Timoshenko Beam Model for Lateral Vibration of Liquid-Phase Microcantilever-Based Sensors

Schultz, Joshua A.; Heinrich, Stephen M.; Josse, Fabien; Dufour, Isabelle; Nigro, Nicholas J.; Beardslee, Luke A.; Brand, Oliver

doi:10.1007/978-3-319-00780-9_15

Cited by 4 publications

(7 citation statements)

References 13 publications

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“…The latter effects become more important at larger b/L ratios, which are the types of geometries that promise larger Q values in the lateral flexural mode according to the analytical formula derived in [18][19][20]. The results of the Timoshenko beam model [21][22][23], presented in Fig. 2, exhibit a departure from linearity in both resonant frequency and Q for the shorter, "stubbier" specimens, trends that are also seen in the data.…”

Section: Case Of Lateral Bending Vibrationssupporting

confidence: 55%

“…However, experimental results show that, for microcantilevers having larger width-to-length ratios, the behaviors predicted by this analytical model differ from measurements. To more accurately model microcantilever resonant behavior in viscous fluids and to improve the understanding of lateral-mode sensor performance, a new analytical model has been developed, incorporating both viscous fluid effects and "Timoshenko beam" effects (shear deformation and rotatory inertia) [21][22][23]. The latter effects become more important at larger b/L ratios, which are the types of geometries that promise larger Q values in the lateral flexural mode according to the analytical formula derived in [18][19][20].…”

Section: Case Of Lateral Bending Vibrationsmentioning

confidence: 99%

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Influence of fluid-structure interaction on microcantilever vibrations: applications to rheological fluid measurement and chemical detection

et al. 2013

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At the microscale, cantilever vibrations depend not only on the microstructure's properties and geometry but also on the properties of the surrounding medium. In fact, when a microcantilever vibrates in a fluid, the fluid offers resistance to the motion of the beam. The study of the influence of the hydrodynamic force on the microcantilever's vibrational spectrum can be used to either (1) optimize the use of microcantilevers for chemical detection in liquid media or (2) extract the mechanical properties of the fluid. The classical method for application (1) in gas is to operate the microcantilever in the dynamic transverse bending mode for chemical detection. However, the performance of microcantilevers excited in this standard out-of-plane dynamic mode drastically decreases in viscous liquid media. When immersed in liquids, in order to limit the decrease of both the resonant frequency and the quality factor, alternative vibration modes that primarily shear the fluid (rather than involving motion normal to the fluid/beam interface) have been studied and tested: these include inplane vibration modes (lateral bending mode and elongation mode). For application (2), the classical method to measure the rheological properties of fluids is to use a rheometer. To overcome the limitations of this classical method, an alternative method based on the use of silicon microcantilevers is presented. The method, which is based on the use of analytical equations for the hydrodynamic force, permits the measurement of the complex shear modulus of viscoelastic fluids over a wide frequency range.

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Section: Case Of Lateral Bending Vibrationssupporting

confidence: 55%

Section: Case Of Lateral Bending Vibrationsmentioning

confidence: 99%

Influence of fluid-structure interaction on microcantilever vibrations: applications to rheological fluid measurement and chemical detection

et al. 2013

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“…The latter effects are neglected in Euler-Bernoulli beam theory but become more important at larger b/L ratios, which are the types of geometries that promise larger Q values in the lateral flexural mode according to the Euler-Bernoulli analytical formula for Q listed above. The results of the Timoshenko beam model [22][23][24], presented in Fig. 5, exhibit a departure from linearity in both resonant frequency and Q for the shorter, "stubbier" specimens, trends that are also seen in the data.…”

Section: Sensors and Actuators Bmentioning

confidence: 58%

“…Elsevier does not grant permission for this article to be further copied/distributed or hosted elsewhere without the express permission from Elsevier. [22][23][24]. The latter effects are neglected in Euler-Bernoulli beam theory but become more important at larger b/L ratios, which are the types of geometries that promise larger Q values in the lateral flexural mode according to the Euler-Bernoulli analytical formula for Q listed above.…”

Section: Sensors and Actuators Bmentioning

confidence: 99%

Effect of hydrodynamic force on microcantilever vibrations: Applications to liquid-phase chemical sensing

Dufour

Lemaire

Caillard

et al. 2014

Sensors and Actuators B: Chemical

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Abstract:At the microscale, cantilever vibrations depend not only on the microstructure's properties and geometry but also on the properties of the surrounding medium. In fact, when a microcantilever vibrates in a fluid, the fluid offers resistance to the motion of the beam. The study of the influence of the hydrodynamic force on the microcantilever's vibrational spectrum can be used to either (1) optimize the use of microcantilevers for chemical detection in liquid media or (2) extract the mechanical properties of the fluid. The classical method for application (1) in gas is to operate the microcantilever in the dynamic transverse bending mode for chemical detection. However, the performance of microcantilevers excited in this standard out-of-plane dynamic mode drastically decreases in viscous liquid media. When immersed in liquids, in order to limit the decrease of both the resonant frequency and the quality factor, and improve sensitivity in sensing applications, alternative vibration modes that primarily shear the fluid (rather than involving motion normal to the fluid/beam interface) have been studied and tested: these include inplane vibration modes (lateral bending mode and elongation mode). For application (2), the classical method to measure the rheological properties of fluids is to use a rheometer. However, such systems require sampling (no insitu measurements) and a relatively large sample volume (a few milliliters). Moreover, the frequency range is limited to low frequencies (less than 200Hz). To overcome the limitations of this classical method, an alternative method based on the use of silicon microcantilevers is presented. The method, which is based on the use of analytical equations for the hydrodynamic force, permits the measurement of the complex shear modulus of viscoelastic fluids over a wide frequency range.

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“…The same reference includes results and discussion associated with higher values of the fluid resistance parameter.) However, at higher values of  , which may be encountered for more viscous and/or denser liquids or for nano-scale devices, the values of resonant frequency and quality factor will show increased sensitivity to load type and the response monitoring scheme; therefore, in such cases one should employ the specific solution that applies to the particular methods of actuation and detection in the physical device [45].…”

Section: Frequency Responsementioning

confidence: 99%

Lateral-Mode Vibration of Microcantilever-Based Sensors in Viscous Fluids Using Timoshenko Beam Theory

Schultz

Heinrich

Josse

et al. 2015

J. Microelectromech. Syst.

Self Cite

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To more accurately model microcantilever resonant behavior in liquids and to improve lateral-mode sensor performance, a new model is developed to incorporate viscous fluid effects and "Timoshenko beam" effects (shear deformation, rotatory inertia). The model is motivated by studies showing that the most promising geometries for lateral-mode sensing are those for which Timoshenko effects are most pronounced.Analytical solutions for beam response due to harmonic tip force and electrothermal loadings are expressed in terms of total and bending displacements, which correspond to laser and piezoresistive readouts, respectively. The influence of shear deformation, rotatory inertia, fluid properties, and actuation/detection schemes on resonant frequencies (fres) and quality factors (Q) are examined, showing that Timoshenko beam effects may reduce fres and Q by up to 40% and 23%, respectively, but are negligible for width-tolength ratios of 1/10 and lower. Comparisons with measurements (in water) indicate that the model predicts the qualitative data trends but underestimates the softening that occurs in stiffer specimens, indicating that support deformation becomes a factor. For thinner specimens the model estimates Q quite well, but exceeds the observed values for thicker specimens, showing that the Stokes resistance model employed should be extended to include pressure effects for these geometries.

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Timoshenko Beam Model for Lateral Vibration of Liquid-Phase Microcantilever-Based Sensors

Cited by 4 publications

References 13 publications

Influence of fluid-structure interaction on microcantilever vibrations: applications to rheological fluid measurement and chemical detection

Influence of fluid-structure interaction on microcantilever vibrations: applications to rheological fluid measurement and chemical detection

Effect of hydrodynamic force on microcantilever vibrations: Applications to liquid-phase chemical sensing

Lateral-Mode Vibration of Microcantilever-Based Sensors in Viscous Fluids Using Timoshenko Beam Theory

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