Vibration mode localization in coupled beam-shaped resonator array

Chatani, Keisuke; Wang, Dong F.; Ikehara, Tsuyoshi; Maeda, Ryutaro

doi:10.1109/nems.2012.6196725

Cited by 10 publications

(11 citation statements)

References 13 publications

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“…Hence, it is necessary to analytically combine two resonators via a common base to ensure a separating distance corresponding to the coupling overhang. As reported in our previous Letter [23][24][25], in the case of without coupling overhang, only one resonance frequency can be obtained for all the resonators. This indicates that all the resonators vibrate individually so that vibration mode localisation cannot be observed.…”

Section: Micromachined or Mems Flow Sensorsmentioning

confidence: 64%

“…Considering the case of two initially identical resonators, the relative change in normalised eigenstate u is given by the authors [17,[21][22][23][24][25] …”

Section: Micromachined or Mems Flow Sensorsmentioning

confidence: 99%

“…Recently, a mechanically‐coupled SCS three‐resonator array was further selected and prepared for vibration localisation evaluation [23–25], because three is the large integer next to two. It is concluded that the amount of amplitude change of coupled three‐resonator is higher than that of the frequency shift of a single‐resonator, and the analytical results are clearly corresponding to the experimental ones.…”

Section: Amplitude Change Enhancement By Vibration Mode Localisationmentioning

confidence: 99%

“…Considering the case of two initially identical resonators, the relative change in normalised eigenstate u is given by the authors [17, 21–25]

\frac{(||, u_{i} - u_{i}^{0})}{(||, u_{i}^{0})} = (\frac{1}{4} + \frac{1}{4 K c / K}) δ, i = 1, 2

where K , Kc are, respectively, the bending stiffnesses of the two resonators and the overhang coupling of the two resonators, whereas δ represents the ratio of the effect mass ( δM ) being detected to the single resonator mass ( M ). The relative change in the eigenvalue λ or resonance frequency of a single resonator is given by

\frac{λ - λ_{0}}{λ_{0}} = \frac{- δ}{2}

Note that the perturbed eigenstates U i , i = 1, 2 start becoming localised in the sense that in each eigenstate one resonator oscillates more (large magnitude) than the other.…”

Section: Geometrical Design and Physics Of Amplitude Change Enhancemementioning

confidence: 99%

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Analytical studies on amplitude change enhancement in coupled aluminium nitride coated single crystal silicon oscillator pair applicable to ultra‐sensitive resonating microfluidic flowmeters

Wang

Chatani

Kozuka

et al. 2013

Micro & Nano Letters

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The use of vibration mode localisation in arrays of micromechanically coupled, nearly identical beam-shaped resonators has been analytically studied for ultra-sensitive resonating-based flowmeters. Eigenstate shifts (amplitude change in this Letter) that are about two times (compared with the single resonator), and orders (compared with the resonator array) of magnitude greater than corresponding shifts in resonant frequency for an induced fluid flow (corresponding to an induced small mass perturbation) are preliminarily obtained by theoretical analysis. When an external force of 100 Pa, corresponding to an estimated fluid flow velocity of about 3.15 m/s, is applied to any one (because of the symmetrical design) of the two coupled aluminium nitride coated single crystal silicon resonators, two orders of the amplitude enhancement can be observed for both the resonators at the higher (second) resonance frequency because of vibration mode localisation, which implies the application possibility to highly sensitive resonating-based flow sensors.1. Micromachined or MEMS flow sensors: The measurement of fluid flow rates is an essential requirement in both industrial and commercial applications. It has been estimated by Hayward [1] that there are more than one hundred different types of flow sensors with a mode of operation based on almost any physical domain. Although several large-scale flowmeter types are commercially available, the continuous development of the three-dimensional techniques of microfabrication and MEMS, with consequent cost reduction and quality improvement, has rapidly extended the market of micromachined or MEMS flow sensors. In particular, applications of micromachined or MEMS sensors to monitor gas and liquid flows hold immense potential because of their valuable characteristics, such as low-energy consumption, relatively good accuracy, the ability to measure very small flow, small size and so on.After the first integrated silicon-based sensor for gas flow measurement [2] appeared in 1974, a higher growth of research works in the field of micromachined or MEMS flow sensors took place in the eighties and about a decade was needed to develop the integration of many microfluidic devices into a single chip [3,4].Based on the working principles, the micromachined or MEMS flow sensors can be distinguished into two groups [5]. The first group contains flow sensors based on heat exchange, named 'thermal flow sensors'; whereas all the other flowmeters based on different working principles rather than thermal exchange, are thus named as 'non-thermal flow sensors', which are also divided into several subgroups depending on the principle of measurement used like cantilever flow sensors, differential pressure-based flow sensors, resonating flow sensors and laser Doppler flowmeters. Amplitude change enhancement by vibration mode localisation:The micro resonator sensor [6-10] is used to detect external stimulus, that is, force, mass, molecular as well as atomic adsorption and so on. The amount of relative change...

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Section: Micromachined or Mems Flow Sensorsmentioning

confidence: 64%

“…Considering the case of two initially identical resonators, the relative change in normalised eigenstate u is given by the authors [17,[21][22][23][24][25] …”

Section: Micromachined or Mems Flow Sensorsmentioning

confidence: 99%

Section: Amplitude Change Enhancement By Vibration Mode Localisationmentioning

confidence: 99%

“…Considering the case of two initially identical resonators, the relative change in normalised eigenstate u is given by the authors [17, 21–25]

\frac{(||, u_{i} - u_{i}^{0})}{(||, u_{i}^{0})} = (\frac{1}{4} + \frac{1}{4 K c / K}) δ, i = 1, 2

\frac{λ - λ_{0}}{λ_{0}} = \frac{- δ}{2}

Note that the perturbed eigenstates U i , i = 1, 2 start becoming localised in the sense that in each eigenstate one resonator oscillates more (large magnitude) than the other.…”

Section: Geometrical Design and Physics Of Amplitude Change Enhancemementioning

confidence: 99%

See 2 more Smart Citations

Analytical studies on amplitude change enhancement in coupled aluminium nitride coated single crystal silicon oscillator pair applicable to ultra‐sensitive resonating microfluidic flowmeters

Wang

Chatani

Kozuka

et al. 2013

Micro & Nano Letters

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“…Recently however, a mechanically-coupled 3-resonator array (SCS) was selected and prepared for vibration localization evaluation [23][24][25], because three is the large integer next to two.…”

Section: Vibration Mode Localizationmentioning

confidence: 99%

Mode localization in coupled AlN/SCS cantilevers for highly sensitive resonating flow meter

Kozuka

Wang

Ikehara³

et al. 2013

The 8th Annual IEEE International Conference on Nano/Micro Engineered and Molecular Systems

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The use of vibration mode localization in arrays of mechanically-coupled, nearly identical beam-shaped resonators has been studied for ultra-sensitive mass detection and analyte identification. Our recent work (NEMS 2012) focused on enhancing the amount of amplitude change due to vibration mode localization with a beam shaped 3-resonator array. The preliminarily results were discussed from view point of vibration characteristic by comparing experimental results with analytical ones, without a small mass perturbation. The present study however try to apply the consequent amplitude change to resonating-based flow meter with a simplified system of beam shaped 2-resonator array (AlN/SCS). The possible application has been analytically discussed from view point of vibration characteristic with a small mass perturbation.

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Picogram-Order Mass Sensors via Cantilever-Based Micro-/Nanostructures

Wang

et al. 2017

Toxinology

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Vibration mode localization in coupled beam-shaped resonator array

Cited by 10 publications

References 13 publications

Analytical studies on amplitude change enhancement in coupled aluminium nitride coated single crystal silicon oscillator pair applicable to ultra‐sensitive resonating microfluidic flowmeters

Analytical studies on amplitude change enhancement in coupled aluminium nitride coated single crystal silicon oscillator pair applicable to ultra‐sensitive resonating microfluidic flowmeters

Mode localization in coupled AlN/SCS cantilevers for highly sensitive resonating flow meter

Picogram-Order Mass Sensors via Cantilever-Based Micro-/Nanostructures

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