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

• Published in: Archive of Mechanical Engineering Vol. 67; no. 4; pp. 451 - 470
• Main Author: Kumar, Saurabh
• Format: Journal Article
• Language: English
• 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
• ISSN: 0004-0738; 2300-1895
• DOI: 10.24425/ame.2020.131700

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.