Static and free vibration analyses of small-scale functionally graded beams possessing a variable length scale parameter using different beam theories

Date

2014-07-01

Author

Aghazadeh, Reza
Ciğeroğlu, Ender
Dağ, Serkan

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This article puts forward a modified couple stress theory based approach of analysis for small-scale functionally graded beams, that possess a variable length scale parameter. Presented procedures are capable of predicting static and dynamic beam responses according to three different beam theories, namely: Euler - Bernoulli beam theory, Timoshenko beam theory and third-order shear deformation beam theory. A variational method is used in conjunction with the modified couple stress theory to derive the governing partial differential equations. All properties of the small-scale functionally graded beams - including the length scale parameter - are assumed to be functions of the thickness coordinate in the derivations. The governing equations are solved numerically through the use of the differential quadrature method (DQM). Numerical results are generated for small-scale functionally graded beams, that comprise ceramic and metallic materials as constituent phases. Both small-scale beams subjected to static loading and those undergoing free vibrations are considered in the computations. Comparisons of the numerical results to those available in the literature point out that developed techniques lead to results of high accuracy. Further numerical results are provided, which demonstrate the responses of small-scale functionally graded beams estimated by the three different beam theories as well as provide insight into the influences of material parameters upon the static deflections and natural vibration frequencies. (C) 2014 Elsevier Masson SAS. All rights reserved.

Subject Keywords

Mechanical Engineering, General Physics and Astronomy, General Materials Science, Mechanics of Materials

URI

https://hdl.handle.net/11511/39925

Journal

EUROPEAN JOURNAL OF MECHANICS A-SOLIDS

DOI

https://doi.org/10.1016/j.euromechsol.2014.01.002

Collections

Department of Mechanical Engineering, Article

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Citation Formats

R. Aghazadeh, E. Ciğeroğlu, and S. Dağ, “Static and free vibration analyses of small-scale functionally graded beams possessing a variable length scale parameter using different beam theories,” EUROPEAN JOURNAL OF MECHANICS A-SOLIDS, pp. 1–11, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39925.