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Copyright © 2018 Julio Claeyssen et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0/

Abstract

Vibration dynamics of elastic beams that are used in nanotechnology, such as atomic force microscope modeling and carbon nanotubes, are considered in terms of a fundamental response within a matrix framework. The modeling equations with piezoelectric and surface scale effects are written as a matrix differential equation subject to tip-sample general boundary conditions and to compatibility conditions for the case of multispan beams. We considered a quadratic and a cubic eigenvalue problem related to the inclusion of smart materials and surface effects. Simulations were performed for a two stepped beam with a piezoelectric patch subject to pulse forcing terms. Results with Timoshenko models that include surface effects are presented for micro- and nanoscale. It was observed that the effects are significant just in nanoscale. We also simulate the frequency effects of a double-span beam in which one segment includes rotatory inertia and shear deformation and the other one neglects both phenomena. The proposed analytical methodology can be useful in the design of micro- and nanoresonator structures that involve deformable flexural models for detecting and imaging of physical and biochemical quantities.

Details

Title
Nanobeams and AFM Subject to Piezoelectric and Surface Scale Effects
Author
Claeyssen, Julio 1   VIAFID ORCID Logo  ; Copetti, Rosemaira 2 ; Tonetto, Leticia 3 ; Carvalho, Joao 4 

 PGMAT, Departamento de Matemática, CCNE, Universidade Federal de Santa Maria, Av. Roraima 1000, 97105-900, Santa Maria, RS, Brazil; PPGMAp-IME, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves, 9500, 91509-900, Porto Alegre, RS, Brazil 
 PGMAT, Departamento de Matemática, CCNE, Universidade Federal de Santa Maria, Av. Roraima 1000, 97105-900, Santa Maria, RS, Brazil 
 Centro de Engenharias, CENG, Universidade Federal de Pelotas, Almirante Barroso, 1734, Pelotas, RS, 96010-280, Brazil 
 PPGMAp-IME, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves, 9500, 91509-900, Porto Alegre, RS, Brazil 
Editor
Phuc Phung-Van
Publication year
2018
Publication date
2018
Publisher
John Wiley & Sons, Inc.
ISSN
16879120
e-ISSN
16879139
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2126536328
Copyright
Copyright © 2018 Julio Claeyssen et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0/