Journal
APPLIED ACOUSTICS
Volume 145, Issue -, Pages 393-398Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.apacoust.2018.08.014
Keywords
Cantilevers; Oscillations; FG; Softening response; Nonlinear
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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. (C) 2018 Elsevier Ltd. All rights reserved.
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