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

Stephen M. Heinrich²  Isabelle Dufour¹ 

[1] Université de Bordeaux, Laboratoire de l’Intégration du Matériau au Système, UMR5218 Pessac 33607, France; E-Mail:;Department of Civil, Construction and Environmental Engineering, Marquette University, Milwaukee, WI 53233, USA

关键词: mass detection;    biosensing;    nanoparticles;    nanomechanics;    micromechanics;    inertial imaging;    mass spectroscopy;    resonant frequency;    rotational inertia;    eccentricity;   

DOI  :  10.3390/s151129209

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.