Nonlinear electro-dynamic analysis of micro-actuators: Effect of material nonlinearity

Jian-she, Peng; Yang, Lijun; Luo, Guang Bing; Yang, Jie

doi:10.1016/j.apm.2013.10.070

Cited by 19 publications

(10 citation statements)

References 24 publications

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“…Since then, mechanics of functionally graded materials and structures has been a focus in solid mechanics and relevant disciplines, and a lot of studies have been carried out [1][2][3][4][5][6][7][8]. The most important feature in the analysis is that the three-dimensional equations governing the problems are partial differential equations with variable coefficients [9]. This usually leads to undesired mathematical difficulty even in the elastic regime, which, however, has also triggered many efforts in seeking for analytical or numerical solutions for FGMs.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation of pressurized functionally graded elastomeric hollow cylinders

Chen

Liu

Kitipornchai

et al. 2017

Composites Part B: Engineering

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Various bifurcation behaviors, including asymmetric axial buckling induced by end thrust, bifurcation under external pressure, and eversion without any loading, of a soft circular hollow cylinder (or cylindrical shell) composed of functionally graded incompressible elastomeric material are considered in a unified way. Based on the nonlinear elasticity theory of a deformable continuous body undergoing large deformation and the linearized incremental theory for a superimposed infinitesimal deformation, an efficient approach for buckling analysis is developed and applied to the cylinder subjected to a combination of axial end thrust and internal/external pressure. It is based on the state-space formalism, which naturally avoids the derivatives of instantaneous material constants, enabling a convenient and accurate numerical implementation. Along with the layerwise method, an analytical characteristic equation (i.e. the bifurcation criterion) governing the general asymmetric buckling of the cylinder is derived. Detailed parametric studies are then carried out for a pressurized soft functionally graded hollow cylinder using an incompressible Mooney-Rivlin material model. The effects of material gradient on bifurcation induced either by end thrust or external pressure are discussed through numerical examples. Not only does this study provide an efficient tool for buckling analysis of soft cylinders, some findings that are unique to a functionally graded material are also highlighted. All in all, it is found highly possible to tune the bifurcation behavior of soft elastomeric cylindrical shells by tailoring material composition and/or adjusting the pressures acting on the surfaces of the cylinder.

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Section: Introductionmentioning

confidence: 99%

Bifurcation of pressurized functionally graded elastomeric hollow cylinders

Chen

Liu

Kitipornchai

et al. 2017

Composites Part B: Engineering

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“…In [8], instability of static pull-in related to electrostatically-A C C E P T E D M A N U S C R I P T actuated microbridges and microcantilevers was investigated by considering different nonlinear effects. Like the work presented in [9], some works studied the dynamics of microcantilever after pull-in. Reference [9] presented a nonlinear dynamic analysis of a micro-actuator made of nonlinear elastic materials.…”

Section: Introductionmentioning

confidence: 96%

“…Like the work presented in [9], some works studied the dynamics of microcantilever after pull-in. Reference [9] presented a nonlinear dynamic analysis of a micro-actuator made of nonlinear elastic materials. The theoretical formulations were based on Bernoulli-Euler beam theory and they were included the effects of mid-plane stretching due to large deformation and material nonlinearity.…”

Section: Introductionmentioning

confidence: 96%

A hybrid solution for analyzing nonlinear dynamics of electrostatically-actuated microcantilevers

Sadeghzadeh

Kabiri

2017

Applied Mathematical Modelling

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Highlights A hybrid solution for nonlinear dynamics of microcantilevers has been introduced  The pure odd-order nonlinear model combined with a distributed parameter system.  A comprehensive model for MEMS before, during and after switching was presented  Two distinct model for before pull-in and after pull-in regimes are combined ACCEPTED MANUSCRIPT AbstractThis paper introduces a closed-form approximation of dynamic response of microcantilevers.The applied load on the system was linearized by Taylor series expansion and to obtain approximate solutions, model of a pure odd-order nonlinear oscillator, subjected to constant excitation was assumed. Pull-in voltage was investigated to analyze the different parameters of the examined microbeam. In order to obtain a comprehensive dynamic model for MEMS devices, before, during and after switching, the pure odd-order nonlinear model was combined with a distributed parameter system and solved after reaching the pull-in voltage.The obtained results demonstrate correct prediction of the static pull-in voltage and also the dynamic deflection of microbeams. By using the same approach, the sensitivity of the pull-in voltage to various geometrical parameters was also investigated. The obtained results indicate that excessive increase in the air gap causes substantial increase in the pull-in voltage; while increasing thickness of microcantilever has even greater effect. It was also observed that for a given thickness of microcantilever, increasing its length beyond a certain amount has no effect on the pull-in voltage.

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“…in which im X (x) is the trial function of the clamped-clamped micro-beam (Peng et al, 2014) and m is the mode number. Substituting Eq.…”

Section: Solution Methodologymentioning

confidence: 99%

Study Neo-Hookean and Yeoh Hyper-Elastic Models in Dielectric Elastomer-Based Micro-Beam Resonators

Barforooshi

Mohammadi

2016

Lat. Am. j. solids struct.

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Micro-bridge resonator with dielectric elastomer that is sandwiched between two electrodes is studied here with geometric and material nonlinearity. Geometric nonlinearity is introduced with Von-Karman strain-displacement relationship. For material nonlinearity that is modeled rarely in articles, two hyper-elastic models are used here. Governing equation of motion for Neo-Hookean and Yeoh models are derived through Hamilton's principle. These equations show that Neo-Hookean is not a suitable model for this case because of inadequate terms, but the Yeoh one is. Governing equation in Yeoh model is solved by analytical Lindstedt-Poincare method. Time history of micro-beam is presented in different modes and it is shown good agreement with numerical method. It is seen that increasing of mode number leads to increasing of frequency. In addition, the influence of different parameters on nonlinear normalized frequency is illustrated.

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Nonlinear electro-dynamic analysis of micro-actuators: Effect of material nonlinearity

Cited by 19 publications

References 24 publications

Bifurcation of pressurized functionally graded elastomeric hollow cylinders

Bifurcation of pressurized functionally graded elastomeric hollow cylinders

A hybrid solution for analyzing nonlinear dynamics of electrostatically-actuated microcantilevers

Study Neo-Hookean and Yeoh Hyper-Elastic Models in Dielectric Elastomer-Based Micro-Beam Resonators

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