Lateral vibration analysis of monatomic chains considering atomic longitudinal displacement

The lateral vibration of monatomic chains considering atomic longitudinal displacements is studied by using the string vibration theory. The modes of lateral vibration of monatomic chains are assumed as the modes of string vibration. Based on the string assumption, the equation of string vibration for monatomic chains is established. Coordinates of the vibration atoms can be calculated by utilizing boundary conditions and symmetry conditions of monatomic chains. The natural angular frequencies of transverse vibration of monatomic chains are calculated by the string vibration method. The tension of the quantum limitation is given and the value of limitation can be used to distinguish nanoelectromechanical systems from quantum-electromechanical Systems. Natural angular frequencies and resonant frequencies of the monatomic chain string are associated with the axial tension acting on the string and the length of monatomic chains, and they can be altered by changing the length of the string and the axial tension acting on the string. The nonlinear vibration of single atomic chain can be analyzed using the improved Lindstedt–Poincaré multiscale method. The study found that the stiffness of the carbon monatomic chain can be altered by changing the length of the string and the tension acting on the string