Size-dependent frequency and stability characteristics of axially moving microbeams based on modified couple stress theory

This investigation aims to explore dynamic characteristics of axially moving Timoshenko microbeams by taking into account size-dependency based on a modified couple stress theory. Size-dependent motion equations and associated boundary conditions are established via Hamilton's principle. In addition, size-dependent axially moving Euler–Bernoulli beam model can be recovered from the present Timoshenko beam model by reinstating the normality assumption. Galerkin method is applied to discretize the partial differential equations into a set of ordinary differential equations, and then the size-dependent dynamic characteristics of axially moving microbeams with simply supported and doubly clamped boundary conditions are numerically determined. It is observed that the microbeams lose stability via a divergence bifurcation in the first mode. The results illustrate that the critical velocity in which the instability occurs and also the natural frequencies significantly increase when the role of size-dependency is of great importance. Finally, the sensitivity of frequencies to velocity and also the influence of size-dependent shear deformation on frequencies and critical velocities are examined.