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| Symplectic method for the forced vibration of bilayers graphene system in steady-state |
| Received:March 16, 2019 Revised:April 24, 2019 |
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| DOI：10.7511/jslx20190316001 |
| KeyWord:bilayer graphene nonlocal theory Hamiltonian system forced vibration symplectic method |
| Author | Institution |
| 范俊海 |
大连理工大学 工程力学系 工业装备结构分析国家重点实验室, 大连 |
| 贾菊芳 |
大连理工大学 工程力学系 工业装备结构分析国家重点实验室, 大连 |
| 赖安迪 |
大连理工大学 工程力学系 工业装备结构分析国家重点实验室, 大连 |
| 周震寰 |
大连理工大学 工程力学系 工业装备结构分析国家重点实验室, 大连 |
| 徐新生 |
大连理工大学 工程力学系 工业装备结构分析国家重点实验室, 大连 |
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| Abstract: |
| A symplectic analytical method is presented for solving the forced vibration of a cantilever graphene system in steady-state in this paper.Based on Eringen's nonlocal continuum field theory,the forced vibration of graphene laminates is introduced into the Hamiltonian system.By using the decomposition technique of boundary conditions,the problem is reduced to three sub-problems of boundary conditions.By means of the symplectic method,the analytical solution of the forced vibration of a bilayer graphene system is obtained,which can be expressed by the symplectic eigenvalues and the symplectic eigensolutions.The numerical results show that the series of symplectic eigensolutions has good convergence and accuracy,which is in good agreement with the published results.The results also show that vibration modes of two laminates occur in the same direction and in the opposite direction under external loads.Under certain parameters,some new phenomena and conclusions are also obtained in this paper. |
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