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Advances in Nano Research
  Volume 11, Number 1, July 2021 , pages 001-17

Size-dependent vibration response of porous graded nanostructure with FEM and nonlocal continuum model
Yogesh Kumar, Ankit Gupta and Abdelouahed Tounsi

    In the present paper, a refined trigonometric higher-order shear deformation theory has been presented with the conjunction of nonlocal theory for the vibrational response of functionally graded (FG) porous nanoplate. The displacement field is chosen based on assumptions that the out of the plane displacement consists of bending and shear components whereas the transverse shear-strain has nonlinear variation along the thickness direction. The number of unknown variables is four, as against five in other renowned shear deformation theories. The governing equations have been derived using Hamilton's principle. A generalized porosity model has also been developed to accommodate both even and uneven type of distribution of porosity in the FG nanoplates. The closed-form solution of simply-supported FG porous nanoplates is obtained and the results are compared with the available reported results. In finite element solution, a C0 continuous isoparametric quadrilateral element has been used with various conventional and unconventional boundary conditions. The effects of various parameters like small-scale effect, aspect ratio, volume fraction index, porosity volume fraction, and thickness ratio have been investigated. The significant influence of small-scale effects and porosity inclusions have been observed in the reported results. It has been reported that both closed-form and finite element solutions with the present theory can make accurate predictions of the free vibration response.
Key Words
    closed-form solution; composite materials; functionally graded (FG) material; Hamilton
Yogesh Kumar and Ankit Gupta: School of Engineering, Shiv Nadar University, Gautama Buddha Nagar, India

Abdelouahed Tounsi: YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea/ 3Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

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