Symmetry breaking in an initially curved pre-stressed micro beam loaded by a distributed electrostatic force

Medina, Lior; Gilat, Rivka; Krylov, Slava

doi:10.1016/j.ijsolstr.2014.02.010

Cited by 59 publications

(34 citation statements)

References 21 publications

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“…So to obtain q b1 and q b2 , we can linearize the governing equations (equation (3.1)) around q 2 = 0 as [16] …”

Section: (C) Snap-through and Symmetry Breaking Criteria (I) Snap-thrmentioning

confidence: 99%

“…However, for the asymmetric bifurcation, the arch may exhibit one of the asymmetric deformations shown in figure 1b. Studies on the symmetric snap-through and asymmetric bifurcation of homogeneous macro/micro/nanobeams have been largely reported in the literature, and the influences of the initial arch rise, beam thickness, residual axial force, uniform temperature variation, size effect and surface effects have been systematically investigated [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Recently, functionally graded materials (FGMs) have been proposed to be used in MEMS [22,23] for their combined properties of improved stress distribution, enhanced thermal resistance and high fracture toughness [24,25].…”

Section: Introductionmentioning

confidence: 99%

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Asymmetric bifurcation of thermally and electrically actuated functionally graded material microbeam

Chen¹,

Meguid²

2016

Proc. R. Soc. A.

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In this paper, we investigate the symmetric snapthrough buckling and the asymmetric bifurcation behaviours of an initially curved functionally graded material (FGM) microbeam subject to the electrostatic force and uniform/non-uniform temperature field. The beam model is developed in the framework of Euler-Bernoulli beam theory, accounting for the through-thickness power law variation of the beam material and the physical neutral plane. Based on the Galerkin decomposition method, the beam model is simplified as a 2 d.f. reduced-order model, from which the necessary snap-through and symmetry breaking criteria are derived. The results of our work reveal the significant effects of the power law index on the snap-through and symmetry breaking criteria. Our results also reveal that the non-uniform temperature field can actuate the FGM microbeam and induce the snap-through and asymmetric bifurcation behaviours.

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“…So to obtain q b1 and q b2 , we can linearize the governing equations (equation (3.1)) around q 2 = 0 as [16] …”

Section: (C) Snap-through and Symmetry Breaking Criteria (I) Snap-thrmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Asymmetric bifurcation of thermally and electrically actuated functionally graded material microbeam

Chen¹,

Meguid²

2016

Proc. R. Soc. A.

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“…In particular, curved micro-beams tend to unveil snap-through instabilities and symmetric/nonsymmetric buckling behaviors. [23][24][25][26][27][28][29][30][31][32][33] In this article, the influence of SQFD on oscillations of a slightly curved micro-beam is considered. The initial shape of the beam is assumed to have a sinusoidal profile.…”

Section: Introductionmentioning

confidence: 99%

Influence of squeeze-film damping on the dynamic behavior of a curved micro-beam

Ouakad

Al‐Qahtani

Hawwa

2016

Advances in Mechanical Engineering

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A fixed-fixed curved micro-beam resonator under the influence of harmonic electrostatic field is considered. Due to the presence of incompressible fluid between the micro-beams and the electrode, a squeeze-film damping affects the dynamic behavior of the resonator. The combined effect of curved geometry and fluid squeeze-film damping is investigated for micro-beams with concave and convex geometries. A reduced-order model is obtained through the application of Galerkin discretization on a coupled fluid-structure system composed of the nonlinear Euler-Bernoulli beam equation and Burgdorfer's model for the neighboring fluid. The dynamic behavior is assessed by investigating the influence of squeeze-film damping on the linear and nonlinear frequency response and the maximum resonant deflection of curved up and curved down micro-beams.

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“…Moghimi Zand (2012) also developed a finite element model and found the significant inertia effect on the dynamic snap-through behavior. Medina et al (2012Medina et al ( , 2014a examined the symmetric snap-through buckling and the asymmetric bifurcation of an electrostatically actuated mircobeam with/without residual stress. They derived the criteria of symmetric snap-through and symmetry breaking for quasi-static loading conditions.…”

Section: Introductionmentioning

confidence: 99%

Snap-Through Buckling of Micro/Nanobeams in Bistable Micro/Nanoelectromechanical Systems

Chen

Meguid

2016

Advances in Nanocomposites

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In this chapter, we investigate the instability behavior of an initially curved micro/nanobeam subject to an electrostatic force. The general governing equations of the curved beam are developed using Euler-Bernoulli beam theory and are solved using the Galerkin decomposition method. Firstly, the size effect on the symmetric snap-through buckling of the microbeam is studied. The size effect is accounted for in the beam model using the modified couple stress theory. The fringing field effect and the intermolecular effects, such as van der Waals and Casimir forces, are also included in the snap-through formulations. The model simulations reveal the significant effect of the beam size, and to a much lesser extent the effect of fringing field and intermolecular forces, upon the snap-through criterion for the curved microbeam. Secondly, the surface effects on the asymmetric bifurcation of the nanobeam are studied. The surface effects, including the surface elasticity and the residual surface tension, are accounted for in the model formulation. The results reveal the significant size effect due to the surface elasticity and the residual surface tension on the symmetry-breaking criterion for the considered nanobeam. IntroductionMicro/nano-electro-mechanical systems (MEMS/NEMS) have aroused great interest for their unique advantages such as small size, high precision, and low power consumption. One benchmark of MEMS/NEMS is the initially straight micro/ nanobeam system driven by electrostatic force, whose static and dynamic behaviors have been largely investigated in the literature (Carr et al.

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Symmetry breaking in an initially curved pre-stressed micro beam loaded by a distributed electrostatic force

Cited by 59 publications

References 21 publications

Asymmetric bifurcation of thermally and electrically actuated functionally graded material microbeam

Asymmetric bifurcation of thermally and electrically actuated functionally graded material microbeam

Influence of squeeze-film damping on the dynamic behavior of a curved micro-beam

Snap-Through Buckling of Micro/Nanobeams in Bistable Micro/Nanoelectromechanical Systems

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