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Sensors 2015, 15(11), 29209-29232; doi:10.3390/s151129209

Toward Higher-Order Mass Detection: Influence of an Adsorbate’s Rotational Inertia and Eccentricity on the Resonant Response of a Bernoulli-Euler Cantilever Beam

1
Department of Civil, Construction and Environmental Engineering, Marquette University, Milwaukee, WI 53233, USA
2
Université de Bordeaux, Laboratoire de l’Intégration du Matériau au Système, UMR5218 Pessac 33607, France
*
Author to whom correspondence should be addressed.
Academic Editor: Montserrat Calleja
Received: 30 September 2015 / Revised: 30 October 2015 / Accepted: 11 November 2015 / Published: 19 November 2015
(This article belongs to the Special Issue Nanomechanics for Sensing and Spectrometry)
View Full-Text   |   Download PDF [3186 KB, uploaded 19 November 2015]   |  

Abstract

In this paper a new theoretical model is derived, the results of which permit a detailed examination of how the resonant characteristics of a cantilever are influenced by a particle (adsorbate) attached at an arbitrary position along the beam’s length. Unlike most previous work, the particle need not be small in mass or dimension relative to the beam, and the adsorbate’s geometric characteristics are incorporated into the model via its rotational inertia and eccentricity relative to the beam axis. For the special case in which the adsorbate’s (translational) mass is indeed small, an analytical solution is obtained for the particle-induced resonant frequency shift of an arbitrary flexural mode, including the effects of rotational inertia and eccentricity. This solution is shown to possess the exact first-order behavior in the normalized particle mass and represents a generalization of analytical solutions derived by others in earlier studies. The results suggest the potential for “higher-order” nanobeam-based mass detection methods by which the multi-mode frequency response reflects not only the adsorbate’s mass but also important geometric data related to its size, shape, or orientation (i.e., the mass distribution), thus resulting in more highly discriminatory techniques for discrete-mass sensing. View Full-Text
Keywords: mass detection; biosensing; nanoparticles; nanomechanics; micromechanics; inertial imaging; mass spectroscopy; resonant frequency; rotational inertia; eccentricity mass detection; biosensing; nanoparticles; nanomechanics; micromechanics; inertial imaging; mass spectroscopy; resonant frequency; rotational inertia; eccentricity
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Heinrich, S.M.; Dufour, I. Toward Higher-Order Mass Detection: Influence of an Adsorbate’s Rotational Inertia and Eccentricity on the Resonant Response of a Bernoulli-Euler Cantilever Beam. Sensors 2015, 15, 29209-29232.

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