双层石墨烯系统稳态受迫振动问题中的辛方法

Symplectic method for the forced vibration of bilayers graphene system in steady-state

针对悬臂石墨烯系统提出一种求解其稳态受迫振动问题的辛解析方法。基于Eringen非局部理论,将石墨烯层板受迫振动问题导入哈密顿体系。采用边界条件分解技术,将问题化为三种边界条件的子问题。通过辛解析方法,得到由辛本征值和辛本征解表示的双层石墨烯系统受迫振动问题的解析解表达式。数值结果表明,辛本征解级数具有很好的收敛性和精度,并与文献结果吻合;在一定的外载激励下可发生同向振动模式和反向振动模式;在一定的参数下,得到一些新的现象和结论。

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.