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On the nonlocal free vibration analysis of functionally graded porous doubly curved shallow nanoshells with variable nonlocal parameters

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Abstract

In this paper, the free vibration behavior of functionally graded (FG) porous doubly curved shallow nanoshells with variable nonlocal parameters is investigated. The classical Eringen’s nonlocal elasticity theory is modified and applied to capture the small size effect of naturally discrete FG nanoshells. The effective material properties of the FG porous doubly curved shallow nanoshells including the nonlocal parameters are graded continuously through the thickness direction via the rule of mixture. A combination of the first-order shear deformation theory and the modified nonlocal elasticity theory is developed to describe the kinematic and constitutive relations of the FG doubly curved shallow nanoshells. The Hamilton’s principle is employed to establish the governing equations of motion of FG porous doubly curved shallow nanoshells and then solved analytically using the Navier’s solution. The accuracy and correctness of the proposed algorithm are demonstrated by comparing its results with those available from other researchers in the existing literature. Moreover, a comprehensive parametric study is presented and discussed in detail to show the effects of the geometric parameters, material properties, porosity, and the variation of the nonlocal parameter on the free vibration behavior of the FG porous doubly curved shallow nanoshells. Especially, the numerical results showed that the variation of the nonlocal parameters has significant effects on the free vibration behavior of the FG porous doubly curved shallow nanoshells. Some new results are also reported which will serve as a benchmark for future analysis of FG porous doubly curved shallow nanoshells.

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Authors and Affiliations

  1. Department of Solid Mechanics, Le Quy Don Technical University, 236 Hoang Quoc Viet Street, Hanoi, Vietnam

    Pham Van Vinh

  2. YFL (Yonsei Frontier Lab), Yonsei University, Seoul, South Korea

    Abdelouahed Tounsi

  3. Department of Civil and Environmental Engineering, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Eastern Province, Saudi Arabia

    Abdelouahed Tounsi

  4. Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes, Sidi Bel Abbès, Algeria

    Abdelouahed Tounsi

  5. Laboratoire de Recherche en Génie Civil, LRGC, Université de Biskra, B.P. 145, R.P. 07000, Biskra, Algeria

    Mohamed-Ouejdi Belarbi

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Van Vinh, P., Tounsi, A. & Belarbi, MO. On the nonlocal free vibration analysis of functionally graded porous doubly curved shallow nanoshells with variable nonlocal parameters. Engineering with Computers 39, 835–855 (2023). https://doi.org/10.1007/s00366-022-01687-6

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