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Title: Parametric effects in nanobeams and AFM

Vibration dynamics of forced cantilever beams that are used in nanotechnology such as atomic force microscope modeling and carbon nanotubes is considered in terms of a fundamental response within a matrix framework. The modeling equations are written as a matrix differential equation subject to tip-sample general boundary conditions. At the junctions, where there are discontinuities due to different material or beam thickness, compatibility conditions are prescribed. Forced responses are given by convolution of the input load with the time domain Green matrix function. The corresponding matrix transfer function and modes of a multispan cantilever beam are determined in terms of solution basis of the same shape generated by a fundamental solution. Simulations were performed for a three stepped beam with a piezoelectric patch subject to pulse forcing terms and with surface effects.
Authors:
; ;  [1] ;  [2]
  1. Institute of Mathematics-PPGMAp, Federal University of Rio Grande do Sul, Av. Bento Gonçalves 9500, 91509-900 Porto Alegre, RS (Brazil)
  2. Department of Mathematics, CCNE, Federal University of Santa Maria, Av. Roraima 1000, 97105-900 Santa Maria, RS (Brazil)
Publication Date:
OSTI Identifier:
22390781
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1637; Journal Issue: 1; Conference: ICNPAA 2014: 10. International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, Narvik (Norway), 15-18 Jul 2014; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 77 NANOSCIENCE AND NANOTECHNOLOGY; ATOMIC FORCE MICROSCOPY; BOUNDARY CONDITIONS; CARBON NANOTUBES; DIFFERENTIAL EQUATIONS; ELECTRIC CONTACTS; GREEN FUNCTION; MATHEMATICAL SOLUTIONS; MATRICES; NANOTECHNOLOGY; PIEZOELECTRICITY; SEMICONDUCTOR JUNCTIONS; SURFACES; TRANSFER FUNCTIONS