Theoretical and Experimental Investigation of the Nonlinear Behavior of an Electrostatically Actuated In-Plane MEMS Arch

Ramini, Abdallah; Hennawi, Qais M. Al; Younis, Mohammad I.

doi:10.1109/jmems.2016.2554659

Cited by 36 publications

(16 citation statements)

References 34 publications

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“…Next, we prove the inherent quadratic nonlinearity of the arch regardless of its actuation method (i.e., whether there is a DC electrostatic force or not), which shows a softening nonlinear response. The nonlinear equation governing the transverse motion w ( x , t ) of the arch beam based on no axial inertia can be written as [ 41 , 42 , 43 , 44 , 45 ]:

where x is the spatial position, t is time, and w 0 is the initial curvature of the arch. The arch has a Young’s modulus E , a material density ρ, and is assumed to have a rectangular cross-sectional area A and a moment of inertia I .…”

Section: Softening Nonlinearity In Arch Microbeammentioning

confidence: 99%

“…It is clear from the integral term of the Equation (1) that the stiffness depends nonlinearly on the displacement, which is a major source of nonlinear behavior. To distinguish the nonlinearities of the arch from that of the electrostatic force, we will assume the force is constant (full modelling of its effect can be found in [ 41 , 42 , 43 , 44 , 45 , 46 ]). The initial shape of the arch is assumed to be

where b 0 is the initial curvature at the middle of arch.…”

Section: Softening Nonlinearity In Arch Microbeammentioning

confidence: 99%

“…Here, we exploit the softening behavior in an arch-shaped beam for memory application. Unlike electrostatically actuated cantilever microbeams, where the softening nonlinear behavior is solely caused by the DC bias voltage, an arch shaped clamped–clamped microbeam shows softening nonlinearity due to its initial curvature [ 41 , 42 , 43 , 44 , 45 , 46 ]. Hence, the nonlinearity in this case is mainly of mechanical origin, and thus is almost independent of the DC bias (does not put any restriction on the amount of bias needed to trigger the nonlinearity), and can even be actuated using other methods, such as piezoelectric.…”

Section: Introductionmentioning

confidence: 99%

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In-Plane MEMS Shallow Arch Beam for Mechanical Memory

et al. 2016

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We demonstrate a memory device based on the nonlinear dynamics of an in-plane microelectromechanical systems (MEMS) clamped–clamped beam resonator, which is deliberately fabricated as a shallow arch. The arch beam is made of silicon, and is electrostatically actuated. The concept relies on the inherent quadratic nonlinearity originating from the arch curvature, which results in a softening behavior that creates hysteresis and co-existing states of motion. Since it is independent of the electrostatic force, this nonlinearity gives more flexibility in the operating conditions and allows for lower actuation voltages. Experimental results are generated through electrical characterization setup. Results are shown demonstrating the switching between the two vibrational states with the change of the direct current (DC) bias voltage, thereby proving the memory concept.

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Section: Softening Nonlinearity In Arch Microbeammentioning

confidence: 99%

where b 0 is the initial curvature at the middle of arch.…”

Section: Softening Nonlinearity In Arch Microbeammentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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In-Plane MEMS Shallow Arch Beam for Mechanical Memory

et al. 2016

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“…Examples of these parameters are bias voltage, axial load, anchor conditions, and excitation frequency, which influence the response of MEMS resonators and determine their usability and range of operation [1][2][3][4][5][6][7][8][9]. The bistability of an arch beam [10][11][12][13], for instance, is one of those phenomena that require tuning of design parameters to predict its occurrence. One of the advantages of MEMS bistable structures, such as buckled beams and arches, is their large strokes compared to monostable and straight structures [14].…”

Section: Introductionmentioning

confidence: 99%

“…Several studies have also investigated the nonlinear vibrations of arch beams [21,[28][29][30][31][32][33][34][35][36][37][38]. Most of these studies are based on the Galerkin discretization [13,14,20,39,40]. Krakover et al [41] demonstrated a displacement sensing technique by monitoring the resonant frequency of a curved beam.…”

Section: Introductionmentioning

confidence: 99%

The Effects of Initial Rise and Axial Loads on MEMS Arches

Tella

Hajjaj

Younis

2017

Journal of Vibration and Acoustics

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Arch microbeams have been utilized and proposed for many uses over the past few years due to their large tunability and bistability. However, recent experimental data have shown different mechanical behaviors of arches when subjected to axial loads, i.e., their stiffness may increase or decrease with applied axial loads. This paper aims to investigate in depth, the influence of the competing effects of initial rise and axial loads on the mechanical behavior of micromachined arches; mainly their static deflection and resonant frequencies. Based on analytical solutions, the static response and eigenvalue problems are analyzed for various values of initial rises and axial loads. Universal curves showing the variation of the first three resonance frequencies of the arch are generated for various values of initial rise under both tensile and compressive axial loads. This study shows that increasing the tensile or compressive axial loads for different values of initial rise may lead to either increase in the stiffness of the beam or initial decrease in the stiffness, which later increases as the axial load is increased depending on the dominant effect of the initial rise of the arch and the axial load. The obtained universal curves represent useful design tools to predict the tunability of arches under axial loads for various values of initial rises. The use of the universal curves is demonstrated with an experimental case study. Analytical formulation is developed to predict the point of minimum where the trend of the resonance frequency versus axial loads changes qualitatively due to the competing effects of axial loads and initial curvature.

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