On the nonlinear mechanics of layered microcantilevers

Mergen H. Ghayesh, Hamed Farokhi, Alireza Gholipour, Shahid Hussain

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

The nonlinear mechanics of three-layered microcantilevers under base excitation is investigated numerically. Employing the modified version of the couple stress-based theory, together with the Bernoulli-Euler beam theory, the potential energy of the three-layered microsystem is derived, while accounting for size effects. Obtaining the kinetic energy, the equations of motion in the longitudinal and transverse directions are derived via Hamilton's principle. Application of the inextensibility condition reduces the two equations of motion to one nonlinear integro-partial differential equation for the transverse oscillation, consisting of geometrical and inertial nonlinearities. The nonlinear equation of partial-differential type is reduced to set of equations of ordinary-differential type through use of a weighted-residual method. Solving the resultant set of discretised equations via a continuation technique gives the frequency-amplitude and force-amplitude responses of the microsystem. The nonlinear response is investigated for different layer composition and different layer thicknesses. The effect of small-scale parameter, as well as base excitation amplitude, is also examined.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalInternational Journal of Engineering Science
Volume120
DOIs
Publication statusPublished - 1 Nov 2017
Externally publishedYes

Fingerprint

Microsystems
Equations of motion
Mechanics
Potential energy
Nonlinear equations
Kinetic energy
Partial differential equations
Chemical analysis

Cite this

Ghayesh, Mergen H. ; Farokhi, Hamed ; Gholipour, Alireza ; Hussain, Shahid. / On the nonlinear mechanics of layered microcantilevers. In: International Journal of Engineering Science. 2017 ; Vol. 120. pp. 1-14.
@article{0a0eceeef204408281b563a736936245,
title = "On the nonlinear mechanics of layered microcantilevers",
abstract = "The nonlinear mechanics of three-layered microcantilevers under base excitation is investigated numerically. Employing the modified version of the couple stress-based theory, together with the Bernoulli-Euler beam theory, the potential energy of the three-layered microsystem is derived, while accounting for size effects. Obtaining the kinetic energy, the equations of motion in the longitudinal and transverse directions are derived via Hamilton's principle. Application of the inextensibility condition reduces the two equations of motion to one nonlinear integro-partial differential equation for the transverse oscillation, consisting of geometrical and inertial nonlinearities. The nonlinear equation of partial-differential type is reduced to set of equations of ordinary-differential type through use of a weighted-residual method. Solving the resultant set of discretised equations via a continuation technique gives the frequency-amplitude and force-amplitude responses of the microsystem. The nonlinear response is investigated for different layer composition and different layer thicknesses. The effect of small-scale parameter, as well as base excitation amplitude, is also examined.",
keywords = "Layered microcantilever, Microsystem, Nonlinear resonance, Numerical simulation, Size effects",
author = "Ghayesh, {Mergen H.} and Hamed Farokhi and Alireza Gholipour and Shahid Hussain",
year = "2017",
month = "11",
day = "1",
doi = "10.1016/j.ijengsci.2017.06.012",
language = "English",
volume = "120",
pages = "1--14",
journal = "International Journal of Engineering Science",
issn = "0020-7225",
publisher = "Elsevier Limited",

}

On the nonlinear mechanics of layered microcantilevers. / Ghayesh, Mergen H.; Farokhi, Hamed; Gholipour, Alireza; Hussain, Shahid.

In: International Journal of Engineering Science, Vol. 120, 01.11.2017, p. 1-14.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On the nonlinear mechanics of layered microcantilevers

AU - Ghayesh, Mergen H.

AU - Farokhi, Hamed

AU - Gholipour, Alireza

AU - Hussain, Shahid

PY - 2017/11/1

Y1 - 2017/11/1

N2 - The nonlinear mechanics of three-layered microcantilevers under base excitation is investigated numerically. Employing the modified version of the couple stress-based theory, together with the Bernoulli-Euler beam theory, the potential energy of the three-layered microsystem is derived, while accounting for size effects. Obtaining the kinetic energy, the equations of motion in the longitudinal and transverse directions are derived via Hamilton's principle. Application of the inextensibility condition reduces the two equations of motion to one nonlinear integro-partial differential equation for the transverse oscillation, consisting of geometrical and inertial nonlinearities. The nonlinear equation of partial-differential type is reduced to set of equations of ordinary-differential type through use of a weighted-residual method. Solving the resultant set of discretised equations via a continuation technique gives the frequency-amplitude and force-amplitude responses of the microsystem. The nonlinear response is investigated for different layer composition and different layer thicknesses. The effect of small-scale parameter, as well as base excitation amplitude, is also examined.

AB - The nonlinear mechanics of three-layered microcantilevers under base excitation is investigated numerically. Employing the modified version of the couple stress-based theory, together with the Bernoulli-Euler beam theory, the potential energy of the three-layered microsystem is derived, while accounting for size effects. Obtaining the kinetic energy, the equations of motion in the longitudinal and transverse directions are derived via Hamilton's principle. Application of the inextensibility condition reduces the two equations of motion to one nonlinear integro-partial differential equation for the transverse oscillation, consisting of geometrical and inertial nonlinearities. The nonlinear equation of partial-differential type is reduced to set of equations of ordinary-differential type through use of a weighted-residual method. Solving the resultant set of discretised equations via a continuation technique gives the frequency-amplitude and force-amplitude responses of the microsystem. The nonlinear response is investigated for different layer composition and different layer thicknesses. The effect of small-scale parameter, as well as base excitation amplitude, is also examined.

KW - Layered microcantilever

KW - Microsystem

KW - Nonlinear resonance

KW - Numerical simulation

KW - Size effects

UR - http://www.scopus.com/inward/record.url?scp=85021125518&partnerID=8YFLogxK

U2 - 10.1016/j.ijengsci.2017.06.012

DO - 10.1016/j.ijengsci.2017.06.012

M3 - Article

VL - 120

SP - 1

EP - 14

JO - International Journal of Engineering Science

JF - International Journal of Engineering Science

SN - 0020-7225

ER -