Thermo-mechanical buckling and nonlinear free vibration analysis of functionally graded beams on nonlinear elastic foundation

In this paper, thermo-mechanical buckling and nonlinear free vibration analysis of functionally graded (FG) beams on nonlinear elastic foundation are investigated. Nonlinear governing partial differential equation (PDE) of motion is derived based on Euler–Bernoulli assumptions together with Von Karm...

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Bibliographic Details
Published in:Composites. Part B, Engineering Engineering, 2012-04, Vol.43 (3), p.1523-1530
Main Authors: Fallah, A., Aghdam, M.M.
Format: Article
Language:English
Subjects:
Applied sciences
B. Buckling
B. Thermo-mechanical
B. Vibration
C. Analytical modeling
composite materials
Composites
equations
Exact sciences and technology
Forms of application and semi-finished materials
Functionally graded beams
Laminates
Physicochemistry of polymers
Polymer industry, paints, wood
Technology of polymers
vibration
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Summary:In this paper, thermo-mechanical buckling and nonlinear free vibration analysis of functionally graded (FG) beams on nonlinear elastic foundation are investigated. Nonlinear governing partial differential equation (PDE) of motion is derived based on Euler–Bernoulli assumptions together with Von Karman strain–displacement relation. Based on the Galerkin’s decomposition method, the nonlinear PDE governing equation is reduced to a nonlinear ordinary differential equation (ODE). He’s variational method is employed to obtain a simple and efficient approximate closed form solution for the resulted nonlinear ODE. Comparison between results of the present work and those available in literature shows accuracy of the presented expressions. Some new results for the thermo-mechanical buckling and nonlinear free vibration analysis of the FG beams such as the effects of vibration amplitude, material inhomogeneity, nonlinear elastic foundation, boundary conditions, geometric parameter and thermal loading are presented to be used in future references.
ISSN:1359-8368
1879-1069
DOI:10.1016/j.compositesb.2011.08.041