The theoretical analysis on damping characteristics of resonant microbeam in vacuum

Li, Bingqian; Wu, Haoyang; Chen, Zhu; Liu, Junhua

doi:10.1016/s0924-4247(99)00072-2

Cited by 54 publications

(44 citation statements)

References 5 publications

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“…Energy dissipation was modeled using statistical thermodynamics by many researches. The Christian model was modified by Kadar (1996) and Li (1999). By comparing the theory and experimental results they found that the theory results are in good agreement with experimental ones.…”

mentioning

confidence: 90%

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

Ghanbari

Hossainpour

Rezazadeh

2015

Lat. Am. j. solids struct.

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In this paper, squeeze film damping in a micro-beam resonator based on micro-polar theory has been investigated. The proposed model for this study consists of a clamped-clamped micro-beam bounded between two fixed layers. The gap between the microbeam and layers is filled with air. As fluid behaves differently in micro scale than macro, the micro-scale fluid field in the gap has been modeled based on micro-polar theory. Equation of motion governing transverse deflection of the micro-beam based on modified couple stress theory and also non-linear Reynolds equation of the fluid field based on micropolar theory have been nondimensionalized, linearized and solved simultaneously in order to calculate the quality factor of the resonator. The effect of micropolar parameters of air on the quality factor has been investigated. The quality factor of the of the micro-beam resonator for different values of non-dimensionalized length scale of the beam, squeeze number and also non-dimensionalized pressure has been calculated and compared to the obtained values of quality factor based on classical theory.

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mentioning

confidence: 90%

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

Ghanbari

Hossainpour

Rezazadeh

2015

Lat. Am. j. solids struct.

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“…At atmospheric pressure the predominant damping mechanism is viscous air damping while when both P ext and P in are low (molecular regime) the quality factor Q is expected to be higher and proportional to x 0 / P diff where P diff is the differential pressure (Hutcherson and Ye 2004;Blom et al 1992;Li et al 1999;Kadar et al 1996;Bao et al 2002). Therefore, as long as P ext > P int , reduction of vibration damping is expected to induce a shift towards high frequency of resonant frequencies related to stiffness/strain changes.…”

Section: Vacuum Measurement Principlementioning

confidence: 99%

“…A possible technique is to integrate a microresonator inside the cavity and to measure its resonant frequency or better, its quality factor Q. At low pressure Q is inversely proportional to the pressure down to values around 10 À3 mbar (Spark et al 2004;Hutcherson and Ye 2004;Blom et al 1992;Li et al 1999;Kadar et al 1996;Bao et al2002). This in-situ technique has a good sensitivity but needs a calibration of the pressure response.…”

Section: Introductionmentioning

confidence: 99%

“…This in-situ technique has a good sensitivity but needs a calibration of the pressure response. Indeed, computed values of Q factor in low vacuum are very dependent on the model used (Hutcherson and Ye 2004;Blom et al 1992;Li et al 1999;Kadar et al 1996;Bao et al 2002) and other damping mechanism like intrinsic damping or support damping may have significant contributions at low pressure. In addition, the pressure response might be modified by thermomechanical stresses induced by the bonding process of the cap wafer.…”

Section: Introductionmentioning

confidence: 99%

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Vacuum measurement in wafer level encapsulations by interference microscopy

et al. 2006

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Vacuum encapsulation is required for various microsensors to improve their performances. In the case of wafer level vacuum encapsulation, dedicated techniques must be developed to measure the background pressure in the bonded cavities. In this paper we investigated ex situ measurement techniques based on the measurement by interference microscopy of the deformation and vibrations of the caps as function of an external pressure. Because these techniques detect the equality between external and internal pressure, they do not require any modelling nor prior calibration. Application to wafer level encapsulations fabricated by goldsilicon eutectic wafer bonding demonstrates that a detection limit in the 10 À2 -10 À1 mbar range can be reached for millimetre size caps.

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“…Low-pressure devices find application in optical MEMS intended for specific applications, where the absorption of light in air has to be avoided. Damping at low pressures close to vacuum has been extensively investigated for high-Q resonator design [2][3][4][5]. Although other damping mechanisms have been identified, the main damping mechanism remains gas damping.…”

Section: Introductionmentioning

confidence: 99%

Fast step-response settling of micro electrostatic actuators operated at low air pressure using input shaping

Mol¹,

Rocha²,

Cretu³

et al. 2009

J. Micromech. Microeng.

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Squeeze-film damping is highly inadequate in low-pressure systems or in systems where air pressure and/or gap dimensions are poorly defined. Input shaping has been used to circumvent the oscillations typically associated with under-damped mass-spring-damper systems and drastically decrease the settling time. The proposed method does not rely on feedback but solely on the system dynamics. The required input signal is derived analytically from the differential equation describing the system. The resulting device response is simulated and experimentally verified on an electrostatically actuated microstructure. Settling occurs even faster than for an equivalent critically damped system.

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The theoretical analysis on damping characteristics of resonant microbeam in vacuum

Cited by 54 publications

References 5 publications

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

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

Vacuum measurement in wafer level encapsulations by interference microscopy

Fast step-response settling of micro electrostatic actuators operated at low air pressure using input shaping

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