Study on the Scale Effect of Nonlinear Vibration of Axial Motion Micro/Nano Plates Based on Nonlocal Strain Gradient Theory

The study of the mechanical behavior of micro-nano materials and structures is one of the main topics and frontier areas in current nanoscience. Under this demand challenge, this paper focuses on a two-dimensional nano-thin plate with axial velocity, establishing a model based on the nonlocal strain gradient theory. The analysis is primarily based on non-classical continuum theory, and the dynamic mechanical behavior and stability of the axially moving nano-plate are studied using numerical methods such as the complex modal method and multiscale method. Considering different boundary conditions, the intrinsic frequency and critical speed of the linear derived system are analyzed. The influence of thin plate deformation is further considered, introducing nonlinear terms. Numerical simulation results show that the vibration frequency of the system changes due to nonlinear effects. Moreover, this frequency variation is closely related to the scale parameters. This research can provide theoretical support for the design and application of nano-components.