Journal
COMPOSITE STRUCTURES
Volume 92, Issue 8, Pages 1877-1887Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.compstruct.2010.01.010
Keywords
Functionally graded beam; Free vibration; Variational method; Shear deformation theory
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Exact solutions are presented to study the free vibration of a beam made of symmetric functionally graded materials. The formulation used is based on a unified higher order shear deformation theory. Material properties are taken to be temperature-dependent, and vary continuously through the thickness according to a power law distribution (P-FGM), or an exponential law distribution (E-FGM) or a sigmoid law distribution (S-FGM). The beam is assumed to be initially stressed by a temperature rise through the thickness. Temperature field is considered constant in xy plane of the beam. Hamilton's principle is used to derive the governing equations of motion. Free vibration frequencies are obtained by solving analytically a system of ordinary differential equations, for different boundary conditions. (C) 2010 Elsevier Ltd. All rights reserved.
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