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Sensors 2014, 14(9), 16296-16310; doi:10.3390/s140916296

Detecting Both the Mass and Position of an Accreted Particle by a Micro/Nano-Mechanical Resonator Sensor

1,* and 2
1
State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
2
Faculty of Information and Automation, Kunming University of Science and Technology, Kunming 650051, China
*
Author to whom correspondence should be addressed.
Received: 24 July 2014 / Revised: 27 August 2014 / Accepted: 27 August 2014 / Published: 2 September 2014
(This article belongs to the Section Physical Sensors)
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Abstract

In the application of a micro-/nano-mechanical resonator, the position of an accreted particle and the resonant frequencies are measured by two different physical systems. Detecting the particle position sometimes can be extremely difficult or even impossible, especially when the particle is as small as an atom or a molecule. Using the resonant frequencies to determine the mass and position of an accreted particle formulates an inverse problem. The Dirac delta function and Galerkin method are used to model and formulate an eigenvalue problem of a beam with an accreted particle. An approximate method is proposed by ignoring the off-diagonal elements of the eigenvalue matrix. Based on the approximate method, the mass and position of an accreted particle can be decoupled and uniquely determined by measuring at most three resonant frequencies. The approximate method is demonstrated to be very accurate when the particle mass is small, which is the application scenario for much of the mass sensing of micro-/nano-mechanical resonators. By solving the inverse problem, the position measurement becomes unnecessary, which is of some help to the mass sensing application of a micro-/nano-mechanical resonator by reducing two measurement systems to one. How to apply the method to the general scenario of multiple accreted particles is also discussed. View Full-Text
Keywords: inverse problem; mass sensing; resonator sensor; resonant frequency; Galerkin method inverse problem; mass sensing; resonator sensor; resonant frequency; Galerkin method
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This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Zhang, Y.; Liu, Y. Detecting Both the Mass and Position of an Accreted Particle by a Micro/Nano-Mechanical Resonator Sensor. Sensors 2014, 14, 16296-16310.

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