Nonlinear dynamics of a geometrically imperfect microbeam based on the modified couple stress theory

Hamed Farokhi, Mergen H. Ghayesh*, Marco Amabili

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

234 Citations (Scopus)


The present study investigates the nonlinear dynamics of a geometrically imperfect microbeam numerically on the basis of the modified couple stress theory. Hamilton's principle is used to obtain the nonlinear partial differential equation of motion for an initially curved beam. The equation of motion is discretized and reduced to a set of nonlinear ordinary differential equations by means of the Galerkin scheme. This set of equations is solved numerically by means of the pseudo-arclength continuation technique which allows the continuation of both stable and unstable solution branches as well as determination of different types of bifurcation. An eigenvalue analysis is also conducted to obtain the linear natural frequencies of the system. The frequency-response curves are constructed for the system with different initial imperfections. Moreover, the frequency-response curves of the system are plotted together as a specific system parameter is varied, in order to highlight the effect of each parameter on the resonant dynamics of the system.

Original languageEnglish
Pages (from-to)11-23
Number of pages13
JournalInternational Journal of Engineering Science
Early online date11 Apr 2013
Publication statusPublished - 1 Jul 2013


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