Nonlinear Vibration of a Functionally Graded Nanobeam Based on the Nonlocal Strain Gradient Theory considering Thickness Effect
In this work, a nonlocal strain gradient beam model considering the thickness effect is developed to study the nonlinear vibration response of a functionally graded nanobeam. The governing equation of the functionally graded nanobeam is derived by using the Euler–Bernoulli beam theory with von Kármá...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Civil Engineering |
| Online Access: | http://dx.doi.org/10.1155/2020/9407673 |
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| author | Dang-Van Hieu The-Hung Duong Gia-Phi Bui |
| author_facet | Dang-Van Hieu The-Hung Duong Gia-Phi Bui |
| author_sort | Dang-Van Hieu |
| collection | DOAJ |
| description | In this work, a nonlocal strain gradient beam model considering the thickness effect is developed to study the nonlinear vibration response of a functionally graded nanobeam. The governing equation of the functionally graded nanobeam is derived by using the Euler–Bernoulli beam theory with von Kármán’s nonlinear strain-gradient relationship and the Hamilton principle. The expression of the nonlinear frequency for the functionally graded nanobeam with pinned-pinned boundary conditions is obtained with the help of Galerkin technique and the Hamiltonian approach. The obtained results show that the effect of thickness is very important for the size-dependent vibration response of the functionally graded nanobeam; the nonlinear vibration response of the nanobeam depends not only on the material length scale parameter and nonlocal parameter but also on the slenderness ratio. Effects of the slenderness ratio and the power-law index on the vibration response of the functionally graded nanobeam are also investigated and discussed. The numerical results show that the nonlocal parameter reduces the nonlinear frequency of the functionally graded nanobeam, while the material length scale parameter increases the nonlinear frequency of the functionally graded nanobeam. The slenderness ratio leads to an increase in the nonlinear frequency of the functionally graded nanobeam, while the power-law index leads to a decrease in the nonlinear frequency of the functionally graded nanobeam. |
| format | Article |
| id | doaj-art-63a175e207e04b178774fcbb63c8b6a9 |
| institution | Kabale University |
| issn | 1687-8086 1687-8094 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Civil Engineering |
| spelling | doaj-art-63a175e207e04b178774fcbb63c8b6a92025-02-03T01:28:17ZengWileyAdvances in Civil Engineering1687-80861687-80942020-01-01202010.1155/2020/94076739407673Nonlinear Vibration of a Functionally Graded Nanobeam Based on the Nonlocal Strain Gradient Theory considering Thickness EffectDang-Van Hieu0The-Hung Duong1Gia-Phi Bui2Thai Nguyen University of Technology, Thainguyen, VietnamThai Nguyen University of Technology, Thainguyen, VietnamUniversity of Transport Technology, Hanoi, VietnamIn this work, a nonlocal strain gradient beam model considering the thickness effect is developed to study the nonlinear vibration response of a functionally graded nanobeam. The governing equation of the functionally graded nanobeam is derived by using the Euler–Bernoulli beam theory with von Kármán’s nonlinear strain-gradient relationship and the Hamilton principle. The expression of the nonlinear frequency for the functionally graded nanobeam with pinned-pinned boundary conditions is obtained with the help of Galerkin technique and the Hamiltonian approach. The obtained results show that the effect of thickness is very important for the size-dependent vibration response of the functionally graded nanobeam; the nonlinear vibration response of the nanobeam depends not only on the material length scale parameter and nonlocal parameter but also on the slenderness ratio. Effects of the slenderness ratio and the power-law index on the vibration response of the functionally graded nanobeam are also investigated and discussed. The numerical results show that the nonlocal parameter reduces the nonlinear frequency of the functionally graded nanobeam, while the material length scale parameter increases the nonlinear frequency of the functionally graded nanobeam. The slenderness ratio leads to an increase in the nonlinear frequency of the functionally graded nanobeam, while the power-law index leads to a decrease in the nonlinear frequency of the functionally graded nanobeam.http://dx.doi.org/10.1155/2020/9407673 |
| spellingShingle | Dang-Van Hieu The-Hung Duong Gia-Phi Bui Nonlinear Vibration of a Functionally Graded Nanobeam Based on the Nonlocal Strain Gradient Theory considering Thickness Effect Advances in Civil Engineering |
| title | Nonlinear Vibration of a Functionally Graded Nanobeam Based on the Nonlocal Strain Gradient Theory considering Thickness Effect |
| title_full | Nonlinear Vibration of a Functionally Graded Nanobeam Based on the Nonlocal Strain Gradient Theory considering Thickness Effect |
| title_fullStr | Nonlinear Vibration of a Functionally Graded Nanobeam Based on the Nonlocal Strain Gradient Theory considering Thickness Effect |
| title_full_unstemmed | Nonlinear Vibration of a Functionally Graded Nanobeam Based on the Nonlocal Strain Gradient Theory considering Thickness Effect |
| title_short | Nonlinear Vibration of a Functionally Graded Nanobeam Based on the Nonlocal Strain Gradient Theory considering Thickness Effect |
| title_sort | nonlinear vibration of a functionally graded nanobeam based on the nonlocal strain gradient theory considering thickness effect |
| url | http://dx.doi.org/10.1155/2020/9407673 |
| work_keys_str_mv | AT dangvanhieu nonlinearvibrationofafunctionallygradednanobeambasedonthenonlocalstraingradienttheoryconsideringthicknesseffect AT thehungduong nonlinearvibrationofafunctionallygradednanobeambasedonthenonlocalstraingradienttheoryconsideringthicknesseffect AT giaphibui nonlinearvibrationofafunctionallygradednanobeambasedonthenonlocalstraingradienttheoryconsideringthicknesseffect |