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Nonlinear vibration of nonlocal four-variable graded plates with porosities implementing homotopy perturbation and Hamiltonian methods

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Abstract

In this paper, new solutions are presented to examine large amplitude vibration of a porous nanoplate resting on a nonlinear hardening elastic foundation modeled by nonlinear four-variable plate theory. The closed-form expression of the nonlinear frequency is obtained using a novel Hamiltonian approach as well as homotopy perturbation method for the first time. Another novelty of these approaches is that they are needless of any iterative process. Based on a modified rule of mixture, the nanopores or nanovoids are considered in the model. Nonlinear governing equations of a four-variable nanoplate with von Karman geometric nonlinearity are obtained using Hamilton’s principle. The dependency of the nonlinear frequency on the porosities, scale parameter, maximum amplitude, material gradation, foundation parameters and geometrical parameters is explored. The proposed solution approach and also obtained results can be used in future investigations on nanostructures.

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Barati, M.R., Shahverdi, H. Nonlinear vibration of nonlocal four-variable graded plates with porosities implementing homotopy perturbation and Hamiltonian methods. Acta Mech 229, 343–362 (2018). https://doi.org/10.1007/s00707-017-1952-y

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  • DOI: https://doi.org/10.1007/s00707-017-1952-y

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