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Structural Engineering and Mechanics
  Volume 79, Number 3, August10 2021 , pages 279-288

A n-order refined theory for free vibration of sandwich beams with functionally graded porous layers
Lazreg Hadji, Royal Madan, Shubhankar Bhowmick and Abdelouahed Tounsi

    In this paper, a simple n-order refined theory is developed for free vibration of a simply supported sandwich beam with functionally graded porous layers. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, and does not require a shear correction factor. The variation of shear stress is parabolic across the thickness and the condition at the top and bottom surface are shear stress-free. Equations of motion are derived from Hamilton's principle. In the solution of the governing equations, the Navier procedure is implemented. For porosity effect, four different porosity distributions namely O, X, V, and homogeneous distribution types are modelled; power-law variation of functionally graded face sheets is considered. Results show the effects of varying gradients, thickness to length ratios, effects of the porosity parameters and porosity types on free vibration of functionally graded sandwich beams for simply supported boundary conditions. The results of the present method were validated with existing literature for both hard (ceramic) core material and soft (metal) core material, and good agreement with the benchmarks is seen. The effect of hard-core and soft-core material on natural frequency is found to be contrasting in nature.
Key Words
    free vibration; functionally graded materials; nth-order four variable refined theory; porosity; sandwich beam
Lazreg Hadji: Laboratory of Geomatics and Sustainable Development, Ibn Khaldoun University of Tiaret, Algeria; Department of Mechanical Engineering, University of Tiaret, BP 78 Zaaroura, Tiaret,14000, Algeria
Royal Madan: Department of Mechanical Engineering, National Institute of Technology Raipur, India
Shubhankar Bhowmick: Department of Mechanical Engineering, National Institute of Technology Raipur, India
Abdelouahed Tounsi: YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

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