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Erschienen in:
2020 | OriginalPaper | Buchkapitel
Free and Forced Vibration Analysis of Functionally Graded Beams Using Finite Element Model Based on Refined Third-Order Theory
verfasst von : M. Altaf Khan, M. Y. Yasin, Mirza Shariq Beg, A. H. Khan
Erschienen in: Emerging Trends in Mechanical Engineering
Verlag: Springer Singapore
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Abstract
This work is dedicated toward the development of the finite element (FE) model based on refined third-order theory (TOT) for the dynamic analysis of functionally graded (FG) beams. Variational approach is employed to derive the governing equations as well as consistent boundary conditions. Two-noded beam element is selected for the discretization of FG beam. The variables \( u_{0} \) and \( \psi_{0} \) are interpolated using C0-continuous linear Lagrangian functions while the presence of the second derivative of the transverse deflection in the variational equation requires C1-continuity and is interpolated using C1-continuous Hermite interpolation functions. Static deflection and free vibration responses are validated from the literature, and new results have been presented for free and forced vibration of FGM beams.