Nonlinear bending and forced vibrations of axially functionally graded tapered microbeams

Mergen H. Ghayesh*, Hamed Farokhi, Alireza Gholipour, Mohammad Tavallaeinejad

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

65 Citations (Scopus)


The forced nonlinear size-dependent vibrations and bending of axially functionally graded (AFG) tapered microbeams are examined incorporating extensibility. Employing the modified version of the couple stress-based theory, the nonlinear partial differential equations for the transverse and longitudinal motions for a clamped-clamped AFG tapered microbeam are obtained via Hamilton's principle. The variation of the mechanical properties and the cross-section of the AFG microbeam along the length are included in the equations of motion based on exponential distributions of the moduli of elasticity, mass density, Poisson's ratio, and cross-sectional area. The Galerkin method is utilised to obtain a set of discretised nonlinear differential equations of ordinary type; this set of equation is solved with the help of Houbolt's finite difference technique together with the Newton-Raphson method. The effects of the small-scale parameter, the gradient index, material properties variation, and the taper ratio on the nonlinear vibrations of the microsystem are investigated.

Original languageEnglish
Pages (from-to)51-62
Number of pages12
JournalInternational Journal of Engineering Science
Early online date29 Jun 2017
Publication statusPublished - 1 Nov 2017


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