Large-amplitude dynamical behaviour of microcantilevers

Hamed Farokhi, Mergen H. Ghayesh, Shahid Hussain

Research output: Contribution to journalArticle

61 Citations (Scopus)

Abstract

This paper aims at analysing the nonlinear size-dependent dynamics of a microcantilever based on the modified couple stress theory. Since one end of the microcantilever is free to move, the system undergoes large deformations; this necessitates the application of a nonlinear theory which is capable of taking into account curvature-related and inertial-related nonlinearities. The expressions for the kinetic and potential energies are developed on the basis of the modified couple stress theory. The energy terms are balanced by the work of a base excitation by means of Hamilton's principle, yielding the continuous model for the system motion. Based on a weighted-residual method, this continuous model is reduced and then solved via an eigenvalue analysis (for the linear analysis) and a continuation method (for the nonlinear analysis); stability analysis is performed via the Floquet theory. It is shown that each source of nonlinearity, in the presence of the length-scale parameter, has a significant effect on the system dynamics.

Original languageEnglish
Pages (from-to)29-41
Number of pages13
JournalInternational Journal of Engineering Science
Volume106
DOIs
Publication statusPublished - 2016
Externally publishedYes

Fingerprint

Nonlinear analysis
Potential energy
Kinetic energy
Dynamical systems

Cite this

@article{b28b6e205d2f476690a94892e529498c,
title = "Large-amplitude dynamical behaviour of microcantilevers",
abstract = "This paper aims at analysing the nonlinear size-dependent dynamics of a microcantilever based on the modified couple stress theory. Since one end of the microcantilever is free to move, the system undergoes large deformations; this necessitates the application of a nonlinear theory which is capable of taking into account curvature-related and inertial-related nonlinearities. The expressions for the kinetic and potential energies are developed on the basis of the modified couple stress theory. The energy terms are balanced by the work of a base excitation by means of Hamilton's principle, yielding the continuous model for the system motion. Based on a weighted-residual method, this continuous model is reduced and then solved via an eigenvalue analysis (for the linear analysis) and a continuation method (for the nonlinear analysis); stability analysis is performed via the Floquet theory. It is shown that each source of nonlinearity, in the presence of the length-scale parameter, has a significant effect on the system dynamics.",
keywords = "Microcantilever, Modified couple stress theory, Size-dependent dynamics, Stability",
author = "Hamed Farokhi and Ghayesh, {Mergen H.} and Shahid Hussain",
year = "2016",
doi = "10.1016/j.ijengsci.2016.03.002",
language = "English",
volume = "106",
pages = "29--41",
journal = "International Journal of Engineering Science",
issn = "0020-7225",
publisher = "Elsevier Limited",

}

Large-amplitude dynamical behaviour of microcantilevers. / Farokhi, Hamed; Ghayesh, Mergen H.; Hussain, Shahid.

In: International Journal of Engineering Science, Vol. 106, 2016, p. 29-41.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Large-amplitude dynamical behaviour of microcantilevers

AU - Farokhi, Hamed

AU - Ghayesh, Mergen H.

AU - Hussain, Shahid

PY - 2016

Y1 - 2016

N2 - This paper aims at analysing the nonlinear size-dependent dynamics of a microcantilever based on the modified couple stress theory. Since one end of the microcantilever is free to move, the system undergoes large deformations; this necessitates the application of a nonlinear theory which is capable of taking into account curvature-related and inertial-related nonlinearities. The expressions for the kinetic and potential energies are developed on the basis of the modified couple stress theory. The energy terms are balanced by the work of a base excitation by means of Hamilton's principle, yielding the continuous model for the system motion. Based on a weighted-residual method, this continuous model is reduced and then solved via an eigenvalue analysis (for the linear analysis) and a continuation method (for the nonlinear analysis); stability analysis is performed via the Floquet theory. It is shown that each source of nonlinearity, in the presence of the length-scale parameter, has a significant effect on the system dynamics.

AB - This paper aims at analysing the nonlinear size-dependent dynamics of a microcantilever based on the modified couple stress theory. Since one end of the microcantilever is free to move, the system undergoes large deformations; this necessitates the application of a nonlinear theory which is capable of taking into account curvature-related and inertial-related nonlinearities. The expressions for the kinetic and potential energies are developed on the basis of the modified couple stress theory. The energy terms are balanced by the work of a base excitation by means of Hamilton's principle, yielding the continuous model for the system motion. Based on a weighted-residual method, this continuous model is reduced and then solved via an eigenvalue analysis (for the linear analysis) and a continuation method (for the nonlinear analysis); stability analysis is performed via the Floquet theory. It is shown that each source of nonlinearity, in the presence of the length-scale parameter, has a significant effect on the system dynamics.

KW - Microcantilever

KW - Modified couple stress theory

KW - Size-dependent dynamics

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=84988980647&partnerID=8YFLogxK

U2 - 10.1016/j.ijengsci.2016.03.002

DO - 10.1016/j.ijengsci.2016.03.002

M3 - Article

VL - 106

SP - 29

EP - 41

JO - International Journal of Engineering Science

JF - International Journal of Engineering Science

SN - 0020-7225

ER -