Nonlinear oscillations of FG cantilevers
Date
2019
Authors
Ghayesh, M.H.
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Journal article
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Applied Acoustics, 2019; 145:393-398
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Mergen H. Ghayesh
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Abstract
The nonlinear vibrations of functionally graded (FG) cantilevers is investigated. The FG system undergoes large-amplitude oscillations as one end is free to move both transversely and axially; this causes large vibrations due to inertial and curvature nonlinear terms in the equation of motion. The FG properties change gradually in the thickness direction according to the Mori-Tanaka method. The constitutive relations are built and Hamilton’s energy/work principle is used giving coupled continuous models. The centreline extensibility is neglected which gives an integro-nonlinear model of the FG system. A reduction version is obtained using Galerkin’s technique. Numerical integrations for frequency/displacement responses are performed using a continuation technique. A dynamic balance between the FG-system nonlinearities gives a vibration of weak softening-type.
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© 2018 Elsevier Ltd. All rights reserved.