In this work, the mixed local/nonlocal elasticity theory is developed for the investigation of the vibration of a circular graphene sheet with a structural defect located in a magnetic field. When graphene is placed in a magnetic field, the Lorentz force is applied to it, which is calculated using Maxwell’s equations. The insufficiency of Eringen’s nonlocal theory (ENT) caused some authors to employ the two-phase theory (TPT) to study nanostructures. Geometric imperfections can happen in the manufacturing process of graphene sheets. Lots of these imperfections can be modeled as a hole. So, in this work, an imperfection is considered as the centric hole. Governing equations, in Newtonian formulation, are extracted in the integrodifferential form. The boundary conditions are selected as clamped at inner and outer edges. To discretize the equation of motion we employ Galerkin’s approach. The solution is validated using a comparison study between the presented results and those that exist in the literature, and the accuracy of the suggested approach is verified. The effectiveness of the mixture parameter, magnetic field, radius of imperfection, and nonlocal parameter is examined on the natural frequency. The results exhibit that an increase in the mixture parameter and magnetic field increases the natural frequency of the graphene sheet.

在这项工作中，开发了混合局部/非局部弹性理论，用于研究具有结构缺陷的圆形石墨烯片在磁场中的振动。当石墨烯置于磁场中时，会对其施加洛伦兹力，该力是使用麦克斯韦方程计算的。Eringen非局域理论（ENT）的不足导致一些作者采用两相理论（TPT）来研究纳米结构。石墨烯片的制造过程中可能会出现几何缺陷。许多这样的缺陷都可以被建模为一个洞。因此，在这项工作中，缺陷被认为是中心孔。牛顿公式中的控制方程以积分微分形式提取。边界条件选择为在内边缘和外边缘处夹紧。为了离散化运动方程，我们采用伽辽金方法。通过所提出的结果与文献中存在的结果之间的比较研究来验证该解决方案，并验证了所建议方法的准确性。检查混合参数、磁场、缺陷半径和非局部参数在固有频率上的有效性。结果表明，混合物参数和磁场的增加增加了石墨烯片的固有频率。