Oscillations of functionally graded microbeams

Ghayesh, Mergen H., Farokhi, Hamed and Gholipour, Alireza (2017) Oscillations of functionally graded microbeams. International Journal of Engineering Science, 110. pp. 35-53. ISSN 0020-7225

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Abstract

The size-dependent oscillations of a third-order shear-deformable functionally graded microbeam are investigated taking into account all the longitudinal and transverse displacements and inertia as well as the rotation and rotary inertia. The modified couple stress theory along with the Mori–Tanaka homogenisation technique is employed to develop formulations for the elastic potential energy as well as the kinetic energy of the system. The energy of the system is balanced by the work of a harmonic excitation force via an energy method based on Hamilton's principle, yielding the size-dependent coupled nonlinear continuous models of the functionally graded system for the longitudinal and transverse displacements as well as the rotational motion. A model reduction procedure, on the basis of a weighted-residual method, is applied without any simplifications on the displacement/inertia/rotation. This operation yields three sets of second-order reduced-order coupled model of the functionally graded system for the longitudinal, transverse, and rotational motions. These reduced-order models are solved via use of a continuation method in order to construct the nonlinear frequency-response and force-response curves of the functionally graded system. A linear analysis is also performed by means of an eigenvalue extraction method in order to determine the linear natural frequencies of the system. It is shown that the material gradient index as well as the length-scale parameter of the functionally graded system affects the system dynamics substantially.

Item Type:	Article
Uncontrolled Keywords:	Microbeam; Functionally graded material; Shear-deformable; Third-order shear-deformation; Motion characteristics
Subjects:	H300 Mechanical Engineering
Department:	Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User:	Paul Burns
Date Deposited:	22 Aug 2018 14:32
Last Modified:	11 Oct 2019 19:30
URI:	http://nrl.northumbria.ac.uk/id/eprint/35447

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