# Free vibration analysis of 2-D FGM beams in thermal environment based on a new third-order shear deformation theory

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https://doi.org/10.15625/0866-7136/10503## Keywords:

2-D FGM beam, temperature-dependent properties, new third-order shear deformation theory, shear rotation, free vibration analysis## Abstract

Free vibration analysis of two-directional functionally graded material (2-D FGM) beams in thermal environment based on a new third-order shear deformation theory is presented. The material properties are assumed to be graded in both the thickness and longitudinal directions by a power law distribution, and they are considered to be temperature-dependent. Equations of motion, in which the shear rotation rather than the cross-sectional rotation is considered to be an independent variable, are constructed from Hamilton's principle. A finite element formulation is derived and employed to compute the vibration characteristics of the beams. The numerical results reveal that the developed formulation is accurate, and it is capable to give accurate natural frequencies by using a small number of elements. A parametric study is carried out to highlight the effects of material composition, temperature rise on the vibration characteristics of the beams.

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*Free vibration analysis of 2-D FGM beams in thermal environment based on a new third-order shear deformation theory*, Vietnam J. Mech.

**40**(2018) 121–140. DOI: https://doi.org/10.15625/0866-7136/10503.

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