Nonlinear free vibration of rectangular plates reinforced with 3D graphene foam: Approximate analytical solution
This paper investigates nonlinear free vibration of three-dimensional graphene foam skeleton reinforced rectangular plates. The three-dimensional graphene foam skeleton can distribute in different patterns along the thickness direction of the plate. According to the mixing rule, the effective Poisso...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-06-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379720305428 |
| _version_ | 1818891105436958720 |
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| author | Mei Wen Teng Yan Qing Wang |
| author_facet | Mei Wen Teng Yan Qing Wang |
| author_sort | Mei Wen Teng |
| collection | DOAJ |
| description | This paper investigates nonlinear free vibration of three-dimensional graphene foam skeleton reinforced rectangular plates. The three-dimensional graphene foam skeleton can distribute in different patterns along the thickness direction of the plate. According to the mixing rule, the effective Poisson’s ratio, mass density and elastic modulus of three-dimensional graphene foam reinforced (3D-GFR) plates are described. In the framework of the von Kármán nonlinear plate theory, Hamilton’s principle is utilized to derive equations of motion. Then, analytical nonlinear frequencies of 3D-GFR plates are solved by using the Galerkin method and the harmonic balance method. Results show that 3D-GFR plates exhibit hardening nonlinearity. The effect of porosity coefficient on nonlinear vibration depends on the foam skeleton distribution. In addition, the nonlinear frequencies of 3D-GFR plates increase as the skeleton weight fraction rises. |
| first_indexed | 2024-12-19T17:35:31Z |
| format | Article |
| id | doaj.art-758c86f05340456e9521c8b3881c8cea |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-19T17:35:31Z |
| publishDate | 2020-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-758c86f05340456e9521c8b3881c8cea2022-12-21T20:12:21ZengElsevierResults in Physics2211-37972020-06-0117103147Nonlinear free vibration of rectangular plates reinforced with 3D graphene foam: Approximate analytical solutionMei Wen Teng0Yan Qing Wang1Department of Mechanics, Northeastern University, Shenyang 110819, ChinaDepartment of Mechanics, Northeastern University, Shenyang 110819, China; Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang 110819, China; Corresponding author.This paper investigates nonlinear free vibration of three-dimensional graphene foam skeleton reinforced rectangular plates. The three-dimensional graphene foam skeleton can distribute in different patterns along the thickness direction of the plate. According to the mixing rule, the effective Poisson’s ratio, mass density and elastic modulus of three-dimensional graphene foam reinforced (3D-GFR) plates are described. In the framework of the von Kármán nonlinear plate theory, Hamilton’s principle is utilized to derive equations of motion. Then, analytical nonlinear frequencies of 3D-GFR plates are solved by using the Galerkin method and the harmonic balance method. Results show that 3D-GFR plates exhibit hardening nonlinearity. The effect of porosity coefficient on nonlinear vibration depends on the foam skeleton distribution. In addition, the nonlinear frequencies of 3D-GFR plates increase as the skeleton weight fraction rises.http://www.sciencedirect.com/science/article/pii/S2211379720305428Reinforced plateThree-dimensional graphene foamNonlinear free vibrationHarmonic balance methodFoam effect |
| spellingShingle | Mei Wen Teng Yan Qing Wang Nonlinear free vibration of rectangular plates reinforced with 3D graphene foam: Approximate analytical solution Results in Physics Reinforced plate Three-dimensional graphene foam Nonlinear free vibration Harmonic balance method Foam effect |
| title | Nonlinear free vibration of rectangular plates reinforced with 3D graphene foam: Approximate analytical solution |
| title_full | Nonlinear free vibration of rectangular plates reinforced with 3D graphene foam: Approximate analytical solution |
| title_fullStr | Nonlinear free vibration of rectangular plates reinforced with 3D graphene foam: Approximate analytical solution |
| title_full_unstemmed | Nonlinear free vibration of rectangular plates reinforced with 3D graphene foam: Approximate analytical solution |
| title_short | Nonlinear free vibration of rectangular plates reinforced with 3D graphene foam: Approximate analytical solution |
| title_sort | nonlinear free vibration of rectangular plates reinforced with 3d graphene foam approximate analytical solution |
| topic | Reinforced plate Three-dimensional graphene foam Nonlinear free vibration Harmonic balance method Foam effect |
| url | http://www.sciencedirect.com/science/article/pii/S2211379720305428 |
| work_keys_str_mv | AT meiwenteng nonlinearfreevibrationofrectangularplatesreinforcedwith3dgraphenefoamapproximateanalyticalsolution AT yanqingwang nonlinearfreevibrationofrectangularplatesreinforcedwith3dgraphenefoamapproximateanalyticalsolution |