients of a micromechanical device

Cited by 15 publications

References 10 publications

Control of pull-in dynamics in a nonlinear thermoelastic electrically actuated microbeam

Control of pull-in dynamics in a nonlinear thermoelastic electrically actuated microbeam

Harmonic and sub-harmonic resonance of MEMS subjected to a weakly non-linear parametric and external excitations

Optimal shape design of three-dimensional MEMS with applications to electrostatic comb drives

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