Nonlinear hardening and softening resonances in micromechanical cantilever-nanotube systems originated from nanoscale geometric nonlinearities

Hanna Cho, Bongwon Jeong, Min Feng Yu, Alexander F Vakakis, D. Michael McFarland, Lawrence Bergman

Research output: Contribution to journalArticle

Abstract

Micro/nanomechanical resonators often exhibit nonlinear behaviors due to their small size and their ease to realize relatively large amplitude oscillation. In this work, we design a nonlinear micromechanical cantilever system with intentionally integrated geometric nonlinearity realized through a nanotube coupling. Multiple scales analysis was applied to study the nonlinear dynamics which was compared favorably with experimental results. The geometrically positioned nanotube introduced nonlinearity efficiently into the otherwise linear micromechanical cantilever oscillator, evident from the acquired responses showing the representative hysteresis loop of a nonlinear dynamic system. It was further shown that a small change in the geometry parameters of the system produced a complete transition of the nonlinear behavior from hardening to softening resonance.

Original languageEnglish (US)
Pages (from-to)2059-2065
Number of pages7
JournalInternational Journal of Solids and Structures
Volume49
Issue number15-16
DOIs
StatePublished - Aug 1 2012

Fingerprint

Geometric Nonlinearity
Cantilever
Softening
Hardening
Nanotubes
hardening
softening
nanotubes
nonlinearity
Hysteresis loops
Resonators
Dynamical systems
Hysteresis Loop
Nonlinear Dynamic System
Multiple Scales
resonators
hysteresis
oscillators
Resonator
oscillations

Keywords

  • Geometric nonlinearity
  • Hardening
  • Micromechanical cantilever oscillation
  • Multiple scales analysis
  • Nanotube
  • Softening

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Materials Science(all)
  • Condensed Matter Physics
  • Applied Mathematics
  • Modeling and Simulation

Cite this

Nonlinear hardening and softening resonances in micromechanical cantilever-nanotube systems originated from nanoscale geometric nonlinearities. / Cho, Hanna; Jeong, Bongwon; Yu, Min Feng; Vakakis, Alexander F; McFarland, D. Michael; Bergman, Lawrence.

In: International Journal of Solids and Structures, Vol. 49, No. 15-16, 01.08.2012, p. 2059-2065.

Research output: Contribution to journalArticle

@article{21c2b795b58e41d49bfbbedfe8ddeb13,
title = "Nonlinear hardening and softening resonances in micromechanical cantilever-nanotube systems originated from nanoscale geometric nonlinearities",
abstract = "Micro/nanomechanical resonators often exhibit nonlinear behaviors due to their small size and their ease to realize relatively large amplitude oscillation. In this work, we design a nonlinear micromechanical cantilever system with intentionally integrated geometric nonlinearity realized through a nanotube coupling. Multiple scales analysis was applied to study the nonlinear dynamics which was compared favorably with experimental results. The geometrically positioned nanotube introduced nonlinearity efficiently into the otherwise linear micromechanical cantilever oscillator, evident from the acquired responses showing the representative hysteresis loop of a nonlinear dynamic system. It was further shown that a small change in the geometry parameters of the system produced a complete transition of the nonlinear behavior from hardening to softening resonance.",
keywords = "Geometric nonlinearity, Hardening, Micromechanical cantilever oscillation, Multiple scales analysis, Nanotube, Softening",
author = "Hanna Cho and Bongwon Jeong and Yu, {Min Feng} and Vakakis, {Alexander F} and McFarland, {D. Michael} and Lawrence Bergman",
year = "2012",
month = "8",
day = "1",
doi = "10.1016/j.ijsolstr.2012.04.016",
language = "English (US)",
volume = "49",
pages = "2059--2065",
journal = "International Journal of Solids and Structures",
issn = "0020-7683",
publisher = "Elsevier Limited",
number = "15-16",

}

TY - JOUR

T1 - Nonlinear hardening and softening resonances in micromechanical cantilever-nanotube systems originated from nanoscale geometric nonlinearities

AU - Cho, Hanna

AU - Jeong, Bongwon

AU - Yu, Min Feng

AU - Vakakis, Alexander F

AU - McFarland, D. Michael

AU - Bergman, Lawrence

PY - 2012/8/1

Y1 - 2012/8/1

N2 - Micro/nanomechanical resonators often exhibit nonlinear behaviors due to their small size and their ease to realize relatively large amplitude oscillation. In this work, we design a nonlinear micromechanical cantilever system with intentionally integrated geometric nonlinearity realized through a nanotube coupling. Multiple scales analysis was applied to study the nonlinear dynamics which was compared favorably with experimental results. The geometrically positioned nanotube introduced nonlinearity efficiently into the otherwise linear micromechanical cantilever oscillator, evident from the acquired responses showing the representative hysteresis loop of a nonlinear dynamic system. It was further shown that a small change in the geometry parameters of the system produced a complete transition of the nonlinear behavior from hardening to softening resonance.

AB - Micro/nanomechanical resonators often exhibit nonlinear behaviors due to their small size and their ease to realize relatively large amplitude oscillation. In this work, we design a nonlinear micromechanical cantilever system with intentionally integrated geometric nonlinearity realized through a nanotube coupling. Multiple scales analysis was applied to study the nonlinear dynamics which was compared favorably with experimental results. The geometrically positioned nanotube introduced nonlinearity efficiently into the otherwise linear micromechanical cantilever oscillator, evident from the acquired responses showing the representative hysteresis loop of a nonlinear dynamic system. It was further shown that a small change in the geometry parameters of the system produced a complete transition of the nonlinear behavior from hardening to softening resonance.

KW - Geometric nonlinearity

KW - Hardening

KW - Micromechanical cantilever oscillation

KW - Multiple scales analysis

KW - Nanotube

KW - Softening

UR - http://www.scopus.com/inward/record.url?scp=84861796128&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861796128&partnerID=8YFLogxK

U2 - 10.1016/j.ijsolstr.2012.04.016

DO - 10.1016/j.ijsolstr.2012.04.016

M3 - Article

AN - SCOPUS:84861796128

VL - 49

SP - 2059

EP - 2065

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

IS - 15-16

ER -