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Steel and Composite Structures Volume 33, Number 3, November10 2019 , pages 403-432 DOI: https://doi.org/10.12989/scs.2019.33.3.403 |
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Free vibration of AFG beams with elastic end restraints |
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Mohsen Bambaeechee
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| Abstract | ||
| Axially functionally graded (AFG) beams are a new class of composite structures that have continuous variations in material and/or geometrical parameters along the axial direction. In this study, the exact analytical solutions for the free vibration of AFG and uniform beams with general elastic supports are obtained by using Euler.Bernoulli beam theory. The elastic supports are modeled with linear rotational and lateral translational springs. Moreover, the material and/or geometrical properties of the AFG beams are assumed to vary continuously and together along the length of the beam according to the power-law forms. Accordingly, the accuracy, efficiency and capability of the proposed formulations are demonstrated by comparing the responses of the numerical examples with the available solutions. In the following, the effects of the elastic end restraints and AFG parameters, namely, gradient index and gradient coefficient, on the values of the first three natural frequencies of the AFG and uniform beams are investigated comprehensively. The analytical solutions are presented in tabular and graphical forms and can be used as the benchmark solutions. Furthermore, the results presented herein can be utilized for design of inhomogeneous beams with various supporting conditions. | ||
| Key Words | ||
| axially functionally graded beams; elastic supports; natural frequencies; free vibration; exact analysis; Euler-Bernoulli beam theory | ||
| Address | ||
| Department of Civil Engineering, Faculty of Engineering, Quchan University of Technology, P.O. Box. 94771-67335, Quchan, Iran. | ||