Study of squeeze film damping in a micro-beam resonator based on micro-polar theory

Ghanbari, Mina; Hossainpour, Siamak; Rezazadeh, Ghader

doi:10.1590/1679-78251364

Cited by 13 publications

(10 citation statements)

References 28 publications

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“…For the microrotation, the Dirichlet boundary condition (ω = 0) or the dynamic boundary condition is often used (see [19][20][21]). The last one, in the form of ω = α 0.5 rot V, 0 < α < 1, will be used in this paper.…”

Section: Flow Equationsmentioning

confidence: 99%

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Squeeze flow modeling with the use of micropolar fluid theory

Kucaba-Pietal

2017

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. The aim of this paper is to study the applicability of micropolar fluid theory to modeling and to calculating tribological squeeze flow characteristics depending on the geometrical dimension of the flow field. Based on analytical solutions in the lubrication regime of squeeze flow between parallel plates, calculations of the load capacity and time required to squeeze the film are performed and compared -as a function of the distance between the plates -for both fluid models: the micropolar model and the Newtonian model. In particular, maximum distance between the plates for which the micropolar effects of the fluid become significant will be established. Values of rheological constants of the fluids, both those experimentally determined and predicted by means of using equilibrium molecular dynamics, have been used in the calculations. The same analysis was performed as a function of dimensionless microstructural parameters. MFT is being widely developed due to its potential use in tribology, microdevices, biotribology, and magnetorheology, to describe the flows in microchannels [10][11][12]. For the past twenty years, significant progress and results supporting the usefulness of MFT to model fluid flow in narrow gaps and passages have been developed. Based on the molecular dynamics method, it was confirmed that during the Poiseuille flow in very narrow channels, the microrotation velocity -not included in the classical continuum theory -does in fact exist and those results are sufficiently consistent with the results obtained based on the analytical solution of the micropolar fluid flow [13][14][15][16][17]. A new method has been developed by Hansen et al. [18] for designating the micropolar viscosity coefficients for real fluids using equilibrium molecular dynamics and values for water have been presented in the same work.Research on scale effect of MFT applicability to microflows modeling started in 2004. It showed that micropolar fluid equations of motion are being reduced to their counterparts in the classical continuum medium (Cauchy) theory, i.e. the Navier-Stokes equations, when the characteristic linear dimension of the flow field is sufficiently large [15,16]. As a result, questions concerning the size of the flow field arose as concerns the effective use of MFT in solving flow problems. HagenPoiseuille fluid flow in this context was studied in detail [16] and a microchannel maximum diameter value, above which the effect of micropolarity is negligibly small, was calculated for some real fluids, including water and blood, and expressed in dimensionless micropolar parameters. Hoffmann et al. (2007) compared the resistance force exerted on a sphere moving in micropolar fluids: water and blood, and showed that deviations are being observed only for small sphere radii.Lubrication-type analysis for squeezing flow is well established, and physical effects such as increased load capacity, etc., have been known since the 1970s, quoted e.g. in [3,4]. The increasing number of articles regarding squeez...

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Section: Flow Equationsmentioning

confidence: 99%

“…The time required for reducing the initial film thickness T m (h) from h o to h was calculated with the micropolar model of the fluid in the gap using equation (21), and compared to the corresponding reducing time …”

Section: Squeeze Film Timementioning

confidence: 99%

Squeeze flow modeling with the use of micropolar fluid theory

Kucaba-Pietal

2017

Bulletin of the Polish Academy of Sciences Technical Sciences

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“…Recently, many works have been done in applying non-classical theories in modeling micro and nano structures. Ghanbari et al (2014) studied squeeze film damping in a micro-beam resonator in which the fluid media was modelled based on micropolar theory. In an other work, Ghanbari et al (2015a) by modeling the behavior of the micro fluid base on micropolar theory, presented a microsensor for measurement of a micro-scale fluid physical properties.…”

Section: Introductionmentioning

confidence: 99%

Studying Torsional Vibration of a Micro-shaft in a Micro-scale Fluid Media based on Non-classical Theories

Ghanbari

Hossainpour

Rezazadeh

2019

Lat. Am. j. solids struct.

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In this paper, torsional vibration of a micro-shaft in interacting with a micro-scale fluid media has been investigated. The presented mathematical model for this study is made up of a micro-shaft with one end fixed and a micro-cylinder at its free end which is immersed in a micro-scale fluid media. The micro-shaft can be actuated torsionally via applying an AC voltage to the capacitive plates around the micro-shaft and the outer fixed cylinder. As fluids and solids behave differently in micro scale than macro, the surrounding fluid field in the gap and also the micro-shaft have been modeled based on non-classical theories. Equation of motion governing angular displacement of the micro-shaft and also equations of motion of the fluid field have been derived based on non-local elasticity and micro-polar theories. The coupled differential equations have been transformed to an enhanced form with homogenous boundary conditions. The enhanced equations have been discretized over the beam and fluid domain using Galerkin method. Effects of non-local parameter of the micro-shaft and also micro-polar parameters of the fluid field on the response of the micro-shaft have been studied. We have shown that micropolar parameters of fluid due to having damping and inertial effects, changes resonance frequency and resonance amplitude of the shaft.

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“…Today, micro-scale structures such as microbeams, microplates, microbars, etc are widely used in Micro-Electro-Mechanical-Systems (MEMS) such as micro-actuators (Padoina et al, 2015), microswitches (Joglekar, and Pawaskar, 2011), Atomic Force Microscopes (AFMs) , micro-resonators (Hassanpour et al, 2007, Ghanbari et al, 2015 and etc. Micro-resonator is a micro-scale structure supposed to vibrate at a certain frequency (usually one of its natural frequencies) and play an important role in MEMS (Hassanpour et al, 2007, Ghanbari et al, 2015.…”

Section: Introductionmentioning

confidence: 99%

“…Micro-resonator is a micro-scale structure supposed to vibrate at a certain frequency (usually one of its natural frequencies) and play an important role in MEMS (Hassanpour et al, 2007, Ghanbari et al, 2015. Hence, modeling the micro-resonators accurately and investigating their vibration behavior seem to be crucial.…”

Section: Introductionmentioning

confidence: 99%

Investigation of Size-Dependency in Free-Vibration of Micro-Resonators Based on the Strain Gradient Theory

Vatankhah

Kahrobaiyan

2016

Lat. Am. j. solids struct.

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This paper investigates the vibration behavior of micro-resonators based on the strain gradient theory, a non-classical continuum theory capable of capturing the size effect appearing in micro-scale structures. The micro-resonator is modeled as a clamped-clamped micro-beam with an attached mass subjected to an axial force. The governing equations of motion and both classical and non-classical sets of boundary conditions are developed based on the strain gradient theory. The normalized natural frequency of the micro-resonator is evaluated and the influences of various parameters are assessed. In addition, the current results are compared to those of the classical and modified couple stress continuum theories.

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Study of squeeze film damping in a micro-beam resonator based on micro-polar theory

Cited by 13 publications

References 28 publications

Squeeze flow modeling with the use of micropolar fluid theory

Squeeze flow modeling with the use of micropolar fluid theory

Studying Torsional Vibration of a Micro-shaft in a Micro-scale Fluid Media based on Non-classical Theories

Investigation of Size-Dependency in Free-Vibration of Micro-Resonators Based on the Strain Gradient Theory

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