Nonlinear resonant behavior of microbeams over the buckled state

Farokhi, Hamed, Ghayesh, Mergen H. and Amabili, Marco (2013) Nonlinear resonant behavior of microbeams over the buckled state. Applied Physics A, 113 (2). pp. 297-307. ISSN 0947-8396

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Official URL: http://dx.doi.org/10.1007/s00339-013-7894-x

Abstract

The present study investigates the nonlinear resonant behavior of a microbeam over its buckled (non-trivial) configuration. The system is assumed to be subjected to an axial load along with a distributed transverse harmonic load. The axial load is increased leading the system to lose the stability via a pitchfork bifurcation; the postbuckling configuration is obtained and the nonlinear resonant response of the system over the buckled state is examined. More specifically, the nonlinear equation of motion is obtained employing Hamilton's principle along with the modified couple stress theory. The continuous system is truncated into a system with finite degrees of freedom; the Galerkin scheme is employed to discretize the nonlinear partial differential equation of motion into a set of ordinary differential equations. This set of equations is solved numerically employing the pseudo-arclength continuation technique; first a nonlinear static analysis is performed upon this set of equations so as to obtain the onset of buckling (supercritical pitchfork bifurcation) and the buckled configuration of the microbeam. The frequency-response and force-response curves of the system are then constructed over the buckled configurations. A comparison is made between the frequency-response curves obtained by means of the modified couple stress and the classical theories. The effect of different system parameters on the frequency-response and force-response curves is also examined.

Item Type: Article
Uncontrolled Keywords: Excitation, Frequency, Force Amplitude, Pitchfork Bifurcation, Length Scale Parameter, Modify Couple Stress Theory
Subjects: H300 Mechanical Engineering
Department: Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User: Paul Burns
Date Deposited: 30 Aug 2018 08:48
Last Modified: 30 Aug 2018 08:48
URI: http://nrl.northumbria.ac.uk/id/eprint/35517

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