Resonance Responses of Geometrically Imperfect Functionally Graded Extensible Microbeams

Mergen Ghayesh*, Hamed Farokhi, Alireza Gholipour, Shahid Hussain, Maziar Arjomandi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)

Abstract

This paper aims at analyzing the size-dependent nonlinear dynamical behavior of a geometrically imperfect microbeam made of a functionally graded (FG) material, taking into account the longitudinal, transverse, and rotational motions. The size-dependent property is modeled by means of the modified couple stress theory, the shear deformation and rotary inertia are modeled using the Timoshenko beam theory, and the graded material property in the beam thickness direction is modeled via the Mori - Tanaka homogenization technique. The kinetic and size-dependent potential energies of the system are developed as functions of the longitudinal, transverse, and rotational motions. On the basis of an energy method, the continuous models of the system motion are obtained. Upon application of a weighted-residual method, the reduced-order model is obtained. A continuation method along with an eigenvalue extraction technique is utilized for the nonlinear and linear analyses, respectively. A special attention is paid on the effects of the material gradient index, the imperfection amplitude, and the length-scale parameter on the system dynamical response.

Original languageEnglish
Article number051002
JournalJournal of Computational and Nonlinear Dynamics
Volume12
Issue number5
Early online date9 Mar 2017
DOIs
Publication statusPublished - 1 Sep 2017

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