Size-dependent performance of microgyroscopes

Ghayesh, Mergen H.; Farokhi, Hamed; Alici, Gürsel

doi:10.1016/j.ijengsci.2015.11.003

Cited by 162 publications

(45 citation statements)

References 31 publications

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“…The nonlocal stress and strain gradient theory was utilized to capture the size effects and the homotopy perturbation technique was used to solve the nonlinear governing equation. Ghayesh et al [43] studied the size-dependent dynamical behavior of a micro-gyroscope under applied DC and AC voltages based on the modified couple F I G U R E 1 Configuration, coordinate system, and geometry of an electrostatically actuated ( ) cantilever or ( ) fully fixed resonator beam stress theory. By use of a weighted-residual method, a reduction procedure was used to get a reduced-order model which was solved by use of a continuation technique.…”

Section: A Literature Reviewmentioning

confidence: 99%

“…Moreover, most of the studies on the dynamic pull-in behavior of electrostatically actuated structures limit to the numerical solution methods. [39][40][41]43,44] In this study, a semi-analytical solution is developed to study the dynamic pull-in instability of electrostatically actuated multilayer nanoresonators using the nonlocal elasticity theory and Euler-Bernoulli beam model. Resonators are modeled as symmetric multilayered beams with fixed-fixed and fixed-free end conditions which are embedded in an elastic medium containing the Winkler and Pasternak elastic foundations.…”

Section: Present Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Also, it is evident from the literature review that the effects of small scale and intermolecular forces should be taken account in the mechanical analysis of nanoscale structures. Moreover, most of the studies on the dynamic pull‐in behavior of electrostatically actuated structures limit to the numerical solution methods . In this study, a semi‐analytical solution is developed to study the dynamic pull‐in instability of electrostatically actuated multilayer nanoresonators using the nonlocal elasticity theory and Euler–Bernoulli beam model.…”

Section: Introductionmentioning

confidence: 99%

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On dynamic pull‐in instability of electrostatically actuated multilayer nanoresonators: A semi‐analytical solution

Taati

2019

Z Angew Math Mech

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Based on the nonlocal Euler–Bernoulli beam theory, a theoretical approach is developed to investigate the effects of small scale and intermolecular force on the dynamic pull‐in behavior of electrostatically actuated nanoresonators. To this purpose, nanoresonators are modeled as multilayer beams with rectangular cross‐sections and fixed‐fixed and fixed‐free end conditions which are embedded in an elastic medium containing Winkler and Pasternak elastic foundations. Also, the effects of nonlocal parameter, fringing field due to the finite width of beams, Casimir or van der Waals intermolecular forces, nonlinear term induced by mid‐plane stretching and Winkler and Pasternak elastic foundations are considered in the mathematical modeling of pull‐in behavior. Finally, a hybrid semi‐analytical method is proposed to solve the nonlinear partial differential equation in two steps using the separation of variable technique. First, the Galerkin method is used to reduce a nonlinear ordinary differential equation with respect to time variable. Next, the parameter expansion method is applied to solve ensuing equation and obtain the time history response of transverse deflection. As case studies, the numerical results including curves of voltage‐normalized frequency, time history of normalized maximum deflection and phase portrait of two six‐layer cantilever and fully fixed beams are presented and discussed in detail. Findings indicate that the effect of small scale on the pull‐in voltages is more significant for both boundary conditions, in comparison with the intermolecular force. Also, it is seen that the pull‐in voltages of cantilever beams become larger by considering the nonlocal effect, contrary to the case of fully fixed beams.

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Section: A Literature Reviewmentioning

confidence: 99%

Section: Present Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On dynamic pull‐in instability of electrostatically actuated multilayer nanoresonators: A semi‐analytical solution

Taati

2019

Z Angew Math Mech

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“…Recent developments have accompanied to design and manufacture smaller micro/nano tubes which have made researchers to promote theoretical and molecular models enabling them to mathematically model such systems with satisfying precision, considering the micro/nano structure small effects which is not feasible utilizing classical continuum theories [16][17][18][19]. Recent research outcomes revealed that materials exhibit strong size-dependent characteristics in micron and nano sizes [20][21][22][23][24][25][26][27][28][29][30][31]. Zhang et al [32] investigated the dynamical behavior of a Timoshenko nanobeam conveying fluid flow considering surface effects using Gurtin and Murdoch surface theorem.…”

Section: Introductionmentioning

confidence: 99%

On the dynamics of micro-tubes conveying fluid on various foundations

2019

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In this paper, using modified couple stress theory, dynamic stability of a cantilevered micro-tube embedded in several types of elastic media is studied. The governing equation for lateral vibrations of the micro-tube conveying fluid is derived using the extended Hamilton's principle. The numerical results are obtained by employing the extended Galerkin's method. For validation purposes, the obtained results for simple cases are compared and findings indicate a very good agreement with those available in the literature. The stability maps of different configurations with different flow velocities are studied and the influences of various parameters such as material length scale, external diameter and different elastic properties on the stability of the system are considered. Results indicate that elastic environments may enlarge the stability regions significantly at larger values of mass ratio parameter while decrease it for smaller values of mass ratio parameter. Moreover, using elastic media mathematically defined by series functions provides the capability to simulate almost any real time operational environment the micro-tube embedded in and results in an optimal stability state of the micro-structure carrying fluid flow.

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Dynamic analysis of nonlinear rotating composite shafts excited by non‐ideal energy source

Kafi

Hosseini

2019

Z Angew Math Mech

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In this article, nonlinear nonstationary vibration of a rotating composite shaft passing through critical speed excited by non-ideal energy source is investigated. Geometrical nonlinearity, gyroscopic effect, rotary inertia and coupling due to material anisotropy are considered, while shear deformation is neglected. By using Hamilton principle, axial-flexural-flexural-torsional-rotational equations of motion for a composite shaft with variable rotational speed are derived. External source is assumed as non-ideal that causes the interaction between external torque and vibrating system.To obtain the approximate analytical solution, perturbation theory (multiple scales method) is applied to reduce the equations in the neighborhood of the first critical speed. Although, the analysis is done for the first critical speed, one-mode discretization is not enough. Indeed, at least two modes is required to obtain accurate results.The effects of external damping, eccentricity, angle of fibers, resistive torque, nonlinear terms, and also the effect of the extensional-torsional coupling on occurrence of Sommerfeld effect are investigated. It is shown that nonlinearity and coupling possess significant effect on the prediction of Sommerfeld phenomenon. Moreover, as observed, with appropriate implementation of layup and stacking sequence, one can obtain the best performance for the nonstationary behavior of composite shaft. K E Y W O R D Scomposite rotor, multiple-scales method, non-ideal source, nonstationary motion, sommerfeld effect

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Size-dependent performance of microgyroscopes

Cited by 162 publications

References 31 publications

On dynamic pull‐in instability of electrostatically actuated multilayer nanoresonators: A semi‐analytical solution

On dynamic pull‐in instability of electrostatically actuated multilayer nanoresonators: A semi‐analytical solution

On the dynamics of micro-tubes conveying fluid on various foundations

Dynamic analysis of nonlinear rotating composite shafts excited by non‐ideal energy source

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