Nonlinear transverse vibration of nano-strings based on the differential type of nonlocal theory

摘要

The nonlinear vibration responses of nano-strings are studied based on the theory of Eringen's nonlocal elasticity.Firstly,the nonlocal differential constitutive model in one-dimensional form which is suitable for a string structure is used,and then the governing equation of motion for the nonlinear vibration of nano-strings is derived by considering the expression of classical Lagrangian strain.In order to solve the non-dimensional nonlinear governing equation of motion,the Galerkin method or Rayleigh-Ritz method is applied,and the nonlinear partial differential equation is approximately transformed into the a set of ordinary differential equations.The ordinary differential equations are then solved by a numerical method,and the nonlinear vibration responses under different time histories are thus obtained.Subsequently,the approximate numerical solution of the nonlinear displacement is solved by the second-order multi-scale method.The nonlinear phenomena in the transverse displacement and the influences of nonlocal scale parameter on the nonlinear vibration characteristics of nano-strings are analyzed accordingly.The results will provide a basis for understanding and controlling the nonlinear dynamics of nano-strings which may act as key components in the booming intelligent nano-systems.