Dynamic behaviour of axially functionally graded beam resting on variable elastic foundation

In this paper, a comprehensive study is carried out on the dynamic behaviour of Euler–Bernoulli and Timoshenko beams resting on Winkler type variable elastic foundation. The material properties of the beam and the stiffness of the foundation are considered to be varying along the length direction. T...

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Bibliographic Details
Published inArchive of Mechanical Engineering Vol. 67; no. 4; pp. 451 - 470
Main Author Kumar, Saurabh
Format Journal Article
LanguageEnglish
Published Warsaw Polish Academy of Sciences 01.10.2020
Subjects
axially functionally graded beam
Beams (structural)
Boundary conditions
Clamping
Elastic foundations
Elastic properties
Engineering
euler-bernoulli beam
Free vibration
Functionally gradient materials
Load
Material properties
Rayleigh-Ritz method
Resonant frequencies
Stiffness
timoshenko beam
Timoshenko beams
variable elastic foundation
Vibration analysis
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ISSN0004-0738
2300-1895
DOI10.24425/ame.2020.131700

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Summary:In this paper, a comprehensive study is carried out on the dynamic behaviour of Euler–Bernoulli and Timoshenko beams resting on Winkler type variable elastic foundation. The material properties of the beam and the stiffness of the foundation are considered to be varying along the length direction. The free vibration problem is formulated using Rayleigh-Ritz method and Hamilton’s principle is applied to generate the governing equations. The results are presented as non-dimensional natural frequencies for different material gradation models and different foundation stiffness variation models. Two distinct boundary conditions viz., clamped-clamped and simply supported-simply supported are considered in the analysis. The results are validated with existing literature and excellent agreement is observed between the results.
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ISSN:0004-0738
2300-1895
DOI:10.24425/ame.2020.131700