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Smart Structures and Systems Volume 25, Number 6, June 2020 , pages 693-705 DOI: https://doi.org/10.12989/sss.2020.25.6.693 |
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Large amplitude free vibrations of FGM shallow curved tubes in thermal environment |
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Hadi Babaei, Yaser Kiani and M. Reza Eslami
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| Abstract | ||
| In the current investigation, large amplitude free vibration behavior of shallow curved pipes (tubes) made of functionally graded materials is investigated. Properties of the tube are distributed across the radius of the tube and are obtained by means of a power law function. It is also assumed that all thermo-mechanical properties are temperature dependent. The governing equations of the tube are obtained using a higher order shear deformation tube theory, where the traction free boundary conditions are satisfied on the top and bottom surfaces of the tube. The von Kármán type of geometrical non-linearity is included into the formulation to consider the large displacements and small strains. Uniform temperature elevation of the tube is also included into the formulation. For the case of tubes which are simply supported in flexure and axially immovable, the governing equations are solved using the two-step perturbation technique. Closed form expressions are provided to obtain the small and large amplitude fundamental natural frequencies of the FGM shallow curved tubes in thermal environment. Numerical results are given to explore the effects of thermal environment, radius ratio, and length to thickness ratio of the tube on the fundamental linear and non-linear frequencies. | ||
| Key Words | ||
| nonlinear free vibration; FGM; shallow curved tube; von Karman nonlinearity; two-step perturbation method; thermal environment | ||
| Address | ||
| (1) Hadi Babaei: Department of Mechanical Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran; (2) Yaser Kiani: Faculty of Engineering, Shahrekord University, Shahrekord, Iran; (3) M. Reza Eslami: Mechanical Engineering Department, Amirkabir University of Technology, Tehran, Iran. | ||