Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory

Mergen H. Ghayesh*, Marco Amabili, Hamed Farokhi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

257 Citations (Scopus)


The nonlinear forced vibrations of a microbeam are investigated in this paper, employing the strain gradient elasticity theory. The geometrically nonlinear equation of motion of the microbeam, taking into account the size effect, is obtained employing a variational approach. Specifically, Hamilton's principle is used to derive the nonlinear partial differential equation governing the motion of the system which is then discretized into a set of second-order nonlinear ordinary differential equations (ODEs) by means of the Galerkin technique. A change of variables is then introduced to this set of second-order ODEs, and a new set of ODEs is obtained consisting of first-order nonlinear ordinary differential equations. This new set is solved numerically employing the pseudo-arclength continuation technique which results in the frequency-response curves of the system. The advantage of this method lies in its capability of continuing both stable and unstable solution branches.

Original languageEnglish
Pages (from-to)52-60
Number of pages9
JournalInternational Journal of Engineering Science
Early online date26 Dec 2012
Publication statusPublished - Feb 2013


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