Nonlinear vibration characteristics of size-dependent moving microbeams considering axial forces

Abstract This paper investigates the nonlinear vibration behavior of viscoelastic microbeams under axial velocity, incorporating both nonlocal strain gradient theory and the microelement method to establish governing equations. Wickert’s quasi-static assumption is utilized for comparison with the effects of classical nonlocal axial forces. Numerical simulations of the natural frequency, mode function, and stability reveal that the linear vibration of the microbeam is scale-dependent. Under the conditions of nonlocal parameter dominance selected herein, the critical velocities of divergence and flutter decrease by 23.1% and 46.0%, respectively, while the dominance of the material
characteristic length parameter increases them by 43.1% and 141.10%, respectively, and the velocity interval of the flutter instability is also affected by the scale parameter. Additionally, the nonlinear frequency is analyzed using the direct multiscale method, showing that the nonlinear effect varies with scale and is dependent on the nonlinear characteristics of the model. Specifically, the model based on classical nonlocal axial force is more sensitive to changes in the material characteristic length parameter, while the model incorporating Wickert’s quasi-static hypothesis is more sensitive to the nonlocal parameter.