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Mass and Force Sensing of an Adsorbate on a Beam Resonator Sensor.

Zhang Y, Zhao YP - Sensors (Basel) (2015)

Bottom Line: Extra instruments are also required.The accuracy of the inverse problem solving method is demonstrated, and how the method can be used in the real application of a nanomechanical resonator is also discussed.Solving the inverse problem is helpful to the development and application of a mechanical resonator sensor for two reasons: reducing extra experimental equipment and achieving better mass sensing by considering more factors.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China. zhangyin@lnm.imech.ac.cn.

ABSTRACT
The mass sensing superiority of a micro-/nano-mechanical resonator sensor over conventional mass spectrometry has been, or at least is being firmly established. Because the sensing mechanism of a mechanical resonator sensor is the shifts of resonant frequencies, how to link the shifts of resonant frequencies with the material properties of an analyte formulates an inverse problem. Besides the analyte/adsorbate mass, many other factors, such as position and axial force, can also cause the shifts of resonant frequencies. The in situ measurement of the adsorbate position and axial force is extremely difficult if not impossible, especially when an adsorbate is as small as a molecule or an atom. Extra instruments are also required. In this study, an inverse problem of using three resonant frequencies to determine the mass, position and axial force is formulated and solved. The accuracy of the inverse problem solving method is demonstrated, and how the method can be used in the real application of a nanomechanical resonator is also discussed. Solving the inverse problem is helpful to the development and application of a mechanical resonator sensor for two reasons: reducing extra experimental equipment and achieving better mass sensing by considering more factors.

No MeSH data available.


The projections of the two intersection curves obtained in Figure 4 and Figure 5 into the − plane. The intersection of the two curves is marked with a circle, which corresponds to(,) = (0.1, 0.3) exactly.
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sensors-15-14871-f006: The projections of the two intersection curves obtained in Figure 4 and Figure 5 into the − plane. The intersection of the two curves is marked with a circle, which corresponds to(,) = (0.1, 0.3) exactly.

Mentions: Figure 4 presents the variation of the first resonant frequency() as the function of and. Here, varies from zero to 0.2; varies from zero to 0.5. Because the C-C beam is a symmetric structure, the adsorbate at and 1 − results in the same change for any arbitrary resonant frequency. Therefore, only half of the beam span is examined here. The level plane is the one with = 23.5217. The intersection of the two planes are marked with a solid line, which indicates the combinations of and resulting in the same first resonant frequency of = 23.5217. This solid line also indicates that the combinations are infinite. Figure 5 presents the variation of the second resonant frequency() as the function of and. The level plane is the one with = 59.5752. Again, the intersection of the two planes is the combination of and resulting the same second resonant frequency of = 59.5752, which is marked as a dashed line. Once again, the dashed line indicates that the infinite combinations of and result the same second resonant frequency of = 59.5752. When, and are given, each eigenfrequency is uniquely determined by Equation (7) as a forward problem. In comparison, in this two-variable case of the inverse problem, for a given eigenfrequency, there are infinite combinations of and. However, when these two curves obtained in Figure 4 and Figure 5 are projected into the− plane, they intersect, and in Figure 6, the intersection point is marked as a circle, which is exactly(,) = (0.1, 0.3). Physically, the reason for the two curves to intersect is that the mechanism mentioned above: and have different impacts on different resonant frequencies; different resonant frequencies respond differently to the given and. Mathematically, as seen in Equation (5), is a coefficient, and is embedded in the function of the mode shape in the mass matrix.


Mass and Force Sensing of an Adsorbate on a Beam Resonator Sensor.

Zhang Y, Zhao YP - Sensors (Basel) (2015)

The projections of the two intersection curves obtained in Figure 4 and Figure 5 into the − plane. The intersection of the two curves is marked with a circle, which corresponds to(,) = (0.1, 0.3) exactly.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4541812&req=5

sensors-15-14871-f006: The projections of the two intersection curves obtained in Figure 4 and Figure 5 into the − plane. The intersection of the two curves is marked with a circle, which corresponds to(,) = (0.1, 0.3) exactly.
Mentions: Figure 4 presents the variation of the first resonant frequency() as the function of and. Here, varies from zero to 0.2; varies from zero to 0.5. Because the C-C beam is a symmetric structure, the adsorbate at and 1 − results in the same change for any arbitrary resonant frequency. Therefore, only half of the beam span is examined here. The level plane is the one with = 23.5217. The intersection of the two planes are marked with a solid line, which indicates the combinations of and resulting in the same first resonant frequency of = 23.5217. This solid line also indicates that the combinations are infinite. Figure 5 presents the variation of the second resonant frequency() as the function of and. The level plane is the one with = 59.5752. Again, the intersection of the two planes is the combination of and resulting the same second resonant frequency of = 59.5752, which is marked as a dashed line. Once again, the dashed line indicates that the infinite combinations of and result the same second resonant frequency of = 59.5752. When, and are given, each eigenfrequency is uniquely determined by Equation (7) as a forward problem. In comparison, in this two-variable case of the inverse problem, for a given eigenfrequency, there are infinite combinations of and. However, when these two curves obtained in Figure 4 and Figure 5 are projected into the− plane, they intersect, and in Figure 6, the intersection point is marked as a circle, which is exactly(,) = (0.1, 0.3). Physically, the reason for the two curves to intersect is that the mechanism mentioned above: and have different impacts on different resonant frequencies; different resonant frequencies respond differently to the given and. Mathematically, as seen in Equation (5), is a coefficient, and is embedded in the function of the mode shape in the mass matrix.

Bottom Line: Extra instruments are also required.The accuracy of the inverse problem solving method is demonstrated, and how the method can be used in the real application of a nanomechanical resonator is also discussed.Solving the inverse problem is helpful to the development and application of a mechanical resonator sensor for two reasons: reducing extra experimental equipment and achieving better mass sensing by considering more factors.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China. zhangyin@lnm.imech.ac.cn.

ABSTRACT
The mass sensing superiority of a micro-/nano-mechanical resonator sensor over conventional mass spectrometry has been, or at least is being firmly established. Because the sensing mechanism of a mechanical resonator sensor is the shifts of resonant frequencies, how to link the shifts of resonant frequencies with the material properties of an analyte formulates an inverse problem. Besides the analyte/adsorbate mass, many other factors, such as position and axial force, can also cause the shifts of resonant frequencies. The in situ measurement of the adsorbate position and axial force is extremely difficult if not impossible, especially when an adsorbate is as small as a molecule or an atom. Extra instruments are also required. In this study, an inverse problem of using three resonant frequencies to determine the mass, position and axial force is formulated and solved. The accuracy of the inverse problem solving method is demonstrated, and how the method can be used in the real application of a nanomechanical resonator is also discussed. Solving the inverse problem is helpful to the development and application of a mechanical resonator sensor for two reasons: reducing extra experimental equipment and achieving better mass sensing by considering more factors.

No MeSH data available.