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Steel and Composite Structures Volume 33, Number 2, October25 2019 , pages 195-208 DOI: https://doi.org/10.12989/scs.2019.33.2.195 |
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Vibration analysis of functionally graded graphene platelet-reinforced composite doubly-curved shallow shells on elastic foundations |
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Mohammed Sobhy and Ashraf M. Zenkour
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| Abstract | ||
| Based on a four-variable shear deformation shell theory, the free vibration analysis of functionally graded graphene platelet-reinforced composite (FGGPRC) doubly-curved shallow shells with different boundary conditions is investigated in this work. The doubly-curved shells are composed of multi nanocomposite layers that are reinforced with graphene platelets. The graphene platelets are uniformly distributed in each individual layer. While, the volume faction of the graphene is graded from layer to other in accordance with a novel distribution law. Based on the suggested distribution law, four types of FGGPRC doubly-curved shells are studied. The present shells are assumed to be rested on elastic foundations. The material properties of each layer are calculated using a micromechanical model. Four equations of motion are deduced utilizing Hamilton's principle and then converted to an eigenvalue problem employing an analytical method. The obtained results are checked by introducing some comparison examples. A detailed parametric investigation is performed to illustrate the influences of the distribution type of volume fraction, shell curvatures, elastic foundation stiffness and boundary conditions on the vibration of FGGPRC doubly-curved shells. | ||
| Key Words | ||
| doubly-curved nanocomposite shells; functionally graded; graphene platelets; vibration; elastic foundations; four-variable shell theory | ||
| Address | ||
| (1) Mohammed Sobhy: Department of Mathematics and Statistics, Faculty of Science, King Faisal University, P.O. Box 400, Hofuf 31982, Saudi Arabia; (2) Ashraf M. Zenkour: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia; (3) Mohammed Sobhy, Ashraf M. Zenkour: Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt. | ||