Nonlinear bending and forced vibrations of axially functionally graded tapered microbeams

Ghayesh, Mergen H., Farokhi, Hamed, Gholipour, Alireza and Tavallaeinejad, Mohammad (2017) Nonlinear bending and forced vibrations of axially functionally graded tapered microbeams. International Journal of Engineering Science, 120. pp. 51-62. ISSN 0020-7225

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Abstract

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.

Item Type:	Article
Uncontrolled Keywords:	Axially functionally graded material; Tapered microbeam; Bending; Forced nonlinear vibration; Modified couple stress theory (MCST)
Subjects:	H300 Mechanical Engineering
Department:	Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User:	Paul Burns
Date Deposited:	14 Aug 2018 09:12
Last Modified:	11 Oct 2019 19:45
URI:	http://nrl.northumbria.ac.uk/id/eprint/35313

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