Micro-inertia effects on the dynamic characteristics of micro-beams considering the couple stress theory

• We present a new model for transverse vibrations of an Euler-Bernoulli beam using the couple stress theory with micro-inertia effects.
• This study revealed that the results of the couple stress are closer to the experimental results than modified couple stress theory.
• The results showed that the micro-inertia depends on the ratio of the length scale to the beam length.
• The effects of the micro-inertia are more important for lower values of the ratio of the length scale to the beam length.

This paper presents a new model for the free transverse vibrations of an Euler–Bernoulli beam using the couple stress theory of elasticity with micro-structure. Introducing the kinematic variables, the strain and kinetic energy expressions (involving micro-inertia effect) have been obtained and the Hamilton principle has been used to derive the governing equations and the related boundary conditions of the free vibrations of fixed–fixed and simply supported beams. A numerical solution has been used to study the natural frequencies, mode shapes and free vibrations of the beams. A comparative result has shown that the bending rigidity predicted by the couple stress, is closer to the experiment result than that predicted by the modified couple stress theory. The results have shown that the bending rigidity of the beams depends on the ratio of the length scale to the beam thickness, whereas the micro-inertia term depends on the ratio of the length scale to the beam length.