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Nonlinear Dynamic Behavior of Porous and Imperfect Bernoulli-Euler Functionally Graded Nanobeams Resting on Winkler Elastic Foundation

Department of Civil Engineering, University of Salerno, 84084 Fisciano, Italy
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Technologies 2020, 8(4), 56; https://doi.org/10.3390/technologies8040056
Received: 30 September 2020 / Revised: 13 October 2020 / Accepted: 14 October 2020 / Published: 20 October 2020
(This article belongs to the Section Innovations in Materials Processing)
Nonlinear free vibrations of functionally graded porous Bernoulli–Euler nano-beams resting on an elastic foundation through a stress-driven nonlocal elasticity model are studied taking into account von Kármán type nonlinearity and initial geometric imperfection. By using the Galerkin method, the governing equations are reduced to a nonlinear ordinary differential equation. The closed form analytical solution of the nonlinear natural flexural frequency is then established using the Hamiltonian approach to nonlinear oscillators. Several comparisons with existing models in the literature are performed to validate the accuracy and reliability of the proposed approach. Finally, a numerical investigation is developed in order to analyze the effects of the gradient index coefficient, porosity volume fraction, initial geometric imperfection, and the Winkler elastic foundation coefficient, on the nonlinear flexural vibrations of metal–ceramic FG porous Bernoulli–Euler nano-beams. View Full-Text
Keywords: nonlinear flexural vibrations; functionally graded porous nanobeams; nonlocal elasticity; stress-driven formulation nonlinear flexural vibrations; functionally graded porous nanobeams; nonlocal elasticity; stress-driven formulation
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MDPI and ACS Style

Penna, R.; Feo, L. Nonlinear Dynamic Behavior of Porous and Imperfect Bernoulli-Euler Functionally Graded Nanobeams Resting on Winkler Elastic Foundation. Technologies 2020, 8, 56. https://doi.org/10.3390/technologies8040056

AMA Style

Penna R, Feo L. Nonlinear Dynamic Behavior of Porous and Imperfect Bernoulli-Euler Functionally Graded Nanobeams Resting on Winkler Elastic Foundation. Technologies. 2020; 8(4):56. https://doi.org/10.3390/technologies8040056

Chicago/Turabian Style

Penna, Rosa, and Luciano Feo. 2020. "Nonlinear Dynamic Behavior of Porous and Imperfect Bernoulli-Euler Functionally Graded Nanobeams Resting on Winkler Elastic Foundation" Technologies 8, no. 4: 56. https://doi.org/10.3390/technologies8040056

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